Journal articles: 'Algorithme du simplexe'

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Zhang, Jing Jun, Huan Chen, and Rui Zhen Gao. "An Improved Genetic Algorithm Based on K₂(m) Triangulation of Continuous Self-Mapping." Advanced Materials Research 295-297 (July 2011): 2515–20. http://dx.doi.org/10.4028/www.scientific.net/amr.295-297.2515.

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In this paper an improved genetic algorithm based on the simplex self-mapping fixed point algorithm is proposed. With this algorithm, the optimal problem of n-dimensional closure function will be transformed as the solution of approximate fixed point problem of n-dimensional standard simplexes by homeomorphism mapping. The genetic operators relying on the integer labels are designed. In this case, whether every individual loading simplex of the population is a completely labeled simplex can be used as an objective convergence criterion. The simulation results demonstrate that the proposed algorithm is valid and effective.

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Trabia, Mohamed B., and Xiao Bin Lu. "A Fuzzy Adaptive Simplex Search Optimization Algorithm." Journal of Mechanical Design 123, no. 2 (1999): 216–25. http://dx.doi.org/10.1115/1.1347991.

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Most optimization algorithms use empirically-chosen fixed parameters as a part of their search strategy. This paper proposes to replace these fixed parameters by adaptive ones to make the search more responsive to changes in the problem by incorporating fuzzy logic in optimization algorithms. The proposed ideas are used to develop a new adaptive form of the simplex search algorithm whose objective is to minimize a function of n variables. The new algorithm is labeled Fuzzy Simplex. The search starts by generating a simplex with n+1 vertices. The algorithm then repeatedly replaces the point with the highest function value by a new point. This process has three components: reflecting the point with the highest function value, expanding, and contracting the simplex. These operations use fuzzy logic controllers whose inputs incorporate the relative weights of the function values at the simplex points. Standard minimization test problems are used to evaluate the efficiency of the algorithm. The Fuzzy Simplex algorithm generally results in a faster convergence. Robustness and sensitivity of the algorithm are also considered. The Fuzzy Simplex algorithm is also applied successfully to several engineering design problems. The results of the Fuzzy Simplex algorithm compare favorably with other available minimization algorithms.

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De-Graft Acquah, Henry, and Sarah Acquah. "Interior point algorithm for solving farm resource allocation problem." Applied Studies in Agribusiness and Commerce 11, no. 1-2 (2017): 45–49. http://dx.doi.org/10.19041/apstract/2017/1-2/6.

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This paper introduces interior point algorithm as an alternative approach to simplex algorithm for solving farm resource allocation problem. The empirical result of interior point algorithm is compared with that of the simplex algorithm. It goes further to address a profit maximization problem. The result revealed several relevant patterns. Results of the interior point algorithm is similar to that of the simplex algorithm. Findings indicated that in both algorithms, the farm is to produce peppers, wheat which is irrigated and weeded manually, hire additional month of labour, and also purchase urea and muriate fertilizer to realize a similar amount of profit. Additionally, both algorithms suggested that practicing crop rotation where beans, if grown, should be altered with wheat cannot be possible since no beans will be grown. The Simplex algorithm saves 39 iterations over Interior Point algorithm in solving the farm resource allocation problem. The findings demonstrate that the interior point algorithm offers a useful alternative to the simplex algorithm when addressing farm resource allocation problem. JEL code: D24, D57, C61, C63, C67

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Zandavi, Seid Miad, Vera Chung, and Ali Anaissi. "Multi-user Remote Lab: Timetable Scheduling Using Simplex Nondominated Sorting Genetic Algorithm." ACM/IMS Transactions on Data Science 2, no. 2 (2021): 1–13. http://dx.doi.org/10.1145/3437260.

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The scheduling of multi-user remote laboratories is modeled as a multimodal function for the proposed optimization algorithm. The hybrid optimization algorithm, hybridization of the Nelder-Mead Simplex algorithm, and Non-dominated Sorting Genetic Algorithm (NSGA), named Simplex Non-dominated Sorting Genetic Algorithm (SNSGA), is proposed to optimize the timetable problem for the remote laboratories to coordinate shared access. The proposed algorithm utilizes the Simplex algorithm in terms of exploration and NSGA for sorting local optimum points with consideration of potential areas. SNSGA is applied to difficult nonlinear continuous multimodal functions, and its performance is compared with hybrid Simplex Particle Swarm Optimization, Simplex Genetic Algorithm, and other heuristic algorithms. The results show that SNSGA has a competitive performance to address timetable problems.

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Amrullah, Muhammad. "PEMODELAN PEMROGRAMAN LINIER DENGAN KOEFISIEN FUNGSI OBJEKTIF, FUNGSI KENDALA DAN VARIABEL KEPUTUSAN BERBENTUK BILANGAN KABUR BESERTA APLIKASINYA." Jurnal Matematika, Statistika dan Komputasi 16, no. 1 (2019): 85. http://dx.doi.org/10.20956/jmsk.v16i1.5802.

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Abstrak Dalam penelitian ini penulis akan mengusulkan algoritma untuk memodelkan masalah pemrograman linear kabur dengan bilangan kabur trapesium menggunakan metode simpleks. Secara khusus dalam aplikasi teori ini adalah masalah pengambilan keputusan pemrograman linear kabur dengan menyajikan metode baru untuk menyelesaikan masalah pemrograman linier kabur dengan menggunakan fungsi ranking. Pada dasarnya, langkah-langkah dalam metode penelitian ini sama dengan dengan metode simpleks yang digunakan untuk memecahkan masalah pemrograman linier tegas.Kata kunci: Fuzzy linear programming, fungsi ranking, metode simpleks. AbstractIn this paper author shall propose an algorithm for solving fuzzy linear programming problems with trapezoidal numbers using a simplex method. In particular, an application of this theory in decision making problems is fuzzy linear programming with a new method for solving fuzzy linear programming problems, by use of rank function. Basically, our method is similar to simplex method that was used for solving linear programming problems in crisp environment before.Keywords: Fuzzy linier programming, rank function, simplex method.

