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Fallah-Mehdipour, E., O. Bozorg Haddad, and M. A. Mariño. "MOPSO algorithm and its application in multipurpose multireservoir operations." Journal of Hydroinformatics 13, no. 4 (2010): 794–811. http://dx.doi.org/10.2166/hydro.2010.105.
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The main reason for applying evolutionary algorithms in multi-objective optimization problems is to obtain near-optimal nondominated solutions/Pareto fronts, from which decision-makers can choose a suitable solution. The efficiency of multi-objective optimization algorithms depends on the quality and quantity of Pareto fronts produced by them. To compare different Pareto fronts resulting from different algorithms, criteria are considered and applied in multi-objective problems. Each criterion denotes a characteristic of the Pareto front. Thus, ranking approaches are commonly used to evaluate different algorithms based on different criteria. This paper presents three multi-objective optimization methods based on the multi-objective particle swarm optimization (MOPSO) algorithm. To evaluate these methods, bi-objective mathematical benchmark problems are considered. Results show that all proposed methods are successful in finding near-optimal Pareto fronts. A ranking method is used to compare the capability of the proposed methods and the best method for further study is suggested. Moreover, the nominated method is applied as an optimization tool in real multi-objective optimization problems in multireservoir system operations. A new technique in multi-objective optimization, called warm-up, based on the PSO algorithm is then applied to improve the quality of the Pareto front by single-objective search. Results show that the proposed technique is successful in finding an optimal Pareto front.
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Mahdi, Samir, and Brahim Nini. "Improved Memetic NSGA-II Using a Deep Neighborhood Search." International Journal of Applied Metaheuristic Computing 12, no. 4 (2021): 138–54. http://dx.doi.org/10.4018/ijamc.2021100108.
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Elitist non-sorted genetic algorithms as part of Pareto-based multi-objective evolutionary algorithms seems to be one of the most efficient algorithms for multi-objective optimization. However, it has some shortcomings, such as low convergence accuracy, uneven Pareto front distribution, and slow convergence. A number of review papers using memetic technique to improve NSGA-II have been published. Hence, it is imperative to improve memetic NSGA-II by increasing its solving accuracy. In this paper, an improved memetic NSGA-II, called deep memetic non-sorted genetic algorithm (DM-NSGA-II), is proposed, aiming to obtain more non-dominated solutions uniformly distributed and better converged near the true Pareto-optimal front. The proposed algorithm combines the advantages of both exact and heuristic approaches. The effectiveness of DM-NSGA-II is validated using well-known instances taken from the standard literature on multi-objective knapsack problem. As will be shown, the performance of the proposed algorithm is demonstrated by comparing it with M-NSGA-II using hypervolume metric.
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Savsani, Vimal, Vivek Patel, Bhargav Gadhvi, and Mohamed Tawhid. "Pareto Optimization of a Half Car Passive Suspension Model Using a Novel Multiobjective Heat Transfer Search Algorithm." Modelling and Simulation in Engineering 2017 (2017): 1–17. http://dx.doi.org/10.1155/2017/2034907.
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Most of the modern multiobjective optimization algorithms are based on the search technique of genetic algorithms; however the search techniques of other recently developed metaheuristics are emerging topics among researchers. This paper proposes a novel multiobjective optimization algorithm named multiobjective heat transfer search (MOHTS) algorithm, which is based on the search technique of heat transfer search (HTS) algorithm. MOHTS employs the elitist nondominated sorting and crowding distance approach of an elitist based nondominated sorting genetic algorithm-II (NSGA-II) for obtaining different nondomination levels and to preserve the diversity among the optimal set of solutions, respectively. The capability in yielding a Pareto front as close as possible to the true Pareto front of MOHTS has been tested on the multiobjective optimization problem of the vehicle suspension design, which has a set of five second-order linear ordinary differential equations. Half car passive ride model with two different sets of five objectives is employed for optimizing the suspension parameters using MOHTS and NSGA-II. The optimization studies demonstrate that MOHTS achieves the better nondominated Pareto front with the widespread (diveresed) set of optimal solutions as compared to NSGA-II, and further the comparison of the extreme points of the obtained Pareto front reveals the dominance of MOHTS over NSGA-II, multiobjective uniform diversity genetic algorithm (MUGA), and combined PSO-GA based MOEA.
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Asadzadeh, Masoud, and Bryan Tolson. "Hybrid Pareto archived dynamically dimensioned search for multi-objective combinatorial optimization: application to water distribution network design." Journal of Hydroinformatics 14, no. 1 (2011): 192–205. http://dx.doi.org/10.2166/hydro.2011.098.
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Pareto archived dynamically dimensioned search (PA-DDS) has been modified to solve combinatorial multi-objective optimization problems. This new PA-DDS algorithm uses discrete-DDS as a search engine and archives all non-dominated solutions during the search. PA-DDS is also hybridized by a general discrete local search strategy to improve its performance near the end of the search. PA-DDS inherits the simplicity and parsimonious characteristics of DDS, so it has only one algorithm parameter and adjusts the search strategy to the user-defined computational budget. Hybrid PA-DDS was applied to five benchmark water distribution network design problems and its performance was assessed in comparison with NSGAII and SPEA2. This comparison was based on a revised hypervolume metric introduced in this study. The revised metric measures the algorithm performance relative to the observed performance variation across all algorithms in the comparison. The revised metric is improved in terms of detecting clear differences between approximations of the Pareto optimal front. Despite its simplicity, Hybrid PA-DDS shows high potential for approximating the Pareto optimal front, especially with limited computational budget. Independent of the PA-DDS results, the new local search strategy is also shown to substantially improve the final NSGAII and SPEA2 Pareto fronts with minimal additional computational expense.
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Tomita, Kouhei, Minami Miyakawa, and Hiroyuki Sato. "Adaptive Control of Dominance Area of Solutions in Evolutionary Many-Objective Optimization." New Mathematics and Natural Computation 11, no. 02 (2015): 135–50. http://dx.doi.org/10.1142/s1793005715400025.
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Controlling the dominance area of solutions (CDAS) relaxes the concept of Pareto dominance with an user-defined parameter S. CDAS with S < 0.5 expands the dominance area and improves the search performance of multi-objective evolutionary algorithms (MOEAs) especially in many-objective optimization problems (MaOPs) by enhancing convergence of solutions toward the optimal Pareto front. However, there is a problem that CDAS with an expanded dominance area (S < 0.5) generally cannot approximate entire Pareto front. To overcome this problem we propose an adaptive CDAS (A-CDAS) that adaptively controls the dominance area of solutions during the solutions search. Our method improves the search performance in MaOPs by approximating the entire Pareto front while keeping high convergence. In early generations, A-CDAS tries to converge solutions toward the optimal Pareto front by using an expanded dominance area with S < 0.5. When we detect convergence of solutions, we gradually increase S and contract the dominance area of solutions to obtain Pareto optimal solutions (POS) covering the entire optimal Pareto front. We verify the effectiveness and the search performance of the proposed A-CDAS on concave and convex DTLZ3 benchmark problems with 2–8 objectives, and show that the proposed A-CDAS achieves higher search performance than conventional non-dominated sorting genetic algorithm II (NSGA-II) and CDAS with an expanded dominance area.
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Schütze, Oliver, Marco Laumanns, Emilia Tantar, Carlos A. Coello Coello, and El-Ghazali Talbi. "Computing Gap Free Pareto Front Approximations with Stochastic Search Algorithms." Evolutionary Computation 18, no. 1 (2010): 65–96. http://dx.doi.org/10.1162/evco.2010.18.1.18103.
