Journal articles: 'Epsilon constraint method'

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Pérez‐Cañedo, Boris, José Luis Verdegay, and Ridelio Miranda Pérez. "An epsilon‐constraint method for fully fuzzy multiobjective linear programming." International Journal of Intelligent Systems 35, no. 4 (January 12, 2020): 600–624. http://dx.doi.org/10.1002/int.22219.

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Kai, Liu, and Ramina Malekalipour Kordestanizadeh. "Designing an Agile Closed-Loop Supply Chain with Environmental Aspects Using a Novel Multiobjective Metaheuristic Algorithm." Mathematical Problems in Engineering 2021 (November 2, 2021): 1–13. http://dx.doi.org/10.1155/2021/3811417.

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Success in supply chain implementation depends on the way of dealing with market changes and customer needs. Agility is a concept that has been introduced in recent years to improve the supply chain. On the other hand, paying attention to environmental problems is another issue, and chains are trying to increase their popularity by focusing on this issue. Considering the importance of this issue, designing a multiobjective closed-loop supply chain network has been discussed in this research. The main contribution of this research is the integration of green and agility concepts in supply chain design. In this regard, a mathematical model is presented with economic, environmental, and agility objectives. First, the mathematical model is solved using the Epsilon constraint method, and then, the multiobjective weed algorithm is proposed to solve the model. The results of comparisons between the two methods show that the multiobjective weed algorithm has performed well in terms of various metrics of NPS, SNS, and Max Spread. In terms of the solving time, the average solving time of this algorithm was about 0.1% of the solving time of the Epsilon constraint method. Moreover, all cases show the superiority of the multiobjective weed algorithm over the Epsilon constraint method in solving the proposed mathematical model.

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Zhou, Jinlong, Juan Zou, Jinhua Zheng, Shengxiang Yang, Dunwei Gong, and Tingrui Pei. "An infeasible solutions diversity maintenance epsilon constraint handling method for evolutionary constrained multiobjective optimization." Soft Computing 25, no. 13 (May 25, 2021): 8051–62. http://dx.doi.org/10.1007/s00500-021-05880-5.

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Agud-Albesa, Lucia, Neus Garrido, Angel A. Juan, Almudena Llorens, and Sandra Oltra-Crespo. "A Weighted and Epsilon-Constraint Biased-Randomized Algorithm for the Biobjective TOP with Prioritized Nodes." Computation 12, no. 4 (April 20, 2024): 84. http://dx.doi.org/10.3390/computation12040084.

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This paper addresses a multiobjective version of the Team Orienteering Problem (TOP). The TOP focuses on selecting a subset of customers for maximum rewards while considering time and fleet size constraints. This study extends the TOP by considering two objectives: maximizing total rewards from customer visits and maximizing visits to prioritized nodes. The MultiObjective TOP (MO-TOP) is formulated mathematically to concurrently tackle these objectives. A multistart biased-randomized algorithm is proposed to solve MO-TOP, integrating exploration and exploitation techniques. The algorithm employs a constructive heuristic defining biefficiency to select edges for routing plans. Through iterative exploration from various starting points, the algorithm converges to high-quality solutions. The Pareto frontier for the MO-TOP is generated using the weighted method, epsilon-constraint method, and Epsilon-Modified Method. Computational experiments validate the proposed approach’s effectiveness, illustrating its ability to generate diverse and high-quality solutions on the Pareto frontier. The algorithms demonstrate the ability to optimize rewards and prioritize node visits, offering valuable insights for real-world decision making in team orienteering applications.

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Mavalizadeh, Hani, and Abdollah Ahmadi. "Hybrid expansion planning considering security and emission by augmented epsilon-constraint method." International Journal of Electrical Power & Energy Systems 61 (October 2014): 90–100. http://dx.doi.org/10.1016/j.ijepes.2014.03.004.

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Jin, Bangti, Buyang Li, and Zhi Zhou. "Pointwise-in-time error estimates for an optimal control problem with subdiffusion constraint." IMA Journal of Numerical Analysis 40, no. 1 (October 30, 2018): 377–404. http://dx.doi.org/10.1093/imanum/dry064.