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Lewis, Andrew, David Abramson, and Tom Peachey. "RSCS: A Parallel Simplex Algorithm for the Nimrod/O Optimization Toolset." Scientific Programming 14, no. 1 (2006): 1–11. http://dx.doi.org/10.1155/2006/906394.

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This paper describes a method of parallelisation of the popular Nelder-Mead simplex optimization algorithms that can lead to enhanced performance on parallel and distributed computing resources. A reducing set of simplex vertices are used to derive search directions generally closely aligned with the local gradient. When tested on a range of problems drawn from real-world applications in science and engineering, this reducing set concurrent simplex (RSCS) variant of the Nelder-Mead algorithm compared favourably with the original algorithm, and also with the inherently parallel multidirectional search algorithm (MDS). All algorithms were implemented and tested in a general-purpose, grid-enabled optimization toolset.

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Trabia, Mohamed B. "A Hybrid Fuzzy Simplex Genetic Algorithm." Journal of Mechanical Design 126, no. 6 (2004): 969–74. http://dx.doi.org/10.1115/1.1803852.

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This paper presents a novel hybrid genetic algorithm that has the ability of the genetic algorithms to avoid being trapped at local minimum while accelerating the speed of local search by using the fuzzy simplex algorithm. The new algorithm is labeled the hybrid fuzzy simplex genetic algorithm (HFSGA). Standard test problems are used to evaluate the efficiency of the algorithm. The algorithm is also applied successfully to several engineering design problems. The HFSGA generally results in a faster convergence toward extremum.

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Ploskas, Nikolaos, Nikolaos Samaras, and Jason Papathanasiou. "A Decision Support System for Solving Linear Programming Problems." International Journal of Decision Support System Technology 6, no. 2 (2014): 46–62. http://dx.doi.org/10.4018/ijdsst.2014040103.

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Linear programming algorithms have been widely used in Decision Support Systems. These systems have incorporated linear programming algorithms for the solution of the given problems. Yet, the special structure of each linear problem may take advantage of different linear programming algorithms or different techniques used in these algorithms. This paper proposes a web-based DSS that assists decision makers in the solution of linear programming problems with a variety of linear programming algorithms and techniques. Two linear programming algorithms have been included in the DSS: (i) revised simplex algorithm and (ii) exterior primal simplex algorithm. Furthermore, ten scaling techniques, five basis update methods and eight pivoting rules have been incorporated in the DSS. All linear programming algorithms and methods have been implemented using MATLAB and converted to Java classes using MATLAB Builder JA, while the web interface of the DSS has been designed using Java Server Pages.

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Irwin, Klee. "Toward the Unification of Physics and Number Theory." Reports in Advances of Physical Sciences 03, no. 01 (2019): 1950003. http://dx.doi.org/10.1142/s2424942419500038.

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This paper introduces the notion of simplex-integers and shows how, in contrast to digital numbers, they are the most powerful numerical symbols that implicitly express the information of an integer and its set theoretic substructure. A geometric analogue to the primality test is introduced: when [Formula: see text] is prime, it divides [Formula: see text] for all [Formula: see text]. The geometric form provokes a novel hypothesis about the distribution of prime-simplexes that, if solved, may lead to a proof of the Riemann hypothesis. Specifically, if a geometric algorithm predicting the number of prime simplexes within any bound [Formula: see text]-simplex or associated [Formula: see text] lattice is discovered, a deep understanding of the error factor of the prime number theorem would be realized — the error factor corresponding to the distribution of the non-trivial zeta zeros, which might be the mysterious link between physics and the Riemann hypothesis [D. Schumayer and D. A. W. Hutchinson, Colloquium: Physics of the Riemann hypothesis, Rev. Mod. Phys. 83 (2011) 307]. It suggests how quantum gravity and particle physicists might benefit from a simplex-integer-based quasicrystal code formalism. An argument is put forth that the unifying idea between number theory and physics is code theory, where reality is information theoretic and 3-simplex integers form physically realistic aperiodic dynamic patterns from which space, time and particles emerge from the evolution of the code syntax.

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MOHAN, S. R., S. K. NEOGY, and T. PARTHASARATHY. "PIVOTING ALGORITHMS FOR SOME CLASSES OF STOCHASTIC GAMES: A SURVEY." International Game Theory Review 03, no. 02n03 (2001): 253–81. http://dx.doi.org/10.1142/s0219198901000385.

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In this paper, we survey the recent literature on computing the value vector and the associated optimal strategies of the players for special cases of zero-sum stochastic games, or in computing a Nash equilibrium point and the corresponding stationary strategies of the players for special cases of nonzero-sum stochastic games, using finite-step algorithms based on pivoting. Examples of finite-step pivoting algorithms are the various simplex-type algorithms, such as the primal simplex or dual simplex method for solving the linear programming problem or Lemke's or Lemke-Howson's algorithm for solving the linear complementarity problem. Also included are Lemke-type algorithms for solving various generalisations of the linear complementarity problem. The survey also includes a few new results and observations.

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Clayton, R. P., and R. F. Martinez-Botas. "Application of generic algorithms in aerodynamic optimisation design procedures." Aeronautical Journal 108, no. 1090 (2004): 611–20. http://dx.doi.org/10.1017/s0001924000000440.