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Recently, a convergence proof of stochastic search algorithms toward finite size Pareto set approximations of continuous multi-objective optimization problems has been given. The focus was on obtaining a finite approximation that captures the entire solution set in some suitable sense, which was defined by the concept of ɛ-dominance. Though bounds on the quality of the limit approximation—which are entirely determined by the archiving strategy and the value of ɛ—have been obtained, the strategies do not guarantee to obtain a gap free approximation of the Pareto front. That is, such approximations A can reveal gaps in the sense that points f in the Pareto front can exist such that the distance of f to any image point F(a), a ∈ A, is “large.” Since such gap free approximations are desirable in certain applications, and the related archiving strategies can be advantageous when memetic strategies are included in the search process, we are aiming in this work for such methods. We present two novel strategies that accomplish this task in the probabilistic sense and under mild assumptions on the stochastic search algorithm. In addition to the convergence proofs, we give some numerical results to visualize the behavior of the different archiving strategies. Finally, we demonstrate the potential for a possible hybridization of a given stochastic search algorithm with a particular local search strategy—multi-objective continuation methods—by showing that the concept of ɛ-dominance can be integrated into this approach in a suitable way.
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Mashwani, Wali Khan. "Comprehensive Survey of the Hybrid Evolutionary Algorithms." International Journal of Applied Evolutionary Computation 4, no. 2 (2013): 1–19. http://dx.doi.org/10.4018/jaec.2013040101.
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Multiobjective evolutionary algorithm based on decomposition (MOEA/D) and an improved non-dominating sorting multiobjective genetic algorithm (NSGA-II) is two well known multiobjective evolutionary algorithms (MOEAs) in the field of evolutionary computation. This paper mainly reviews their hybrid versions and some other algorithms which are developed for solving multiobjective optimization problems (MOPs. The mathematical formulation of a MOP and some basic definitions for tackling MOPs, including Pareto optimality, Pareto optimal set (PS), Pareto front (PF) are provided in Section 1. Section 2 presents a brief introduction to hybrid MOEAs. The authors present literature review in subsections. Subsection 2.1 provides memetic multiobjective evolutionary algorithms. Subsection 2.2 presents the hybrid versions of well-known Pareto dominance based MOEAs. Subsection 2.4 summarizes some enhanced Versions of MOEA/D paradigm. Subsection 2.5 reviews some multimethod search approaches dealing optimization problems.
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CHEN, JIANYONG, QIUZHEN LIN, and QINGBIN HU. "APPLICATION OF NOVEL CLONAL ALGORITHM IN MULTIOBJECTIVE OPTIMIZATION." International Journal of Information Technology & Decision Making 09, no. 02 (2010): 239–66. http://dx.doi.org/10.1142/s0219622010003804.
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In this paper, a novel clonal algorithm applied in multiobjecitve optimization (NCMO) is presented, which is designed from the improvement of search operators, i.e. dynamic mutation probability, dynamic simulated binary crossover (D-SBX) operator and hybrid mutation operator combining with Gaussian and polynomial mutations (GP-HM) operator. The main notion of these approaches is to perform more coarse-grained search at initial stage in order to speed up the convergence toward the Pareto-optimal front. Once the solutions are getting close to the Pareto-optimal front, more fine-grained search is performed in order to reduce the gaps between the solutions and the Pareto-optimal front. Based on this purpose, a cooling schedule is adopted in these approaches, reducing the parameters gradually to a minimal threshold, the aim of which is to keep a desirable balance between fine-grained search and coarse-grained search. By this means, the exploratory capabilities of NCMO are enhanced. When compared with various state-of-the-art multiobjective optimization algorithms developed recently, simulation results show that NCMO has remarkable performance.
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Wang, Mingzhao, Yuping Wang, and Xiaoli Wang. "A Space Division Multiobjective Evolutionary Algorithm Based on Adaptive Multiple Fitness Functions." International Journal of Pattern Recognition and Artificial Intelligence 30, no. 03 (2016): 1659005. http://dx.doi.org/10.1142/s0218001416590059.
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The weighted sum of objective functions is one of the simplest fitness functions widely applied in evolutionary algorithms (EAs) for multiobjective programming. However, EAs with this fitness function cannot find uniformly distributed solutions on the entire Pareto front for nonconvex and complex multiobjective programming. In this paper, a novel EA based on adaptive multiple fitness functions and adaptive objective space division is proposed to overcome this shortcoming. The objective space is divided into multiple regions of about the same size by uniform design, and one fitness function is defined on each region by the weighted sum of objective functions to search for the nondominated solutions in this region. Once a region contains fewer nondominated solutions, it is divided into several sub-regions and one additional fitness function is defined on each sub-region. The search will be carried out simultaneously in these sub-regions, and it is hopeful to find more nondominated solutions in such a region. As a result, the nondominated solutions in each region are changed adaptively, and eventually are uniformly distributed on the entire Pareto front. Moreover, the complexity of the proposed algorithm is analyzed. The proposed algorithm is applied to solve 13 test problems and its performance is compared with that of 10 widely used algorithms. The results show that the proposed algorithm can effectively handle nonconvex and complex problems, generate widely spread and uniformly distributed solutions on the entire Pareto front, and outperform those compared algorithms.
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Shankar, K., and Akshay S. Baviskar. "Improved hybrid Strength Pareto Evolutionary Algorithms for multi-objective optimization." International Journal of Intelligent Computing and Cybernetics 11, no. 1 (2018): 20–46. http://dx.doi.org/10.1108/ijicc-12-2016-0063.
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Purpose The purpose of this paper is to design an improved multi-objective algorithm with better spread and convergence than some current algorithms. The proposed application is for engineering design problems. Design/methodology/approach This study proposes two novel approaches which focus on faster convergence to the Pareto front (PF) while adopting the advantages of Strength Pareto Evolutionary Algorithm-2 (SPEA2) for better spread. In first method, decision variables corresponding to the optima of individual objective functions (Utopia Point) are strategically used to guide the search toward PF. In second method, boundary points of the PF are calculated and their decision variables are seeded to the initial population. Findings The proposed methods are tested with a wide range of constrained and unconstrained multi-objective test functions using standard performance metrics. Performance evaluation demonstrates the superiority of proposed algorithms over well-known existing algorithms (such as NSGA-II and SPEA2) and recent ones such as NSLS and E-NSGA-II in most of the benchmark functions. It is also tested on an engineering design problem and compared with a currently used algorithm. Practical implications The algorithms are intended to be used for practical engineering design problems which have many variables and conflicting objectives. A complex example of Welded Beam has been shown at the end of the paper. Social implications The algorithm would be useful for many design problems and social/industrial problems with conflicting objectives. Originality/value This paper presents two novel hybrid algorithms involving SPEA2 based on: local search; and Utopia point directed search principles. This concept has not been investigated before.
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Nobahari, Hadi, Mahdi Nikusokhan, and Patrick Siarry. "A Multi-Objective Gravitational Search Algorithm Based on Non-Dominated Sorting." International Journal of Swarm Intelligence Research 3, no. 3 (2012): 32–49. http://dx.doi.org/10.4018/jsir.2012070103.
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This paper proposes an extension of the Gravitational Search Algorithm (GSA) to multi-objective optimization problems. The new algorithm, called Non-dominated Sorting GSA (NSGSA), utilizes the non-dominated sorting concept to update the gravitational acceleration of the particles. An external archive is also used to store the Pareto optimal solutions and to provide some elitism. It also guides the search toward the non-crowding and the extreme regions of the Pareto front. A new criterion is proposed to update the external archive and two new mutation operators are also proposed to promote the diversity within the swarm. Numerical results show that NSGSA can obtain comparable and even better performances as compared to the previous multi-objective variant of GSA and some other multi-objective optimization algorithms.
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Xu, Gongguo, Xiusheng Duan, and Ganlin Shan. "Multi-sensor multi-objective optimization deployment on complex terrain based on Pareto optimal theory." International Journal of Modeling, Simulation, and Scientific Computing 10, no. 04 (2019): 1950023. http://dx.doi.org/10.1142/s1793962319500235.