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Abstract In this work we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation that involves a fractional derivative of order $\alpha \in (0,1)$ in time. The fully discrete scheme is obtained by applying the conforming linear Galerkin finite element method in space, L1 scheme/backward Euler convolution quadrature in time, and the control variable by a variational-type discretization. With a space mesh size $h$ and time stepsize $\tau $ we establish the following order of convergence for the numerical solutions of the optimal control problem: $O(\tau ^{\min ({1}/{2}+\alpha -\epsilon ,1)}+h^2)$ in the discrete $L^2(0,T;L^2(\varOmega ))$ norm and $O(\tau ^{\alpha -\epsilon }+\ell _h^2h^2)$ in the discrete $L^{\infty }(0,T;L^2(\varOmega ))$ norm, with any small $\epsilon>0$ and $\ell _h=\ln (2+1/h)$. The analysis relies essentially on the maximal $L^p$-regularity and its discrete analogue for the subdiffusion problem. Numerical experiments are provided to support the theoretical results.

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Tartibu, L. K., B. Sun, and M. A. E. Kaunda. "Optimal design study of thermoacoustic regenerator with lexicographic optimization method." Journal of Engineering, Design and Technology 13, no. 3 (July 6, 2015): 499–519. http://dx.doi.org/10.1108/jedt-09-2012-0039.

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Purpose – This paper aims to illustrate the use of the augmented epsilon-constraint method implemented in general algebraic modelling system (GAMS), aimed at optimizing the geometry of a thermoacoustic regenerator. Thermoacoustic heat engines provide a practical solution to the problem of heat management where heat can be pumped or spot cooling can be produced. However, the most inhibiting characteristic of thermoacoustic cooling is their current lack of efficiencies. Design/methodology/approach – Lexicographic optimization is presented as an alternative optimization technique to the common used weighting methods. This approach establishes a hierarchical order among all the optimization objectives instead of giving them a specific (and most of the time, arbitrary) weight. Findings – A practical example is given, in a hypothetical scenario, showing how the proposed optimization technique may help thermoacoustic regenerator designers to identify Pareto optimal solutions when dealing with geometric parameters. This study highlights the fact that the geometrical parameters are interdependent, which support the use of a multi-objective approach for optimization in thermoacoustic. Originality/value – The research output from this paper can be a valuable resource to support designers in building efficient thermoacoustic device. The research illustrates the use of a lexicographic optimization to provide more meaningful results describing the geometry of thermoacoustic regenerator. It applies the epsilon-constraint method (AUGMENCON) to solve a five-criteria mixed integer non-linear problem implemented in GAMS (GAM software).

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Estrin, Ron, and Michael P. Friedlander. "A perturbation view of level-set methods for convex optimization." Optimization Letters 14, no. 8 (June 12, 2020): 1989–2006. http://dx.doi.org/10.1007/s11590-020-01609-9.

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Abstract Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again across a range of algorithms for convex problems. Here we demonstrate that strong duality is a necessary condition for the level-set approach to succeed. In the absence of strong duality, the level-set method identifies $$\epsilon $$ ϵ -infeasible points that do not converge to a feasible point as $$\epsilon $$ ϵ tends to zero. The level-set approach is also used as a proof technique for establishing sufficient conditions for strong duality that are different from Slater’s constraint qualification.

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Bamogo, W., K. Some, and G. A. Degla. "PERFORMANCE STUDY OF MULTIOBJECTIVE OPTIMIZER METHOD BASED ON GREY WOLF ATTACK TECHNICS." Journal of Computer Science and Applied Mathematics 5, no. 2 (September 30, 2023): 53——73. http://dx.doi.org/10.37418/jcsam.5.2.2.

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This paper proposes a performance study for the Multiobjective Optimizer based on the Grey Wolf Attack technics (MOGWAT). It is a method of solving multiobjective optimization problems. The method consists of the resolution of an unconstrained single objective optimization problem, which is derived from the aggregation of objective functions by the $\epsilon$-constraint approach and the penalization of constraints by a Lagrangian function. Then, Pareto-optimal solutions are obtained using the stochastic method based on the Grey Wolf Optimizer. To evaluate the method, three theorems have been formulated to demonstrate the convergence of the proposed algorithm and the optimality of the obtained solutions. Six test problems from the literature have been successfully dealt with, and the obtained results have been compared to two other methods. We have evaluated two performance parameters, including the generational distance for the approximation error and the spread for the coverage of the Pareto front. Based on these numerical findings, it can be concluded that MOGWAT outperforms two other methods.

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Bozoklar, Emine, and Ebru Yılmaz. "Designing Sustainable Flexible Manufacturing Cells with Multi-Objective Optimization Models." Applied Sciences 14, no. 1 (December 25, 2023): 203. http://dx.doi.org/10.3390/app14010203.