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AbstractDirect optimisation techniques using different methods are presented and compared for the solution of two common flows: a two dimensional diffuser and a drag minimisation problem of a fixed area body. The methods studied are a truncated Newton algorithm (gradient method), a simplex approach (direct search method) and a genetic algorithm (stochastic method). The diffuser problem has a known solution supported by experimental data, it has one design performance measure (the pressure coefficient) and two design variables. The fixed area body also has one performance measure (the drag coefficient), but this time there are four design variables; no experimental data is available, this computation is performed to assess the speed/progression of solution.In all cases the direct search approach (simplex method) required significantly smaller number of evaluations than the generic algorithm method. The simplest approach, the gradient method (Newton) performed equally to the simplex approach for the diffuser problem but it was unable to provide a solution to the four-variable problem of a fixed area body drag minimisation. The level of robustness obtained by the use of generic algorithm is in principle superior to the other methods, but a large price in terms of evaluations has to be paid.

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Stágel, Bálint, Péter Tar, and István Maros. "The Pannon Optimizier – A Linear Programming Solver for Research Purposes." MACRo 2015 1, no. 1 (2015): 293–301. http://dx.doi.org/10.1515/macro-2015-0029.

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AbstractThe simplex algorithm is one of the most widely used linear optimization algorithms. Although its history goes back to the 1950’s it is still an evergreen topic because it is usually the hidden computational engine behind other algorithms. Thus its performance heavily affects other optimization systems. The implementation of the simplex algorithm is not a trivial task. An efficient implementation uses very complex methods. Since most of the open-source systems can hardly be used for research purposes the development of a structured and well-documented system is relevant. In this talk we present our own state-of-the-art solver and our development experiences.

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Ukić, Šime, Marko Rogošić, Mirjana Novak, Ena Šimović, Vesna Tišler, and Tomislav Bolanča. "Optimization of IC Separation Based on Isocratic-to-Gradient Retention Modeling in Combination with Sequential Searching or Evolutionary Algorithm." Journal of Analytical Methods in Chemistry 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/549729.

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Gradient ion chromatography was used for the separation of eight sugars: arabitol, cellobiose, fructose, fucose, lactulose, melibiose, N-acetyl-D-glucosamine, and raffinose. The separation method was optimized using a combination of simplex or genetic algorithm with the isocratic-to-gradient retention modeling. Both the simplex and genetic algorithms provided well separated chromatograms in a similar analysis time. However, the simplex methodology showed severe drawbacks when dealing with local minima. Thus the genetic algorithm methodology proved as a method of choice for gradient optimization in this case. All the calculated/predicted chromatograms were compared with the real sample data, showing more than a satisfactory agreement.

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Niño-Mora, José. "A Fast-Pivoting Algorithm for Whittle’s Restless Bandit Index." Mathematics 8, no. 12 (2020): 2226. http://dx.doi.org/10.3390/math8122226.

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The Whittle index for restless bandits (two-action semi-Markov decision processes) provides an intuitively appealing optimal policy for controlling a single generic project that can be active (engaged) or passive (rested) at each decision epoch, and which can change state while passive. It further provides a practical heuristic priority-index policy for the computationally intractable multi-armed restless bandit problem, which has been widely applied over the last three decades in multifarious settings, yet mostly restricted to project models with a one-dimensional state. This is due in part to the difficulty of establishing indexability (existence of the index) and of computing the index for projects with large state spaces. This paper draws on the author’s prior results on sufficient indexability conditions and an adaptive-greedy algorithmic scheme for restless bandits to obtain a new fast-pivoting algorithm that computes the n Whittle index values of an n-state restless bandit by performing, after an initialization stage, n steps that entail (2/3)n3+O(n2) arithmetic operations. This algorithm also draws on the parametric simplex method, and is based on elucidating the pattern of parametric simplex tableaux, which allows to exploit special structure to substantially simplify and reduce the complexity of simplex pivoting steps. A numerical study demonstrates substantial runtime speed-ups versus alternative algorithms.

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Ansari, A. H. "Easy Simplex (AHA Simplex) Algorithm." Journal of Applied Mathematics and Physics 07, no. 01 (2019): 23–30. http://dx.doi.org/10.4236/jamp.2019.71003.

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Hough, C. L., and Y. Chang. "Constrained Cutting Rate-Tool Life Characteristic Curve, Part 2: Convex Programs." Journal of Manufacturing Science and Engineering 120, no. 1 (1998): 160–65. http://dx.doi.org/10.1115/1.2830093.

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Based on the concept in Part 1, Theory and General Case, algorithms to determine the constrained R-T characteristic curve are established for convex constrained machining economics problems. The first algorithm is for posynomial problems with the linear-logarithmic tool life equation. The R-T curve may be determined by applying the simplex method to the log-dual problems. Sensitivity analysis of the optimal simplex tableau enables obtaining the loci of optima easily. The second algorithm is for the quadratic posylognomial problems with quadratic-logarithmic tool life equation using the property of primal-dual feasibility. End milling examples constructed in Part 1 illustrate the algorithm comparing to the exhaustive method.

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Ahandani, Morteza Alinia, and Hosein Alavi-Rad. "Hybridizing Shuffled Frog Leaping and Shuffled Complex Evolution Algorithms Using Local Search Methods." International Journal of Applied Evolutionary Computation 5, no. 1 (2014): 30–51. http://dx.doi.org/10.4018/ijaec.2014010103.