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Multiple optimization objectives are often taken into account during the process of sensor deployment. Aiming at the problem of multi-sensor deployment in complex environment, a novel multi-sensor deployment method based on the multi-objective intelligent search algorithm is proposed. First, the complex terrain is modeled by the multi-attribute grid technology to reduce the computational complexity, and a truncation probability sensing model is presented. Two strategies, the local mutation operation and parameter adaptive operation, are introduced to improve the optimization ability of quantum particle swarm optimization (QPSO) algorithm, and then an improved multi-objective intelligent search algorithm based on QPSO is put forward to get the Pareto optimal front. Then, considering the multi-objective deployment requirements, a novel multi-sensor deployment method based on the multi-objective optimization theory is built. Simulation results show that the proposed method can effectively deal with the problem of multi-sensor deployment and provide more deployment schemes at once. Compared with the traditional algorithms, the Pareto optimal fronts achieved by the improved multi-objective search algorithm perform better on both convergence time and solution diversity aspects.
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Mozaffari, Ahmad. "Synchronous self-learning Pareto strategy." International Journal of Intelligent Computing and Cybernetics 11, no. 2 (2018): 197–233. http://dx.doi.org/10.1108/ijicc-05-2017-0050.
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Purpose In recent decades, development of effective methods for optimizing a set of conflicted objective functions has been absorbing an increasing interest from researchers. This refers to the essence of real-life engineering systems and complex natural mechanisms which are generally multi-modal, non-convex and multi-criterion. Until now, several deterministic and stochastic methods have been proposed to cope with such complex systems. Advanced soft computational methods such as evolutionary games (cooperative and non-cooperative), Pareto-based techniques, fuzzy evolutionary methods, cooperative bio-inspired algorithms and neuro-evolutionary systems have effectively come to the aid of researchers to build up efficient paradigms with application to vector optimization. The paper aims to discuss this issue. Design/methodology/approach A novel hybrid algorithm called synchronous self-learning Pareto strategy (SSLPS) is presented for the sake of vector optimization. The method is the ensemble of evolutionary algorithms (EA), swarm intelligence (SI), adaptive version of self-organizing map (CSOM) and a data shuffling mechanism. EA are powerful numerical optimization algorithms capable of finding a global extreme point over a wide exploration domain. SI techniques (the swarm of bees in our case) can improve both intensification and robustness of exploration. CSOM network is an unsupervised learning methodology which learns the characteristics of non-dominated solutions and, thus, enhances the quality of the Pareto front. Findings To prove the effectiveness of the proposed method, the authors engage a set of well-known benchmark functions and some well-known rival optimization methods. Additionally, SSLPS is employed for optimal design of shape memory alloy actuator as a nonlinear multi-modal real-world engineering problem. The experiments show the acceptable potential of SSLPS for handling both numerical and engineering multi-objective problems. Originality/value To the author’s best knowledge, the proposed algorithm is among the rare multi-objective methods which fosters the use of automated unsupervised learning for increasing the intensity of Pareto front (while preserving the diversity). Also, the research evaluates the power of hybridization of SI and EA for efficient search.
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Chen, Taowei, Yiming Yu, and Kun Zhao. "A Multi-objective Particle Swarm Optimization Based on P System Theory." MATEC Web of Conferences 232 (2018): 03039. http://dx.doi.org/10.1051/matecconf/201823203039.
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Particle swarm optimization(PSO) algorithm has been widely applied in solving multi-objective optimization problems(MOPs) since it was proposed. However, PSO algorithms updated the velocity of each particle using a single search strategy, which may be difficult to obtain approximate Pareto front for complex MOPs. In this paper, inspired by the theory of P system, a multi-objective particle swarm optimization (PSO) algorithm based on the framework of membrane system(PMOPSO) is proposed to solve MOPs. According to the hierarchical structure, objects and rules of P system, the PSO approach is used in elementary membranes to execute multiple search strategy. And non-dominated sorting and crowding distance is used in skin membrane for improving speed of convergence and maintaining population diversity by evolutionary rules. Compared with other multi-objective optimization algorithm including MOPSO, dMOPSO, SMPSO, MMOPSO, MOEA/D, SPEA2, PESA2, NSGAII on a benchmark series function, the experimental results indicate that the proposed algorithm is not only feasible and effective but also have a better convergence to true Pareto front.
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Bibi, Nazia, Zeeshan Anwar, and Ali Ahsan. "Comparison of Search-Based Software Engineering Algorithms for Resource Allocation Optimization." Journal of Intelligent Systems 25, no. 4 (2016): 629–42. http://dx.doi.org/10.1515/jisys-2015-0016.
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AbstractA project manager balances the resource allocation using resource leveling algorithms after assigning resources to project activities. However, resource leveling does not ensure optimized allocation of resources. Furthermore, the duration and cost of a project may increase after leveling resources. The objectives of resource allocation optimization used in our research are to (i) increase resource utilization, (ii) decrease project cost, and (iii) decrease project duration. We implemented three search-based software engineering algorithms, i.e. multiobjective genetic algorithm, multiobjective particle swarm algorithm (MOPSO), and elicit nondominated sorting evolutionary strategy. Twelve experiments to optimize the resource allocation are performed on a published case study. The experimental results are analyzed and compared in the form of Pareto fronts, average Pareto fronts, percent increase in resource utilization, percent decrease in project cost, and percent decrease in project duration. The experimental results show that MOPSO is the best technique for resource optimization because after optimization with MOPSO, resource utilization is increased and the project cost and duration are reduced.
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Chen, Bili, Wenhua Zeng, Yangbin Lin, and Qi Zhong. "An Enhanced Differential Evolution Based Algorithm with Simulated Annealing for Solving Multiobjective Optimization Problems." Journal of Applied Mathematics 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/931630.
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An enhanced differential evolution based algorithm, named multi-objective differential evolution with simulated annealing algorithm (MODESA), is presented for solving multiobjective optimization problems (MOPs). The proposed algorithm utilizes the advantage of simulated annealing for guiding the algorithm to explore more regions of the search space for a better convergence to the true Pareto-optimal front. In the proposed simulated annealing approach, a new acceptance probability computation function based on domination is proposed and some potential solutions are assigned a life cycle to have a priority to be selected entering the next generation. Moreover, it incorporates an efficient diversity maintenance approach, which is used to prune the obtained nondominated solutions for a good distributed Pareto front. The feasibility of the proposed algorithm is investigated on a set of five biobjective and two triobjective optimization problems and the results are compared with three other algorithms. The experimental results illustrate the effectiveness of the proposed algorithm.
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Hao, Zhai Liu, Zu Yuan Liu, and Bai Wei Feng. "Application of Multi-Objective Optimization Algorithm Based on Physical Programming in Ship Conceptual Design." Advanced Materials Research 904 (March 2014): 408–13. http://dx.doi.org/10.4028/www.scientific.net/amr.904.408.
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Ship optimization design is a typical multi-objective problem. The multi-objective optimization algorithm based on physical programming is able to obtain evenly distributed Pareto front. But the number of Pareto solutions and the search positions of pseudo-preference structures still exit some disadvantages that are improved in this paper. Firstly uniform design for mixture experiments is used to arbitrarily set the number of Pareto solutions and evenly distribute the search positions of pseudo-preference structures. Then the objective space is searched by shrinking of search domain and rotation of pseudo-preference structure technology. The optimization quality is able to be improved. Finally, the improved multi-objective optimization algorithm is applied to ship conceptual design optimization and compared with the multi-objective evolutionary algorithm to verify the effectiveness of the improved algorithm.
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Kumar, Rajeev, and Peter Rockett. "Improved Sampling of the Pareto-Front in Multiobjective Genetic Optimizations by Steady-State Evolution: A Pareto Converging Genetic Algorithm." Evolutionary Computation 10, no. 3 (2002): 283–314. http://dx.doi.org/10.1162/106365602760234117.