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Having sustainable and flexible features is crucial for manufacturing companies considering the increasing competition in the globalized world. This study considers three aspects of sustainability, namely economic, social, and environmental factors, in the design of flexible manufacturing cells. Three different multi-objective integer mathematical programming models were developed with the objective of minimizing the costs associated with carbon emissions, inter-cellular movements, machine processing, machine replacement, worker training, and additional salary (bonus). Simultaneously, these models aim to minimize the carbon emission amount of the cells within the environmental dimension scope. The developed models are a goal programming model, an epsilon constraint method, and an augmented epsilon constraint (AUGMECON) method. In these models, alternative routes of parts are considered while assigning parts to machines. The results are obtained using the LINGO 20.0 optimization program with a developed illustrative example. The obtained results are tested and compared by performing sensitivity analyses. The sensitivity analyses include examinations of the effects of changes in part demands, machine capacity values, carbon limit value, and the maximum number of workers in cells.

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Laumanns, Marco, Lothar Thiele, and Eckart Zitzler. "An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method." European Journal of Operational Research 169, no. 3 (March 2006): 932–42. http://dx.doi.org/10.1016/j.ejor.2004.08.029.

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Pirouz, Behzad, and Esmaile Khorram. "A COMPUTATIONAL APPROACH BASED ON THE \epsilon-CONSTRAINT METHOD IN MULTI-OBJECTIVE OPTIMIZATION PROBLEMS." Advances and Applications in Statistics 49, no. 6 (December 9, 2016): 453–83. http://dx.doi.org/10.17654/as049060453.

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Stoilova, Svetla. "An Integrated Multi-Criteria and Multi-Objective Optimization Approach for Establishing the Transport Plan of Intercity Trains." Sustainability 12, no. 2 (January 17, 2020): 687. http://dx.doi.org/10.3390/su12020687.

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The development of the transport plan must take into account various criteria impacting the transport process. The main objective of the study is to propose an integrated approach to determine the transport plan of passenger trains. The methodology consists of five steps. In the first step, the criteria for optimization of the transport plan were defined. In the second step, variants of the transport plan were formulated. In the third step, the weights of the criteria are determined by applying the step-wise weight assessment ratio analysis method (SWARA) multi-criteria method. The multi-objective optimization was conducted in the fourth step. The following multi-objective optimization approaches were used and compared: weighted sum method (WSM), compromise programming method (CP), and the epsilon–constraint method (EC). The study proposes a modified epsilon–constraint method (MEC) by applying normalization of each objective function according to the maximal value of the solution by individual optimization for each objective function, and hybrid methods: hybrid WSM and EC, hybrid WSM and MEC, hybrid CP and EC, and Hybrid CP and MEC. The impact of the variation of passenger flows on the choice of an optimal transport plan was studied in the fifth step. The Laplace’s criterion, Hurwitz’s criterion, and Savage’s criterion were applied to come to a decision. The approbation of the methodology was demonstrated through the case study of Bulgaria’s railway network. Suitable variant of transport plan is proposed.

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Yuan, Yu, Pengcheng Wang, and Minghui Wang. "Multi-Objective Stochastic Synchronous Timetable Optimization Model Based on a Chance-Constrained Programming Method Combined with Augmented Epsilon Constraint Algorithm." Mathematical Problems in Engineering 2022 (August 28, 2022): 1–18. http://dx.doi.org/10.1155/2022/9222636.

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The design of the timetable is essential to improve the service quality of the public transport system. A lot of random factors in the actual operation environment will affect the implementation of the synchronous timetable, and adjusting timetables to improve synchronization will break the order of normal service and increase the cost of operation. A multi-objective bus timetable optimization problem is characterized by considering the randomness of vehicle travel time and passenger transfer demand. A multi-objective optimization model is proposed, aiming at minimizing the total waiting time of passengers in the whole bus network and the inconsistency between the timetable after synchronous optimization and the original timetable. Through large sample analysis, it is found that the random variables in the model obey normal distribution, so the stochastic programming problem is transformed into the traditional deterministic programming problem by the chance-constrained programming method. A model solving method based on the augmented epsilon-constraint algorithm is designed. Examples show that when the random variables are considered, the proposed algorithm can obtain multiple high-quality Pareto optimal solutions in a short time, which can provide more practical benefits for decisionmakers. Ignoring the random influence will reduce the effectiveness of the schedule optimization scheme. Finally, sensitivity analysis of random variables and constraint confidence in the model is made.

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Fan, Zhun, Wenji Li, Xinye Cai, Han Huang, Yi Fang, Yugen You, Jiajie Mo, Caimin Wei, and Erik Goodman. "An improved epsilon constraint-handling method in MOEA/D for CMOPs with large infeasible regions." Soft Computing 23, no. 23 (February 4, 2019): 12491–510. http://dx.doi.org/10.1007/s00500-019-03794-x.