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In this research, a study was carried out to exploit the hybrid schemes combining two classical local search techniques i.e. Nelder–Mead simplex search method and bidirectional random optimization with two meta-heuristic methods i.e. the shuffled frog leaping and the shuffled complex evolution, respectively. In this hybrid methodology, each subset of meta-heuristic algorithms is improved by a hybrid strategy that is combined from evolutionary process of each subset in related algorithm and a local search method. These hybrid algorithms are evaluated on low and high dimensional continuous benchmark functions and the obtained results are compared with their non-hybrid competitors. The obtained results demonstrate that the hybrid algorithm combined from shuffled frog leaping and Nelder–Mead simplex has a better success rate but a higher number of function evaluations on low-dimensional functions than the shuffled frog leaping. Whereas on high-dimensional functions it has a better success rate and a faster performance. Also the hybrid algorithm combined from shuffled complex evolution and bidirectional random optimization obtains a better performance in terms of success rate and function evaluations than shuffled complex evolution on low dimensional functions; whereas on high-dimensional functions, it obtains a better success rate but a slower performance. Also a comparison of our hybrid algorithms with the other evolutionary algorithms reported in the literature confirms our proposed algorithms have the best performance among all compared algorithms.

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Chang, Ping-Teng, Chih-Sheng Lin, Kuo-Chen Hung, Han-Hsiang Lee, and Ching-Hsiang Chang. "Collaboration and Competition Process." International Journal of Artificial Life Research 1, no. 3 (2010): 62–90. http://dx.doi.org/10.4018/jalr.2010070107.

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The hybridization of genetic algorithms and the simplex method have been proven in literature as useful and promising in optimizations. Therefore, this paper proposes a multi-teams genetic-algorithm (MT-GA) hybrid developed toward extending the previous simplex-GA hybrids. The approach utilizes the simplex method as a united team and multi-teams collaboration and also competition search process in conjunction with the GAs. It is designed such that it has multi-teams with self-evolution (parallel applications of the simplex method), multi-teams communication and even mutual stimulation, and multi-teams survival competition as well as non-elite team breakup for individual relearning (with GAs) and re-forming the new teams. The extension of multi-teams GA thus provides the advantages and as previous simplex-GAs has been proved to outperform a number of other approaches. The experiments in this research show that the MT-GA generally outperforms the existing simplex-GAs for the indices of convergence rate (CPU time required), efficiency (number of function evaluations), and effectiveness (accuracy). Also, a further functional experiment of the MT-GA shows that the MT-GA can be a useful improved algorithm for the function optimization problems.

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Lu, Yuting, Yongquan Zhou, and Xiuli Wu. "A Hybrid Lightning Search Algorithm-Simplex Method for Global Optimization." Discrete Dynamics in Nature and Society 2017 (2017): 1–23. http://dx.doi.org/10.1155/2017/8342694.

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In this paper, a novel hybrid lightning search algorithm-simplex method (LSA-SM) is proposed to solve the shortcomings of lightning search algorithm (LSA) premature convergence and low computational accuracy and it is applied to function optimization and constrained engineering design optimization problems. The improvement adds two major optimization strategies. Simplex method (SM) iteratively optimizes the current worst step leaders to avoid the population searching at the edge, thus improving the convergence accuracy and rate of the algorithm. Elite opposition-based learning (EOBL) increases the diversity of population to avoid the algorithm falling into local optimum. LSA-SM is tested by 18 benchmark functions and five constrained engineering design problems. The results show that LSA-SM has higher computational accuracy, faster convergence rate, and stronger stability than other algorithms and can effectively solve the problem of constrained nonlinear optimization in reality.

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Cheng, Xiang, Su Li Wang, and Shu Wu Cheng. "Application of Optimization Algorithm for Ceramic Formulations." Advanced Materials Research 518-523 (May 2012): 3938–42. http://dx.doi.org/10.4028/www.scientific.net/amr.518-523.3938.

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ceramic formula; genetic algorithm; the simplex method; particle swarm optimization Abstract. The composition of ceramic materials determines its performance, so ceramic formula determines the performance of the product. The factors, such as supply of local raw materials, chemical composition, and raw material price, determine the formula. Selecting raw materials from a variety of raw materials which are consistent with the target formula and the percentage content of the chemical composition is a very important job. The chemical composition in the ceramic material is various, and the traditional method is to calculate the formula by hand. The workload is very heavy, and the results are often not accurate, and don’t meet actual requirements. By minimizing the deviation of chemical composition and mineral ingredients, the chemical and comprehensive formula optimization models of ceramic preform body were constructed. Several typical optimization algorithms were used to construct the formula model, such as particle swarm optimization, genetic algorithms and Nelder-Mead simplex method. The experimental results were presented and compared and it concluded that the particle swarm optimization algorithm is superior to the other optimization algorithms.

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Kazakovtsev, Lev, Ivan Rozhnov, Aleksey Popov, and Elena Tovbis. "Self-Adjusting Variable Neighborhood Search Algorithm for Near-Optimal k-Means Clustering." Computation 8, no. 4 (2020): 90. http://dx.doi.org/10.3390/computation8040090.

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The k-means problem is one of the most popular models in cluster analysis that minimizes the sum of the squared distances from clustered objects to the sought cluster centers (centroids). The simplicity of its algorithmic implementation encourages researchers to apply it in a variety of engineering and scientific branches. Nevertheless, the problem is proven to be NP-hard which makes exact algorithms inapplicable for large scale problems, and the simplest and most popular algorithms result in very poor values of the squared distances sum. If a problem must be solved within a limited time with the maximum accuracy, which would be difficult to improve using known methods without increasing computational costs, the variable neighborhood search (VNS) algorithms, which search in randomized neighborhoods formed by the application of greedy agglomerative procedures, are competitive. In this article, we investigate the influence of the most important parameter of such neighborhoods on the computational efficiency and propose a new VNS-based algorithm (solver), implemented on the graphics processing unit (GPU), which adjusts this parameter. Benchmarking on data sets composed of up to millions of objects demonstrates the advantage of the new algorithm in comparison with known local search algorithms, within a fixed time, allowing for online computation.