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Previous work on multiobjective genetic algorithms has been focused on preventing genetic drift and the issue of convergence has been given little attention. In this paper, we present a simple steady-state strategy, Pareto Converging Genetic Algorithm (PCGA), which naturally samples the solution space and ensures population advancement towards the Pareto-front. PCGA eliminates the need for sharing/niching and thus minimizes heuristically chosen parameters and procedures. A systematic approach based on histograms of rank is introduced for assessing convergence to the Pareto-front, which, by definition, is unknown in most real search problems. We argue that there is always a certain inheritance of genetic material belonging to a population, and there is unlikely to be any significant gain beyond some point; a stopping criterion where terminating the computation is suggested. For further encouraging diversity and competition, a nonmigrating island model may optionally be used; this approach is particularly suited to many difficult (real-world) problems, which have a tendency to get stuck at (unknown) local minima. Results on three benchmark problems are presented and compared with those of earlier approaches. PCGA is found to produce diverse sampling of the Pareto-front without niching and with significantly less computational effort
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Long, Kim C., William S. Duff, John W. Labadie, Mitchell J. Stansloski, Walajabad S. Sampath, and Edwin K. P. Chong. "Multi-objective fatigue life optimization using Tabu Genetic Algorithms." International Journal of Structural Integrity 6, no. 6 (2015): 677–88. http://dx.doi.org/10.1108/ijsi-12-2014-0066.
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Purpose – The purpose of this paper is to present a real world application of an innovative hybrid system reliability optimization algorithm combining Tabu search with an evolutionary algorithm (TSEA). This algorithm combines Tabu search and Genetic algorithm to provide a more efficient search method. Design/methodology/approach – The new algorithm is applied to an aircraft structure to optimize its reliability and maintain its structural integrity. For retrofitting the horizontal stabilizer under severe stall buffet conditions, a decision support system (DSS) is developed using the TSEA algorithm. This system solves a reliability optimization problem under cost and configuration constraints. The DSS contains three components: a graphical user interface, a database and several modules to provide the optimized retrofitting solutions. Findings – The authors found that the proposed algorithm performs much better than state-of-the-art methods such as Strength Pareto Evolutionary Algorithms on bench mark problems. In addition, the proposed TSEA method can be easily applied to complex real world optimization problem with superior performance. When the full combination of all input variables increases exponentially, the DSS become very efficient. Practical implications – This paper presents an application of the TSEA algorithm for solving nonlinear multi-objective reliability optimization problems embedded in a DSS. The solutions include where to install doublers and stiffeners. Compromise programming is used to rank all non-dominant solutions. Originality/value – The proposed hybrid algorithm (TSEA) assigns fitness based upon global dominance which ensures its convergence to the non-dominant front. The high efficiency of this algorithm came from using Tabu list to guidance the search to the Pareto-optimal solutions.
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Kapse, Swapnil Prakash, and Shankar Krishnapillai. "An Improved Multi-Objective Particle Swarm Optimization Based on Utopia Point Guided Search." International Journal of Applied Metaheuristic Computing 9, no. 4 (2018): 71–96. http://dx.doi.org/10.4018/ijamc.2018100104.
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This article demonstrates the implementation of a novel local search approach based on Utopia point guided search, thus improving the exploration ability of multi- objective Particle Swarm Optimization. This strategy searches for best particles based on the criteria of seeking solutions closer to the Utopia point, thus improving the convergence to the Pareto-optimal front. The elite non-dominated selected particles are stored in an archive and updated at every iteration based on least crowding distance criteria. The leader is chosen among the candidates in the archive using the same guided search. From the simulation results based on many benchmark tests, the new algorithm gives better convergence and diversity when compared to existing several algorithms such as NSGA-II, CMOPSO, SMPSO, PSNS, DE+MOPSO and AMALGAM. Finally, the proposed algorithm is used to solve mechanical design based multi-objective optimization problems from the literature, where it shows the same advantages.
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Medi, Alexandre, Tenda Okimoto, and Katsumi Inoue. "A Two-Phase Complete Algorithm for Multi-Objective Distributed Constraint Optimization." Journal of Advanced Computational Intelligence and Intelligent Informatics 18, no. 4 (2014): 573–80. http://dx.doi.org/10.20965/jaciii.2014.p0573.
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A Distributed Constraint Optimization Problem (DCOP) is a fundamental problem that can formalize various applications related to multi-agent cooperation. Many application problems in multi-agent systems can be formalized as DCOPs. However, many real world optimization problems involve multiple criteria that should be considered separately and optimized simultaneously. A Multi-Objective Distributed Constraint Optimization Problem (MO-DCOP) is an extension of a mono-objective DCOP. Compared to DCOPs, there exists few works on MO-DCOPs. In this paper, we develop a novel complete algorithm for solving an MO-DCOP. This algorithm utilizes a widely used method called Pareto Local Search (PLS) to generate an approximation of the Pareto front. Then, the obtained information is used to guide the search thresholds in a Branch and Bound algorithm. In the evaluations, we evaluate the runtime of our algorithm and show empirically that using a Pareto front approximation obtained by a PLS algorithm allows to significantly speed-up the search in a Branch and Bound algorithm.
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Tawhid, Mohamed A., and Vimal Savsani. "∊-constraint heat transfer search (∊-HTS) algorithm for solving multi-objective engineering design problems." Journal of Computational Design and Engineering 5, no. 1 (2017): 104–19. http://dx.doi.org/10.1016/j.jcde.2017.06.003.
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Abstract In this paper, an effective ∊-constraint heat transfer search (∊-HTS) algorithm for the multi-objective engineering design problems is presented. This algorithm is developed to solve multi-objective optimization problems by evaluating a set of single objective sub-problems. The effectiveness of the proposed algorithm is checked by implementing it on multi-objective benchmark problems that have various characteristics of Pareto front such as discrete, convex, and non-convex. This algorithm is also tested for several distinctive multi-objective engineering design problems, such as four bar truss problem, gear train problem, multi-plate disc brake design, speed reducer problem, welded beam design, and spring design problem. Moreover, the numerical experimentation shows that the proposed algorithm generates the solution to represent true Pareto front. Highlights A novel multi-objective optimization (MOO) algorithm is proposed. Proposed algorithm is presented to obtain the Pareto-optimal solutions. The multi-objective optimization algorithm compared with other work in the literature. Test performance of proposed algorithm on MOO benchmark/design engineering problems.
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Li, Miqing. "Is Our Archiving Reliable? Multiobjective Archiving Methods on “Simple” Artificial Input Sequences." ACM Transactions on Evolutionary Learning and Optimization 1, no. 3 (2021): 1–19. http://dx.doi.org/10.1145/3465335.
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In evolutionary multiobjective optimisation ( EMO ), archiving is a common component that maintains an (external or internal) set during the search process, typically with a fixed size, in order to provide a good representation of high-quality solutions produced. Such an archive set can be used solely to store the final results shown to the decision maker, but in many cases may participate in the process of producing solutions (e.g., as a solution pool where the parental solutions are selected). Over the last three decades, archiving stands as an important issue in EMO, leading to the emergence of various methods such as those based on Pareto, indicator, or decomposition criteria. Such methods have demonstrated their effectiveness in literature and have been believed to be good options to many problems, particularly those having a regular Pareto front shape, e.g., a simplex shape. In this article, we challenge this belief. We do this through artificially constructing several sequences with extremely simple shapes, i.e., 1D/2D simplex Pareto front. We show the struggle of predominantly used archiving methods which have been deemed to well handle such shapes. This reveals that the order of solutions entering the archive matters, and that current EMO algorithms may not be fully capable of maintaining a representative population on problems with linear Pareto fronts even in the case that all of their optimal solutions can be found.
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Yang, Kaifeng, Li Mu, Dongdong Yang, Feng Zou, Lei Wang, and Qiaoyong Jiang. "Multiobjective Memetic Estimation of Distribution Algorithm Based on an Incremental Tournament Local Searcher." Scientific World Journal 2014 (2014): 1–21. http://dx.doi.org/10.1155/2014/836272.
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A novel hybrid multiobjective algorithm is presented in this paper, which combines a new multiobjective estimation of distribution algorithm, an efficient local searcher andε-dominance. Besides, two multiobjective problems with variable linkages strictly based on manifold distribution are proposed. The Pareto set to the continuous multiobjective optimization problems, in the decision space, is a piecewise low-dimensional continuous manifold. The regularity by the manifold features just build probability distribution model by globally statistical information from the population, yet, the efficiency of promising individuals is not well exploited, which is not beneficial to search and optimization process. Hereby, an incremental tournament local searcher is designed to exploit local information efficiently and accelerate convergence to the true Pareto-optimal front. Besides, sinceε-dominance is a strategy that can make multiobjective algorithm gain well distributed solutions and has low computational complexity,ε-dominance and the incremental tournament local searcher are combined here. The novel memetic multiobjective estimation of distribution algorithm, MMEDA, was proposed accordingly. The algorithm is validated by experiment on twenty-two test problems with and without variable linkages of diverse complexities. Compared with three state-of-the-art multiobjective optimization algorithms, our algorithm achieves comparable results in terms of convergence and diversity metrics.