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Du, Yawei, Lixin Xie, Jie Liu, Yuxin Wang, Yingjun Xu, and Shichang Wang. "Multi-objective optimization of reverse osmosis networks by lexicographic optimization and augmented epsilon constraint method." Desalination 333, no. 1 (January 2014): 66–81. http://dx.doi.org/10.1016/j.desal.2013.10.028.

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Khalilzadeh, Mohammad, Rose Balafshan, and Ashkan Hafezalkotob. "Multi-objective mathematical model based on fuzzy hybrid multi-criteria decision-making and FMEA approach for the risks of oil and gas projects." Journal of Engineering, Design and Technology 18, no. 6 (June 1, 2020): 1997–2016. http://dx.doi.org/10.1108/jedt-01-2020-0020.

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Purpose The purpose of this study is to provide a comprehensive framework for analyzing risk factors in oil and gas projects. Design/methodology/approach This paper consists of several sections. In the first section, 19 common potential risks in the projects of Pars Oil and Gas Company were finalized in six groups using the Lawshe validation method. These factors were identified through previous literature review and interviews with experts. Then, using the “best-worst multi-criteria decision-making” method, the study measured the weights associated with the performance evaluation indicators of each risk. Consequently, failure mode and effects analysis (FMEA) and the grey relational analysis (GRA)-VIKOR mixed method were used to rank and determine the critical risks. Finally, to assign response strategies to each critical risk, a zero-one multi-objective mathematical programming model was proposed and developed Epsilon-constraint method was used to solve it. Findings Given the typical constraints of projects which are time, cost and quality, of the projects that companies are often faced with, this study presents the identified risks of oil and gas projects to the managers of the oil and gas company in accordance with the priority given in the present research and the response to each risk is also suggested to be used by managers based on their organizational circumstances. Originality/value This study aims at qualitative management of cost risks of oil and gas projects (case study of Pars Oil and Gas Company) by combining FMEA, best worst and GRA-VIKOR methods under fuzzy environment and Epsilon constraints. According to studies carried out in previous studies, the simultaneous management of quantitative and qualitative cost of risk of oil and gas projects in Iran has not been carried out and the combination of these methods has also been innovated.

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Herrero, J. M., G. Reynoso-Meza, M. Martínez, X. Blasco, and J. Sanchis. "A Smart-Distributed Pareto Front Using the ev-MOGA Evolutionary Algorithm." International Journal on Artificial Intelligence Tools 23, no. 02 (April 2014): 1450002. http://dx.doi.org/10.1142/s021821301450002x.

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Obtaining multi-objective optimization solutions with a small number of points smartly distributed along the Pareto front is a challenge. Optimization methods, such as the normalized normal constraint (NNC), propose the use of a filter to achieve a smart Pareto front distribution. The NCC optimization method presents several disadvantages related with the procedure itself, initial condition dependency, and computational burden. In this article, the epsilon-variable multi-objective genetic algorithm (ev-MOGA) is presented. This algorithm characterizes the Pareto front in a smart way and removes the disadvantages of the NNC method. Finally, examples of a three-bar truss design and controller tuning optimizations are presented for comparison purposes.

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Abdelaziz, Fouad Ben, Mohamed Amer, and Hazim El-Baz. "An Epsilon Constraint Method for selecting Indicators for use in Neural Networks for Stock Market Forecasting." INFOR: Information Systems and Operational Research 52, no. 3 (August 2014): 116–25. http://dx.doi.org/10.3138/infor.52.3.116.

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Aghaei, J., N. Amjady, and H. A. Shayanfar. "Multi-objective electricity market clearing considering dynamic security by lexicographic optimization and augmented epsilon constraint method." Applied Soft Computing 11, no. 4 (June 2011): 3846–58. http://dx.doi.org/10.1016/j.asoc.2011.02.022.

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Devi, S. Prasanna, S. Manivannan, and K. Suryaprakasa Rao. "Comparison of nongradient methods with hybrid Taguchi-based epsilon constraint method for multiobjective optimization of cylindrical fin heat sink." International Journal of Advanced Manufacturing Technology 63, no. 9-12 (February 28, 2012): 1081–94. http://dx.doi.org/10.1007/s00170-012-3985-7.