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Papamanthou, Charalampos, Konstantinos Paparrizos, and Nikolaos Samaras. "A parametric visualization software for the assignment problem." Yugoslav Journal of Operations Research 15, no. 1 (2005): 147–58. http://dx.doi.org/10.2298/yjor0501147p.

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In this paper we present a parametric visualization software used to assist the teaching of the Network Primal Simplex Algorithm for the assignment problem (AP). The assignment problem is a special case of the balanced transportation problem. The main functions of the algorithm and design techniques are also presented. Through this process, we aim to underline the importance and necessity of using such educational methods in order to improve the teaching of Computer Algorithms.

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Nyiam, Paschal B., and Abdellah Salhi. "A comparative study of two key algorithms in multiple objective linear programming." Journal of Algorithms & Computational Technology 13 (January 2019): 174830261987042. http://dx.doi.org/10.1177/1748302619870424.

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Multiple objective linear programming problems are solved with a variety of algorithms. While these algorithms vary in philosophy and outlook, most of them fall into two broad categories: those that are decision space-based and those that are objective space-based. This paper reports the outcome of a computational investigation of two key representative algorithms, one of each category, namely the parametric simplex algorithm which is a prominent representative of the former and the primal variant of Bensons Outer-approximation algorithm which is a prominent representative of the latter. The paper includes a procedure to compute the most preferred nondominated point which is an important feature in the implementation of these algorithms and their comparison. Computational and comparative results on problem instances ranging from small to medium and large are provided.

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Abida, Habib, and Ronald D. Townsend. "Parameter optimization in modelling unsteady compound channel flows." Canadian Journal of Civil Engineering 19, no. 3 (1992): 441–46. http://dx.doi.org/10.1139/l92-053.

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Optimization methods are used to estimate data for routing floods through open compound channels (main channels with flood plain zones). These data include the irregular channel section geometry and the varying boundary roughness. Differences between simulated and observed stages and discharges are minimized using three optimization algorithms: Powell's method, Rosenbrock's algorithm, and the Nelder and Meade simplex method. Powells' method performed poorly; however, both the Rosenbrock and simplex methods yielded good results. The estimated data using the Rosenbrock and simplex methods were used to route different flood events observed in a laboratory channel. Simulated peak stages and discharges were in good agreement with those estimated using actual routing data. Key words: compound channel, flood routing, lateral momentum transfer, optimization, unsteady flow.

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Zhou, Chong, Shengjie Li, Yuhe Zhang, Zhikun Chen, and Cuijun Zhang. "Enhancing Backtracking Search Algorithm using Reflection Mutation Strategy Based on Sine Cosine." Algorithms 12, no. 11 (2019): 225. http://dx.doi.org/10.3390/a12110225.

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Backtracking Search Algorithm (BSA) is a younger population-based evolutionary algorithm and widely researched. Due to the introduction of historical population and no guidance toward to the best individual, BSA does not adequately use the information in the current population, which leads to a slow convergence speed and poor exploitation ability of BSA. To address these drawbacks, a novel backtracking search algorithm with reflection mutation based on sine cosine is proposed, named RSCBSA. The best individual found so far is employed to improve convergence speed, while sine and cosine math models are introduced to enhance population diversity. To sufficiently use the information in the historical population and current population, four individuals are selected from the historical or current population randomly to construct an unit simplex, and the center of the unit simplex can enhance exploitation ability of RSCBSA. Comprehensive experimental results and analyses show that RSCBSA is competitive enough with other state-of-the-art meta-heuristic algorithms.

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Parker, L. R., M. R. Cave, and R. M. Barnes. "Comparison of simplex algorithms." Analytica Chimica Acta 175 (1985): 231–37. http://dx.doi.org/10.1016/s0003-2670(00)82735-x.

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Pošík, Petr, and Waltraud Huyer. "Restarted Local Search Algorithms for Continuous Black Box Optimization." Evolutionary Computation 20, no. 4 (2012): 575–607. http://dx.doi.org/10.1162/evco_a_00087.

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Several local search algorithms for real-valued domains (axis parallel line search, Nelder-Mead simplex search, Rosenbrock's algorithm, quasi-Newton method, NEWUOA, and VXQR) are described and thoroughly compared in this article, embedding them in a multi-start method. Their comparison aims (1) to help the researchers from the evolutionary community to choose the right opponent for their algorithm (to choose an opponent that would constitute a hard-to-beat baseline algorithm), (2) to describe individual features of these algorithms and show how they influence the algorithm on different problems, and (3) to provide inspiration for the hybridization of evolutionary algorithms with these local optimizers. The recently proposed Comparing Continuous Optimizers (COCO) methodology was adopted as the basis for the comparison. The results show that in low dimensional spaces, the old method of Nelder and Mead is still the most successful among those compared, while in spaces of higher dimensions, it is better to choose an algorithm based on quadratic modeling, such as NEWUOA or a quasi-Newton method.

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Ding, Xiaodong, and Chengliang Wang. "A Novel Algorithm of Stochastic Chance-Constrained Linear Programming and Its Application." Mathematical Problems in Engineering 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/139271.

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The computation problem is discussed for the stochastic chance-constrained linear programming, and a novel direct algorithm, that is, simplex algorithm based on stochastic simulation, is proposed. The considered programming problem in this paper is linear programming with chance constraints and random coefficients, and therefore the stochastic simulation is an important implement of the proposed algorithm. By theoretical analysis, the theory basis of the proposed algorithm is obtained and, by numerical examples, the feasibility and validness of this algorithm are illustrated. The detailed algorithm procedure is given, which is easily converted into the executable codes of software tools. Then, we compare it with some algorithms to verify its superiority. Finally, a practical example is presented to show its practicability.