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Xu, Jianjian, and Dan Bai. "Multi-Objective Optimal Operation of the Inter-Basin Water Transfer Project Considering the Unknown Shapes of Pareto Fronts." Water 11, no. 12 (2019): 2644. http://dx.doi.org/10.3390/w11122644.
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Studies have shown that the performance of multi-objective evolutionary algorithms depends to a large extent on the shape of the Pareto fronts of the problem. Although, most existing algorithms have poor applicability in dealing with this problem, especially in the multi-objective optimization operation of reservoirs with unknown Pareto fronts. Therefore, this paper introduces an evolutionary algorithm with strong versatility and robustness named the Multi-Objective Evolutionary Algorithm with Reference Point Adaptation (AR-MOEA). In this paper, we take two water conservancy hubs (Huangjinxia and Sanhekou) of the Hanjiang to Wei River Water Diversion Project as example, and build a multi-objective operation model including water supply, ecology, and power generation. We use the AR-MOEA, the Non-dominated Sorting Genetic Algorithm II (NSGA-II), the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) and the Indicator-Based Evolutionary Algorithm (IBEA) to search the optimal solutions, respectively. We analyze the performance of four algorithms and the operation rules in continuous dry years. The results indicate that (1) the AR-MOEA can overcome the difficulty of the shape and distribution of the unknown Pareto fronts in the multi-objective model. (2) AR-MOEA can improve the convergence and uniformity of the Pareto solution. (3) If we make full use of the regulation ability of the Sanhekou reservoir in the dry season, the water supply for coping with possible continuous dry years can be guaranteed. The study results contribute to the identification of the relationship among objectives, and is valued for water resources management of the Hanjiang to Wei River Water Diversion Project.
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Sadeghi-Tabas, S., S. Z. Samadi, A. Akbarpour, and M. Pourreza-Bilondi. "Sustainable groundwater modeling using single- and multi-objective optimization algorithms." Journal of Hydroinformatics 19, no. 1 (2016): 97–114. http://dx.doi.org/10.2166/hydro.2016.006.
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This study presents the first attempt to link the multi-algorithm genetically adaptive search method (AMALGAM) with a groundwater model to define pumping rates within a well distributed set of Pareto solutions. The pumping rates along with three minimization objectives, i.e. minimizing shortage affected by the failure to supply, modified shortage index and minimization of extent of drawdown within prespecified regions, were chosen to define an optimal solution for groundwater drawdown and subsidence. Hydraulic conductivity, specific yield parameters of a modular three-dimensional finite-difference (MODFLOW) groundwater model were first optimized using Cuckoo optimization algorithm (COA) by minimizing the sum of absolute deviation between the observed and simulated water table depths. These parameters were then applied in AMALGAM to optimize the pumping rate variables for an arid groundwater system in Iran. The Pareto parameter sets yielded satisfactory results when maximum and minimum drawdowns of the aquifer were defined in a range of −40 to +40 cm/year. Overall, ‘Modelling – Optimization – Simulation’ procedure was capable to compute a set of optimal solutions displayed on a Pareto front. The proposed optimal solution provides sustainable groundwater management alternatives to decision makers in arid region.
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Ramprabhu, T., Vimal Savsani, Sohil Parsana, Nishil Radadia, Mohak Sheth, and Nisarg Sheth. "Multi-Objective Optimization of EDM Process Parameters by Using Passing Vehicle Search (PVS) Algorithm." Defect and Diffusion Forum 382 (January 2018): 138–46. http://dx.doi.org/10.4028/www.scientific.net/ddf.382.138.
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Electro-Discharge Machining (EDM) is very popular for machining high-strength conductive materials for aerospace and automotive application. These machining involve a range of processing parameters. In order to optimize these for the best performance, a trade-off has to be decided for the responses achieved through machining. Conventional algorithms have long been replaced by advanced optimization algorithms. Performance of meta-heuristic algorithms in relation to traditional deterministic approaches for multi-modal, non-linear engineering problems is very promising in recent days. In this paper, a multi-objective optimization approach is applied using a population-based meta-heuristic algorithm called Passing Vehicle Search (PVS) for optimizing process parameters of various mathematical models formulated by different authors. Different approaches depending on case have been adopted for formulating the multi-objective PVS algorithm and pareto front is obtained for each case to extract the desired results. The performance of multi-objective PVS is compared with different intelligent computing models employed in prior studies and better results are shown in case of former. This approach can be extended to various mathematical models besides those covered in the paper to obtain better optimization results.
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Ni, Peng, Jiale Gao, Yafei Song, Wen Quan, and Qinghua Xing. "A New Method for Dynamic Multi-Objective Optimization Based on Segment and Cloud Prediction." Symmetry 12, no. 3 (2020): 465. http://dx.doi.org/10.3390/sym12030465.
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In the real world, multi-objective optimization problems always change over time in most projects. Once the environment changes, the distribution of the optimal solutions would also be changed in decision space. Sometimes, such change may obey the law of symmetry, i.e., the minimum of the objective function in such environment is its maximum in another environment. In such cases, the optimal solutions keep unchanged or vibrate in a small range. However, in most cases, they do not obey the law of symmetry. In order to continue the search that maintains previous search advantages in the changed environment, some prediction strategy would be used to predict the operation position of the Pareto set. Because of this, the segment and multi-directional prediction is proposed in this paper, which consists of three mechanisms. First, by segmenting the optimal solutions set, the prediction about the changes in the distribution of the Pareto front can be ensured. Second, by introducing the cloud theory, the distance error of direction prediction can be offset effectively. Third, by using extra angle search, the angle error of prediction caused by the Pareto set nonlinear variation can also be offset effectively. Finally, eight benchmark problems were used to verify the performance of the proposed algorithm and compared algorithms. The results indicate that the algorithm proposed in this paper has good convergence and distribution, as well as a quick response ability to the changed environment.
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Ying, Weiqin, Bin Wu, Yu Wu, Yali Deng, Hainan Huang, and Zhenyu Wang. "Efficient Conical Area Differential Evolution with Biased Decomposition and Dual Populations for Constrained Optimization." Complexity 2019 (February 20, 2019): 1–18. http://dx.doi.org/10.1155/2019/7125037.
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The constraint-handling methods using multiobjective techniques in evolutionary algorithms have drawn increasing attention from researchers. This paper proposes an efficient conical area differential evolution (CADE) algorithm, which employs biased decomposition and dual populations for constrained optimization by borrowing the idea of cone decomposition for multiobjective optimization. In this approach, a conical subpopulation and a feasible subpopulation are designed to search for the global feasible optimum, along the Pareto front and the feasible segment, respectively, in a cooperative way. In particular, the conical subpopulation aims to efficiently construct and utilize the Pareto front through a biased cone decomposition strategy and conical area indicator. Neighbors in the conical subpopulation are fully exploited to assist each other to find the global feasible optimum. Afterwards, the feasible subpopulation is ranked and updated according to a tolerance-based rule to heighten its diversity in the early stage of evolution. Experimental results on 24 benchmark test cases reveal that CADE is capable of resolving the constrained optimization problems more efficiently as well as producing solutions that are significantly competitive with other popular approaches.
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Brockhoff, Dimo, Tobias Wagner, and Heike Trautmann. "2 Indicator-Based Multiobjective Search." Evolutionary Computation 23, no. 3 (2015): 369–95. http://dx.doi.org/10.1162/evco_a_00135.
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In multiobjective optimization, set-based performance indicators are commonly used to assess the quality of a Pareto front approximation. Based on the scalarization obtained by these indicators, a performance comparison of multiobjective optimization algorithms becomes possible. The [Formula: see text] and the hypervolume (HV) indicator represent two recommended approaches which have shown a correlated behavior in recent empirical studies. Whereas the HV indicator has been comprehensively analyzed in the last years, almost no studies on the [Formula: see text] indicator exist. In this extended version of our previous conference paper, we thus perform a comprehensive investigation of the properties of the [Formula: see text] indicator in a theoretical and empirical way. The influence of the number and distribution of the weight vectors on the optimal distribution of [Formula: see text] solutions is analyzed. Based on a comparative analysis, specific characteristics and differences of the [Formula: see text] and HV indicator are presented. Furthermore, the [Formula: see text] indicator is integrated into an indicator-based steady-state evolutionary multiobjective optimization algorithm (EMOA). It is shown that the so-called [Formula: see text]-EMOA can accurately approximate the optimal distribution of [Formula: see text] solutions regarding [Formula: see text].
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Yan, Xiaohui, Zhicong Zhang, Jianwen Guo, Shuai Li, and Kaishun Hu. "A Novel Algorithm to Scheduling Optimization of Melting-Casting Process in Copper Alloy Strip Production." Discrete Dynamics in Nature and Society 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/147980.
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Melting-casting is the first process in copper alloy strip production. The schedule scheme on this process affects the subsequent processes greatly. In this paper, we build the multiobjective model of melting-casting scheduling problem, which considers minimizing the makespan and total weighted earliness and tardiness penalties comprehensively. A novel algorithm, which we called Multiobjective Artificial Bee Colony/Decomposition (MOABC/D) algorithm, is proposed to solve this model. The algorithm combines the framework of Multiobjective Evolutionary Algorithm/Decomposition (MOEA/D) and the neighborhood search strategy of Artificial Bee Colony algorithm. The results on instances show that the proposed MOABC/D algorithm outperforms the other two comparison algorithms both on the distributions of the Pareto front and the priority in the optimal selection results.
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Belakaria, Syrine, Aryan Deshwal, and Janardhan Rao Doppa. "Multi-Fidelity Multi-Objective Bayesian Optimization: An Output Space Entropy Search Approach." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 06 (2020): 10035–43. http://dx.doi.org/10.1609/aaai.v34i06.6560.
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We study the novel problem of blackbox optimization of multiple objectives via multi-fidelity function evaluations that vary in the amount of resources consumed and their accuracy. The overall goal is to appromixate the true Pareto set of solutions by minimizing the resources consumed for function evaluations. For example, in power system design optimization, we need to find designs that trade-off cost, size, efficiency, and thermal tolerance using multi-fidelity simulators for design evaluations. In this paper, we propose a novel approach referred as Multi-Fidelity Output Space Entropy Search for Multi-objective Optimization (MF-OSEMO) to solve this problem. The key idea is to select the sequence of candidate input and fidelity-vector pairs that maximize the information gained about the true Pareto front per unit resource cost. Our experiments on several synthetic and real-world benchmark problems show that MF-OSEMO, with both approximations, significantly improves over the state-of-the-art single-fidelity algorithms for multi-objective optimization.
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Li, Yu-Jing, and Hong-Nan Li. "Interactive evolutionary multi-objective optimization and decision-making on life-cycle seismic design of bridge." Advances in Structural Engineering 21, no. 15 (2018): 2227–40. http://dx.doi.org/10.1177/1369433218770819.
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Considering future seismic risk and life-cycle cost, the life-cycle seismic design of bridge is formulated as a preference-based multi-objective optimization and decision-making problem, in which the conflicting design criteria that minimize life-cycle cost and maximize seismic capacity are treated simultaneously. Specifically, the preference information based on theoretical analysis and engineering judgment is embedded in the optimization procedure. Based on reasonable displacement ductility, the cost preference and safety preference information are used to progressively construct value function, directing the evolutionary multi-objective optimization algorithm’s search to more preferred solutions. The seismic design of a reinforced concrete pier is presented as an application example using the proposed procedure for the global Pareto front corresponding with engineering designers’ preference. The results indicate that the proposed model is available to find the global Pareto front satisfying the corresponding preference and overcoming the difficulties of the traditional multi-objective optimization algorithm in obtaining a full approximation of the entire Pareto optimal front for large-dimensional problems as well as cognitive difficulty in selecting one preferred solution from all these solutions.
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Knowles, Joshua D., and David W. Corne. "Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy." Evolutionary Computation 8, no. 2 (2000): 149–72. http://dx.doi.org/10.1162/106365600568167.
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We introduce a simple evolution scheme for multiobjective optimization problems, called the Pareto Archived Evolution Strategy (PAES). We argue that PAES may represent the simplest possible nontrivial algorithm capable of generating diverse solutions in the Pareto optimal set. The algorithm, in its simplest form, is a (1+1) evolution strategy employing local search but using a reference archive of previously found solutions in order to identify the approximate dominance ranking of the current and candidate solution vectors. (1+1)-PAES is intended to be a baseline approach against which more involved methods may be compared. It may also serve well in some real-world applications when local search seems superior to or competitive with population-based methods. We introduce (1+λ) and (μ+λ) variants of PAES as extensions to the basic algorithm. Six variants of PAES are compared to variants of the Niched Pareto Genetic Algorithm and the Nondominated Sorting Genetic Algorithm over a diverse suite of six test functions. Results are analyzed and presented using techniques that reduce the attainment surfaces generated from several optimization runs into a set of univariate distributions. This allows standard statistical analysis to be carried out for comparative purposes. Our results provide strong evidence that PAES performs consistently well on a range of multiobjective optimization tasks.
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Ye, Chunling, Zhengyan Mao, and Mandan Liu. "A Novel Multi-Objective Five-Elements Cycle Optimization Algorithm." Algorithms 12, no. 11 (2019): 244. http://dx.doi.org/10.3390/a12110244.
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Inspired by the mechanism of generation and restriction among five elements in Chinese traditional culture, we present a novel Multi-Objective Five-Elements Cycle Optimization algorithm (MOFECO). During the optimization process of MOFECO, we use individuals to represent the elements. At each iteration, we first divide the population into several cycles, each of which contains several individuals. Secondly, for every individual in each cycle, we judge whether to update it according to the force exerted on it by other individuals in the cycle. In the case of an update, a local or global update is selected by a dynamically adjustable probability P s ; otherwise, the individual is retained. Next, we perform combined mutation operations on the updated individuals, so that a new population contains both the reserved and updated individuals for the selection operation. Finally, the fast non-dominated sorting method is adopted on the current population to obtain an optimal Pareto solution set. The parameters’ comparison of MOFECO is given by an experiment and also the performance of MOFECO is compared with three classic evolutionary algorithms Non-dominated Sorting Genetic Algorithm II (NSGA-II), Multi-Objective Particle Swarm Optimization algorithm (MOPSO), Pareto Envelope-based Selection Algorithm II (PESA-II) and two latest algorithms Knee point-driven Evolutionary Algorithm (KnEA) and Non-dominated Sorting and Local Search (NSLS) on solving test function sets Zitzler et al’s Test suite (ZDT), Deb et al’s Test suite (DTLZ), Walking Fish Group (WFG) and Many objective Function (MaF). The experimental results indicate that the proposed MOFECO can approach the true Pareto-optimal front with both better diversity and convergence compared to the five other algorithms.
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Li, H., and D. Landa-Silva. "An Adaptive Evolutionary Multi-Objective Approach Based on Simulated Annealing." Evolutionary Computation 19, no. 4 (2011): 561–95. http://dx.doi.org/10.1162/evco_a_00038.