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Xu, Senlin, and Shulin Liu. "HOMOTOPY SIMPLEX PIVOT ALGORITHM." Acta Mathematica Scientia 11, no. 1 (1991): 111–20. http://dx.doi.org/10.1016/s0252-9602(18)30434-x.

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Evans, D. J., and G. M. Megson. "A systolic simplex algorithm." International Journal of Computer Mathematics 38, no. 1-2 (1991): 1–30. http://dx.doi.org/10.1080/00207169108803954.

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Bulut, Hasan. "Multiloop transportation simplex algorithm." Optimization Methods and Software 32, no. 6 (2016): 1206–17. http://dx.doi.org/10.1080/10556788.2016.1260568.

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Allamigeon, Xavier, Pascal Benchimol, Stéphane Gaubert, and Michael Joswig. "Tropicalizing the Simplex Algorithm." SIAM Journal on Discrete Mathematics 29, no. 2 (2015): 751–95. http://dx.doi.org/10.1137/130936464.

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Corley, H. W., Jay Rosenberger, Wei-Chang Yeh, and T. K. Sung. "The cosine simplex algorithm." International Journal of Advanced Manufacturing Technology 27, no. 9-10 (2005): 1047–50. http://dx.doi.org/10.1007/s00170-004-2278-1.

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Neptune, R. R. "Optimization Algorithm Performance in Determining Optimal Controls in Human Movement Analyses." Journal of Biomechanical Engineering 121, no. 2 (1999): 249–52. http://dx.doi.org/10.1115/1.2835111.

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The objective of this study was to evaluate the performance of different multivariate optimization algorithms by solving a “tracking” problem using a forward dynamic model of pedaling. The tracking problem was defined as solving for the muscle controls (muscle stimulation onset, offset, and magnitude) that minimized the error between experimentally collected kinetic and kinematic data and the simulation results of pedaling at 90 rpm and 250 W. Three different algorithms were evaluated: a downhill simplex method, a gradient-based sequential quadratic programming algorithm, and a simulated annealing global optimization routine. The results showed that the simulated annealing algorithm performed far superior to the conventional routines by converging more rapidly and avoiding local minima.

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CHÁVEZ, TIMOTHY MICHAEL, та DUC THAI NGUYEN. "Efficient Algorithms for Identifying Loop Formation and Computing θ Value for Solving Minimum Cost Flow Network Problems". WSEAS TRANSACTIONS ON CIRCUITS AND SYSTEMS 20 (28 червня 2021): 107–17. http://dx.doi.org/10.37394/23201.2021.20.14.

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While the minimum cost flow (MCF) problems have been well documented in many publications, due to its broad applications, little or no effort have been devoted to explaining the algorithms for identifying loop formation and computing the θ value needed to solve MCF network problems. This paper proposes efficient algorithms, and MATLAB computer implementation, for solving MCF problems. Several academic and real-life network problems have been solved to validate the proposed algorithms; the numerical results obtained by the developed MCF code have been compared and matched with the built-in MATLAB function Linprog() (Simplex algorithm) for further validation.

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CLARKSON, KENNETH L., RICHARD COLE, and ROBERT E. TARJAN. "RANDOMIZED PARALLEL ALGORITHMS FOR TRAPEZOIDAL DIAGRAMS." International Journal of Computational Geometry & Applications 02, no. 02 (1992): 117–33. http://dx.doi.org/10.1142/s0218195992000081.

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We describe randomized parallel algorithms for building trapezoidal diagrams of line segments in the plane. The algorithms are designed for a CRCW PRAM. For general segments, we give an algorithm requiring optimal O(A+n log n) expected work and optimal O( log n) time, where A is the number of intersecting pairs of segments. If the segments form a simple chain, we give an algorithm requiring optimal O(n) expected work and O( log n log log n log * n) expected time , and a simpler algorithm requiring O(n log * n) expected work. The serial algorithm corresponding to the latter is among the simplest known algorithms requiring O(n log * n) expected operations. For a set of segments forming K chains, we give an algorithm requiring O(A+n log * n+K log n) expected work and O( log n log log n log * n) expected time. The parallel time bounds require the assumption that enough processors are available, with processor allocations every log n steps.

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Mrzljak, Vedran, Nikola Anđelić, Ivan Lorencin, and Sandi Sandi Baressi Šegota. "The influence of various optimization algorithms on nuclear power plant steam turbine exergy efficiency and destruction." Pomorstvo 35, no. 1 (2021): 69–86. http://dx.doi.org/10.31217/p.35.1.8.

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This paper presents an exergy analysis of the whole turbine, turbine cylinders and cylinder parts in four different operating regimes. Analyzed turbine operates in nuclear power plant while three of four operating regimes are obtained by using optimization algorithms – SA (Simplex Algorithm), GA (Genetic Algorithm) and IGSA (Improved Genetic-Simplex Algorithm). IGSA operating regime gives the highest developed mechanical power of the whole turbine equal to 1022.48 MW, followed by GA (1020.06 MW) and SA (1017.16 MW), while in Original operating regime whole turbine develop mechanical power equal to 996.29 MW. In addition, IGSA causes the highest increase in developed mechanical power of almost all cylinders and cylinder parts in comparison to the Original operating regime. All observed optimization algorithms increases the exergy destruction of the whole turbine in comparison to Original operating regime - the lowest increase causes IGSA, followed by GA and finally SA. The highest exergy efficiency of the whole turbine, equal to 85.92% is obtained by IGSA, followed by GA (85.89%) and SA (85.82%), while the lowest exergy efficiency is obtained in Original operating regime (85.70%). Analyzed turbine, which operates by using wet steam is low influenced by the ambient temperature change. IGSA, which shows dominant performance in exergy analysis parameters of the analyzed turbine, in certain situations is overpowered by GA. Therefore, in optimization of steam turbine performance, IGSA and GA can be recommended.