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A multi-objective optimization problem can be solved by decomposing it into one or more single objective subproblems in some multi-objective metaheuristic algorithms. Each subproblem corresponds to one weighted aggregation function. For example, MOEA/D is an evolutionary multi-objective optimization (EMO) algorithm that attempts to optimize multiple subproblems simultaneously by evolving a population of solutions. However, the performance of MOEA/D highly depends on the initial setting and diversity of the weight vectors. In this paper, we present an improved version of MOEA/D, called EMOSA, which incorporates an advanced local search technique (simulated annealing) and adapts the search directions (weight vectors) corresponding to various subproblems. In EMOSA, the weight vector of each subproblem is adaptively modified at the lowest temperature in order to diversify the search toward the unexplored parts of the Pareto-optimal front. Our computational results show that EMOSA outperforms six other well established multi-objective metaheuristic algorithms on both the (constrained) multi-objective knapsack problem and the (unconstrained) multi-objective traveling salesman problem. Moreover, the effects of the main algorithmic components and parameter sensitivities on the search performance of EMOSA are experimentally investigated.
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Zitzler, Eckart, Kalyanmoy Deb, and Lothar Thiele. "Comparison of Multiobjective Evolutionary Algorithms: Empirical Results." Evolutionary Computation 8, no. 2 (2000): 173–95. http://dx.doi.org/10.1162/106365600568202.
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In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Pareto-optimal front (e.g., multimodality and deception). By investigating these different problem features separately, it is possible to predict the kind of problems to which a certain technique is or is not well suited. However, in contrast to what was suspected beforehand, the experimental results indicate a hierarchy of the algorithms under consideration. Furthermore, the emerging effects are evidence that the suggested test functions provide sufficient complexity to compare multiobjective optimizers. Finally, elitism is shown to be an important factor for improving evolutionary multiobjective search.
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Yuan, Xiaohui, Zhihuan Chen, Yanbin Yuan, Yuehua Huang, and Xiaopan Zhang. "A Strength Pareto Gravitational Search Algorithm for Multi-Objective Optimization Problems." International Journal of Pattern Recognition and Artificial Intelligence 29, no. 06 (2015): 1559010. http://dx.doi.org/10.1142/s0218001415590107.
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A novel strength Pareto gravitational search algorithm (SPGSA) is proposed to solve multi-objective optimization problems. This SPGSA algorithm utilizes the strength Pareto concept to assign the fitness values for agents and uses a fine-grained elitism selection mechanism to keep the population diversity. Furthermore, the recombination operators are modeled in this approach to decrease the possibility of trapping in local optima. Experiments are conducted on a series of benchmark problems that are characterized by difficulties in local optimality, nonuniformity, and nonconvexity. The results show that the proposed SPGSA algorithm performs better in comparison with other related works. On the other hand, the effectiveness of two subtle means added to the GSA are verified, i.e. the fine-grained elitism selection and the use of SBX and PMO operators. Simulation results show that these measures not only improve the convergence ability of original GSA, but also preserve the population diversity adequately, which enables the SPGSA algorithm to have an excellent ability that keeps a desirable balance between the exploitation and exploration so as to accelerate the convergence speed to the true Pareto-optimal front.
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De Ath, George, Richard M. Everson, Alma A. M. Rahat, and Jonathan E. Fieldsend. "Greed Is Good: Exploration and Exploitation Trade-offs in Bayesian Optimisation." ACM Transactions on Evolutionary Learning and Optimization 1, no. 1 (2021): 1–22. http://dx.doi.org/10.1145/3425501.
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The performance of acquisition functions for Bayesian optimisation to locate the global optimum of continuous functions is investigated in terms of the Pareto front between exploration and exploitation. We show that Expected Improvement (EI) and the Upper Confidence Bound (UCB) always select solutions to be expensively evaluated on the Pareto front, but Probability of Improvement is not guaranteed to do so and Weighted Expected Improvement does so only for a restricted range of weights. We introduce two novel -greedy acquisition functions. Extensive empirical evaluation of these together with random search, purely exploratory, and purely exploitative search on 10 benchmark problems in 1 to 10 dimensions shows that -greedy algorithms are generally at least as effective as conventional acquisition functions (e.g., EI and UCB), particularly with a limited budget. In higher dimensions, -greedy approaches are shown to have improved performance over conventional approaches. These results are borne out on a real-world computational fluid dynamics optimisation problem and a robotics active learning problem. Our analysis and experiments suggest that the most effective strategy, particularly in higher dimensions, is to be mostly greedy, occasionally selecting a random exploratory solution.
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Bastos-Filho, Carmelo J. A., and Augusto C. S. Guimarães. "Multi-Objective Fish School Search." International Journal of Swarm Intelligence Research 6, no. 1 (2015): 23–40. http://dx.doi.org/10.4018/ijsir.2015010102.
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The authors propose in this paper a very first version of the Fish School Search (FSS) algorithm for Multi-Objective Optimization. The proposal allows the optimization of problems with two or more conflicting objectives. The authors incorporated the dominance concept within the traditional FSS operators, creating a new approach called Multi-objective Fish School Search, MOFSS. They also adapted the barycenter concept deployed in the original FSS, which was replaced by the set of existing solutions in an external archive created to store the non-dominated solutions found during the search process. From their results in the DTLZ set of benchmark functions, the authors observed that the MOFSS obtained a similar performance when compared to well-known and well-established multi-objective swarm-based optimization algorithms. They detected some convergence problems in functions with a high number of local Pareto fronts. However, adaptive schemes can be used in future work to overcome this weakness.
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Babu, Sabbavarapu Ramana, Vegesina Ramachandra Raju, and Koona Ramji. "DESIGN FOR OPTIMAL PERFORMANCE OF 3-RPS PARALLEL MANIPULATOR USING EVOLUTIONARY ALGORITHMS." Transactions of the Canadian Society for Mechanical Engineering 37, no. 2 (2013): 135–60. http://dx.doi.org/10.1139/tcsme-2013-0009.
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This paper presents an optimal kinematic design for a general type of 3-RPS spatial parallel manipulator based on multi-objective optimization. The objective functions considered are Global Conditioning Index (GCI), Global stiffness Index (GSI) and Workspace volume. The objective functions are optimized simultaneously to improve the dexterity as well as the workspace volume which represents the working capacity of a parallel manipulator. A multi-objective Evolutionary Algorithm based on the control elitist non-dominated sorting genetic algorithm is adopted to find the true optimal Pareto front. A constraint Jacobian matrix is derived analytically and the manipulator workspace is generated by numerical search method. The static analysis of the manipulator is also carried out to determine the compliance of the end-effecter.
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Qiu, Feiyue, Guodao Zhang, Ping-Kuo Chen, et al. "A Novel Multi-Objective Model for the Cold Chain Logistics Considering Multiple Effects." Sustainability 12, no. 19 (2020): 8068. http://dx.doi.org/10.3390/su12198068.
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This paper focuses on solving a problem of green location-routing with cold chain logistics (GLRPCCL). Considering the sustainable effects of the economy, environment, society, and cargos, we try to establish a multi-objective model to minimize the total cost, the full set of greenhouse gas (GHG) emissions, the average waiting time, and the total quality degradation. Several practical demands were considered: heterogeneous fleet (HF), time windows (TW), simultaneous pickup and delivery (SPD), and a feature of mixed transportation. To search the optimal Pareto front of such a nondeterministic polynomial hard problem, we proposed an optimization framework that combines three multi-objective evolutionary algorithms (MOEAs) and also developed two search mechanisms for a large composite neighborhood described by 16 operators. Extensive analysis was conducted to empirically assess the impacts of several problem parameters (i.e., distribution strategy, fleet composition, and depots’ time windows and costs) on Pareto solutions in terms of the performance indicators. Based on the experimental results, this provides several managerial insights for the sustainale logistics companies.
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Ermis, Gülcin, and Can Akkan. "Search algorithms for improving the pareto front in a timetabling problem with a solution network-based robustness measure." Annals of Operations Research 275, no. 1 (2017): 101–21. http://dx.doi.org/10.1007/s10479-017-2646-5.
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da Cruz, André R. "An Improved Nondominated Sorting Algorithm." International Journal of Natural Computing Research 3, no. 4 (2012): 20–42. http://dx.doi.org/10.4018/jncr.2012100102.