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Zeng, M., and W. Q. Tao. "A comparison study of the convergence characteristics and robustness for four variants of SIMPLE‐family at fine grids." Engineering Computations 20, no. 3 (2003): 320–40. http://dx.doi.org/10.1108/02644400310467234.

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A comparative study is performed to reveal the convergence characteristics and the robustness of four variants in the semi‐implicit method for pressure‐linked equations (SIMPLE)‐family: SIMPLE, SIMPLE revised (SIMPLER), SIMPLE consistent (SIMPLEC), and SIMPLE extrapolation (SIMPLEX). The focus is concentrated in the solution at fine grid system. Four typical fluid flow and heat transfer problems are taken as the numerical examples (lid‐driven cavity flow, flow in an axisymmetric sudden expansion, flow in an annulus with inner surface rotating and the natural convection in a square enclosure). It is found that an appropriate convergence condition should include both mass conservation and momentum conservation requirements. For the four problems computed, the SIMPLEX always requires the largest computational time, the SIMPLER comes the next, and the computational time of SIMPLE and SIMPLEC are the least. As far as the robustness is concerned, the SIMPLE algorithm is the worst, the SIMPLER comes the next and the robustness of SIMPLEX and SIMPLEC are superior to the others. The SIMPLEC algorithm is then recommended, especially for the computation at a fine grid system. Brief discussion is provided to further reveal the reasons which may account for the difference of the four algorithms.

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Kuno, Takahito, and Jianming Shi. "Linear programs with an additional separable concave constraint." Journal of Applied Mathematics and Decision Sciences 8, no. 3 (2004): 155–74. http://dx.doi.org/10.1155/s1173912604000100.

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In this paper, we develop two algorithms for globally optimizing a special class of linear programs with an additional concave constraint. We assume that the concave constraint is defined by a separable concave function. Exploiting this special structure, we apply Falk-Soland's branch-and-bound algorithm for concave minimization in both direct and indirect manners. In the direct application, we solve the problem alternating local search and branch-and-bound. In the indirect application, we carry out the bounding operation using a parametric right-hand-side simplex algorithm.

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Samaras, Nikolaos, Angelo Sifelaras, and Charalampos Triantafyllidis. "A primal-dual exterior point algorithm for linear programming problems." Yugoslav Journal of Operations Research 19, no. 1 (2009): 123–32. http://dx.doi.org/10.2298/yjor0901123s.

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The aim of this paper is to present a new simplex type algorithm for the Linear Programming Problem. The Primal - Dual method is a Simplex - type pivoting algorithm that generates two paths in order to converge to the optimal solution. The first path is primal feasible while the second one is dual feasible for the original problem. Specifically, we use a three-phase-implementation. The first two phases construct the required primal and dual feasible solutions, using the Primal Simplex algorithm. Finally, in the third phase the Primal - Dual algorithm is applied. Moreover, a computational study has been carried out, using randomly generated sparse optimal linear problems, to compare its computational efficiency with the Primal Simplex algorithm and also with MATLAB's Interior Point Method implementation. The algorithm appears to be very promising since it clearly shows its superiority to the Primal Simplex algorithm as well as its robustness over the IPM algorithm.

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Liu, Jie, and Yu-ping Wang. "An Improved Central Force Optimization Algorithm for Multimodal Optimization." Journal of Applied Mathematics 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/895629.

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This paper proposes the hybrid CSM-CFO algorithm based on the simplex method (SM), clustering technique, and central force optimization (CFO) for unconstrained optimization. CSM-CFO is still a deterministic swarm intelligent algorithm, such that the complex statistical analysis of the numerical results can be omitted, and the convergence intends to produce faster and more accurate by clustering technique and good points set. When tested against benchmark functions, in low and high dimensions, the CSM-CFO algorithm has competitive performance in terms of accuracy and convergence speed compared to other evolutionary algorithms: particle swarm optimization, evolutionary program, and simulated annealing. The comparison results demonstrate that the proposed algorithm is effective and efficient.

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Han, Lei, Xia Wang, and Guang Wei Wang. "Maximum Power Point Tracking for the Micro-Scale Photovoltaic Power System." Applied Mechanics and Materials 734 (February 2015): 771–74. http://dx.doi.org/10.4028/www.scientific.net/amm.734.771.

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In this paper, we give a comprehensive consideration on the maximum power point tracking (MPPT) algorithm for micro-scale solar energy harvesting system. Basing on the comparison analysis the MPPT algorithm of fractional open circuit voltage (FOCV) is certificated to be the simplest method among all the algorithms focus on small size photovoltaic devices. As a validation, an example is given to demonstrate the effectiveness of the proposed idea.

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Ozaki, Naoto, Hiroshi Tezuka, and Mary Inaba. "A Simple Acceleration Method for the Louvain Algorithm." International Journal of Computer and Electrical Engineering 8, no. 3 (2016): 207–18. http://dx.doi.org/10.17706/ijcee.2016.8.3.207-218.

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Jeyanthi, K. Meena alias, and A. P. Kabilan. "A Simple Adaptive Beamforming Algorithm with interference Suppression." International Journal of Engineering and Technology 1, no. 1 (2009): 67–70. http://dx.doi.org/10.7763/ijet.2009.v1.12.

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Chen, Ta Tau, and Sung Chun Kuo. "Fuzzy Simplex-Type Sliding-Mode Control." Applied Mechanics and Materials 284-287 (January 2013): 2244–48. http://dx.doi.org/10.4028/www.scientific.net/amm.284-287.2244.

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In this paper, a novel fuzzy simplex sliding-mode controller is proposed for controlling a multivariable nonlinear system. Here, the fuzzy logic control (FLC) algorithm and simplex sliding-mode control (SSMC) theory are integrated to improve the system states response and to reduce system states chattering phenomenon of the controlled system for simplex control method. Hence, from this motivation yields the so-called fuzzy simplex sliding mode control (FSSMC) scheme. the fuzzy logic control algorithm and simplex sliding mode control algorithm is integrated to improve the system states response and chattering phenomenon. In this paper, at first, we introduce the principle of simplex method, and then develop the fuzzy controls based on the simplex method. Finally, a numerical example is proposed to illustrate the advantages of the proposed controllers, the simulation results demonstrate that the fuzzy simplex type sliding mode control scheme is a good solution to the chattering problem in the simplex sliding mode control.

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Geranis, George, Konstantinos Paparizzos, and Angelo Sifaleras. "A dual exterior point simplex type algorithm for the minimum cost network flow problem." Yugoslav Journal of Operations Research 19, no. 1 (2009): 157–70. http://dx.doi.org/10.2298/yjor0901157g.

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A new dual simplex type algorithm for the Minimum Cost Network Flow Problem (MCNFP) is presented. The proposed algorithm belongs to a special 'exterior- point simplex type' category. Similarly to the classical network dual simplex algorithm (NDSA), this algorithm starts with a dual feasible tree-solution and reduces the primal infeasibility, iteration by iteration. However, contrary to the NDSA, the new algorithm does not always maintain a dual feasible solution. Instead, the new algorithm might reach a basic point (tree-solution) outside the dual feasible area (exterior point - dual infeasible tree).

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Fauzi, Hilman, and Uzma Batool. "A Three-bar Truss Design using Single-solution Simulated Kalman Filter Optimizer." Mekatronika 1, no. 2 (2019): 98–102. http://dx.doi.org/10.15282/mekatronika.v1i2.4991.

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    Three-bar truss is a structure that is important in the field of civil engineering. Design of the three-bar truss is thus an interesting problem in engineering. Metaheuristic approach has been employed to get near-optimal solution of this problem. A study to investigate the effectiveness of a new single-solution simulated Kalman filter (ssSKF) algorithm in three-bar truss design is presented in this paper. The solution obtained by the ssSKF is as good as hybrid lightning search algorithm-simplex method and better than solutions produced other algorithms in literature.   

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LIU, LIANJUN, LI ZHAO, YOUDONG MAO, DONG YU, JINGWEN XU, and YUANXIANG LI. "USING EVOLUTIONARY ALGORITHM TO CALCULATE THE GROUND-STATE ENERGY OF DOUBLE-ELECTRON ATOMS IN A UNIFORM MAGNETIC FIELD (B ≤ 109G)." International Journal of Modern Physics C 11, no. 01 (2000): 183–94. http://dx.doi.org/10.1142/s012918310000016x.

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It is very difficult to calculate the accurate ground-state energies of the double-electron atom like helium in a uniform magnetic field. By using the modified configuration interaction (MCI) method and the evolutionary algorithm (EA), we obtained highly accurate results. We discuss the role of magnetic field in the ground state of the double-electron system and the possibility of variational ground-state energy calculation by using evolutionary algorithm directly. Results show that compared with other algorithms, such as the simplex method, EA is more efficient in calculating atomic energies, and can be used in other fields of physics.

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Bani Abdelrahman, Ra’ed, Rafat Alshorman, Walter Hussak, and Amitabh Trehan. "Specification of Synchronous Network Flooding in Temporal Logic." International Arab Journal of Information Technology 17, no. 6 (2020): 867–74. http://dx.doi.org/10.34028/iajit/17/6/5.

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In distributed network algorithms, network flooding algorithm is considered one of the simplest and most fundamental algorithms. This research specifies the basic synchronous memory-less network flooding algorithm where nodes on the network don’t have memory, for any fixed size of network, in Linear Temporal Logic. The specification can be customized to any single network topology or class of topologies. A specification of the termination problem is formulated and used to compare different topologies for earlier termination. This research gives a worked example of one topology resulting in earlier termination than another, for which we perform a formal verification using the model checker NuSMV

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Nasseri, Seyed Hadi, and Ali Ebrahimnejad. "Sensitivity Analysis on Linear Programming Problems with Trapezoidal Fuzzy Variables." International Journal of Operations Research and Information Systems 2, no. 2 (2011): 22–39. http://dx.doi.org/10.4018/joris.2011040102.

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In the real word, there are many problems which have linear programming models and sometimes it is necessary to formulate these models with parameters of uncertainty. Many numbers from these problems are linear programming problems with fuzzy variables. Some authors considered these problems and have developed various methods for solving these problems. Recently, Mahdavi-Amiri and Nasseri (2007) considered linear programming problems with trapezoidal fuzzy data and/or variables and stated a fuzzy simplex algorithm to solve these problems. Moreover, they developed the duality results in fuzzy environment and presented a dual simplex algorithm for solving linear programming problems with trapezoidal fuzzy variables. Here, the authors show that this presented dual simplex algorithm directly using the primal simplex tableau algorithm tenders the capability for sensitivity (or post optimality) analysis using primal simplex tableaus.

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Journal articles on the topic 'Algorithme du simplexe'

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