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This paper presents a new procedure for the nondominated sorting with constraint handling to be used in a multiobjective evolutionary algorithm. The strategy uses a sorting algorithm and binary search to classify the solutions in the correct level of the Pareto front. In a problem with objective functions, using solutions in the population, the original nondominated sorting algorithm, used by NSGA-II, has always a computational cost of in a naïve implementation. The complexity of the new algorithm can vary from in the best case and in the worst case. A experiment was executed in order to compare the new algorithm with the original and another improved version of the Deb’s algorithm. Results reveal that the new strategy is much better than other versions when there are many levels in Pareto front. It is also concluded that is interesting to alternate the new algorithm and the improved Deb’s version during the evolution of the evolutionary algorithm.
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Abreu, Nuno, and Aníbal Matos. "Minehunting Mission Planning for Autonomous Underwater Systems Using Evolutionary Algorithms." Unmanned Systems 02, no. 04 (2014): 323–49. http://dx.doi.org/10.1142/s2301385014400081.
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Autonomous underwater vehicles (AUVs) are increasingly being used to perform mine countermeasures (MCM) operations but its capabilities are limited by the efficiency of the planning process. Here we study the problem of multiobjective MCM mission planning with AUVs. The vehicle should cover the operating area while maximizing the probability of detecting the targets and minimizing the required energy and time to complete the mission. A multi-stage algorithm is proposed and evaluated. Our algorithm combines an evolutionary algorithm (EA) with a local search procedure, aiming at a more flexible and effective exploration and exploitation of the search space. An artificial neural network (ANN) model was also integrated in the evolutionary procedure to guide the search. The combination of different techniques creates another problem, related to the high amount of parameters that needs to be tuned. Thus, the effect of these parameters on the quality of the obtained Pareto Front was assessed. This allowed us to define an adaptive tuning procedure to control the parameters while the algorithm is executed. Our algorithm is compared against an implementation of a known EA as well as another mission planner and the results from the experiments show that the proposed strategy can efficiently identify a higher quality solution set.
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Huang, Junhao, Weize Sun, and Lei Huang. "Joint Structure and Parameter Optimization of Multiobjective Sparse Neural Network." Neural Computation 33, no. 4 (2021): 1113–43. http://dx.doi.org/10.1162/neco_a_01368.
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This work addresses the problem of network pruning and proposes a novel joint training method based on a multiobjective optimization model. Most of the state-of-the-art pruning methods rely on user experience for selecting the sparsity ratio of the weight matrices or tensors, and thus suffer from severe performance reduction with inappropriate user-defined parameters. Moreover, networks might be inferior due to the inefficient connecting architecture search, especially when it is highly sparse. It is revealed in this work that the network model might maintain sparse characteristic in the early stage of the backpropagation (BP) training process, and evolutionary computation-based algorithms can accurately discover the connecting architecture with satisfying network performance. In particular, we establish a multiobjective sparse model for network pruning and propose an efficient approach that combines BP training and two modified multiobjective evolutionary algorithms (MOEAs). The BP algorithm converges quickly, and the two MOEAs can search for the optimal sparse structure and refine the weights, respectively. Experiments are also included to prove the benefits of the proposed algorithm. We show that the proposed method can obtain a desired Pareto front (PF), leading to a better pruning result comparing to the state-of-the-art methods, especially when the network structure is highly sparse.
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Molina-Pérez, Daniel, Edgar Alfredo Portilla-Flores, Eduardo Vega-Alvarado, Maria Bárbara Calva-Yañez, and Gabriel Sepúlveda-Cervantes. "A Novel Multi-Objective Harmony Search Algorithm with Pitch Adjustment by Genotype." Applied Sciences 11, no. 19 (2021): 8931. http://dx.doi.org/10.3390/app11198931.
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In this work, a new version of the Harmony Search algorithm for solving multi-objective optimization problems is proposed, MOHSg, with pitch adjustment using genotype. The main contribution consists of adjusting the pitch using the crowding distance by genotype; that is, the distancing in the search space. This adjustment automatically regulates the exploration–exploitation balance of the algorithm, based on the distribution of the harmonies in the search space during the formation of Pareto fronts. Therefore, MOHSg only requires the presetting of the harmony memory accepting rate and pitch adjustment rate for its operation, avoiding the use of a static bandwidth or dynamic parameters. MOHSg was tested through the execution of diverse test functions, and it was able to produce results similar or better than those generated by algorithms that constitute search variants of harmonies, representative of the state-of-the-art in multi-objective optimization with HS.
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Yasear, Shaymah Akram, and Ku Ruhana Ku-Mahamud. "Non-dominated sorting Harris’s hawk multi-objective optimizer based on reference point approach." Indonesian Journal of Electrical Engineering and Computer Science 15, no. 3 (2019): 1603. http://dx.doi.org/10.11591/ijeecs.v15.i3.pp1603-1614.
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A non-dominated sorting Harris’s hawk multi-objective optimizer (NDSHHMO) algorithm is presented in this paper. The algorithm is able to improve the population diversity, convergence of non-dominated solutions toward the Pareto front, and prevent the population from trapping into local optimal. This was achieved by integrating fast non-dominated sorting with the original Harris’s hawk multi-objective optimizer (HHMO). Non-dominated sorting divides the objective space into levels based on fitness values and then selects non-dominated solutions to produce the next generation of hawks. A set of well-known multi-objective optimization problems has been used to evaluate the performance of the proposed NDSHHMO algorithm. The results of the NDSHHMO algorithm were verified against the results of an HHMO algorithm. Experimental results demonstrate the efficiency of the proposed NDSHHMO algorithm in terms of enhancing the ability of convergence toward the Pareto front and significantly improve the search ability of the HHMO.
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Shu, Liang You, and Ling Xiao Yang. "Manufacturer Order Fulfillment Based on Multi-Objective Optimization NSGA II Model." Applied Mechanics and Materials 340 (July 2013): 136–40. http://dx.doi.org/10.4028/www.scientific.net/amm.340.136.
Full textAbstract:
The aim of this paper is to study the production and delivery decision problem in the Manufacturer Order Fulfillment. Owing to the order fulfillment optimization condition of the manufacturer, the multi-objective optimization model of manufacturers' production and delivery has been founded. The solution of the multi-objective optimization model is also very difficult. Fast and Elitist Non-dominated Sorting Genetic Algorithm (NSGA II) have been applied successfully to various test and real-world optimization problems. These population based the algorithm provide a diverse set of non-dominated solutions. The obtained non-dominated set is close to the true Pareto-optimal front. But its convergence to the true Pareto-optimal front is not guaranteed. Hence SBX is used as a local search procedure. The proposed procedure is successfully applied to a special case. The results validate that the algorithm is effective to the multi-objective optimization model.
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Wei, Lixin, JinLu Zhang, Rui Fan, Xin Li, and Hao Sun. "Covariance matrix adaptive strategy for a multi-objective evolutionary algorithm based on reference point." Journal of Intelligent & Fuzzy Systems 39, no. 5 (2020): 7315–32. http://dx.doi.org/10.3233/jifs-200749.
Full textAbstract:
In this article, an effective method, called an adaptive covariance strategy based on reference points (RPCMA-ES) is proposed for multi-objective optimization. In the proposed algorithm, search space is divided into independent sub-regions by calculating the angle between the objective vector and the reference vector. The reference vectors can be used not only to decompose the original multi-objective optimization problem into a number of single-objective subproblems, but also to elucidate user preferences to target a preferred subset of the whole Pareto front (PF). In this respect, any single objective optimizers can be easily used in this algorithm framework. Inspired by the multi-objective estimation of distribution algorithms, covariance matrix adaptation evolution strategy (CMA-ES) is involved in RPCMA-ES. A state-of-the-art optimizer for single-objective continuous functions is the CMA-ES, which has proven to be able to strike a good balance between the exploration and the exploitation of search space. Furthermore, in order to avoid falling into local optimality and make the new mean closer to the optimal solution, chaos operator is added based on CMA-ES. By comparing it with four state-of-the-art multi-objective optimization algorithms, the simulation results show that the proposed algorithm is competitive and effective in terms of convergence and distribution.