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Khalili-Damghani, Kaveh, Majid Nojavan, and Madjid Tavana. "Solving fuzzy Multidimensional Multiple-Choice Knapsack Problems: The multi-start Partial Bound Enumeration method versus the efficient epsilon-constraint method." Applied Soft Computing 13, no. 4 (April 2013): 1627–38. http://dx.doi.org/10.1016/j.asoc.2013.01.014.

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Lolagari, Hossein, Amir Daneshvar, Mahdi Madanchi Zaj, and Fereydon Rahnamay Roodposhti. "Sustainable Financing Model considering Project Risk." Discrete Dynamics in Nature and Society 2022 (September 7, 2022): 1–19. http://dx.doi.org/10.1155/2022/2838913.

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Implementing various projects in each country leads to the development of that country. The necessity of implementing any project is to finance that project through different methods. In this regard, the cost of financing projects, determining the amount of financing from each technique, and the risk of financing projects are among the things that have caused problems for managers and decision makers. This study presents a new sustainable financing model for international projects in Iran. The main objectives are to minimize the financing cost and risk of funding the projects. Based on the proposed conceptual model based on fuzzy hierarchy analysis, it was observed that Iran’s economic conditions, with a weight coefficient of 0.34, have the highest risk in financing projects. Therefore, a two-objective model was designed by determining the weighting coefficients to reduce costs and financing risks. Additionally, the epsilon constraint methods and NSGA II algorithm were used. Comparative results between the two algorithms show that financing projects must be changed to reduce the risk of sustainable financing of international projects, which can lead to an increase in the total cost of financing projects. On the other hand, it was observed that the NSGA II algorithm obtained 32 efficient answers (a combination of how projects are financed). Each of the received answers has advantages over the other solutions obtained. The epsilon constraint method also brought 11 efficient answers, demonstrating that the domestic capital market can provide 54.89% of the deficit budget of the country’s international projects. Furthermore, 44.81% of the project deficit budget can be financed from a foreign bank loan source, and only 0.2% of the budget can be funded through the company’s internal resources.

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Wang, Wanqi, Yun Bao, and Sihui Long. "Rescheduling Urban Rail Transit Trains to Serve Passengers from Uncertain Delayed High-Speed Railway Trains." Sustainability 14, no. 9 (May 9, 2022): 5718. http://dx.doi.org/10.3390/su14095718.

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This paper develops a multi-objective mixed-integer linear programming model for the problem of robust rescheduling for capacitated urban rail transit (URT) trains to serve passengers from delayed high-speed railway (HSR) trains. The capacity of each extra train is not assumed to be unlimited in this paper. Robust passenger assignment constraints are developed to ensure that delayed passengers can board the URT trains under different random delay scenarios of HSR operations. Robust dispatching constraints of URT trains are designed for a stable disrupting number of URT trains across different scenarios. The multi-objective model is used to maximize the number of expected transported passengers and minimize the number of extra trains and operation-ending time of all extra trains. An iterative solution approach based on a revised version of the epsilon-constraint method combined with the weighted-sum method is designed for the computation of the multi-objective model. Computational experiments are performed on the Beijing URT lines and the Beijing-Shanghai HSR line. We evaluate the impact of the robustness constraints of passenger assignment and the number of extra trains to ensure that the number of trains are maintained and the passengers can successfully take the trains during different delayed scenarios.

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Taha, Ahmed, Mauricio Patón, David R. Penas, Julio R. Banga, and Jorge Rodríguez. "Optimal evaluation of energy yield and driving force in microbial metabolic pathway variants." PLOS Computational Biology 19, no. 7 (July 6, 2023): e1011264. http://dx.doi.org/10.1371/journal.pcbi.1011264.

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This work presents a methodology to evaluate the bioenergetic feasibility of alternative metabolic pathways for a given microbial conversion, optimising their energy yield and driving forces as a function of the concentration of metabolic intermediates. The tool, based on thermodynamic principles and multi-objective optimisation, accounts for pathway variants in terms of different electron carriers, as well as energy conservation (proton translocating) reactions within the pathway. The method also accommodates other constraints, some of them non-linear, such as the balance of conserved moieties. The approach involves the transformation of the maximum energy yield problem into a multi-objective mixed-integer linear optimisation problem which is then subsequently solved using the epsilon-constraint method, highlighting the trade-off between yield and rate in metabolic reactions. The methodology is applied to analyse several pathway alternatives occurring during propionate oxidation in anaerobic fermentation processes, as well as to the reverse TCA cycle pathway occurring during autotrophic microbial CO2 fixation. The results obtained using the developed methodology match previously reported literature and bring about insights into the studied pathways.

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Villacrés, Ricardo, and Diego Carrión. "Optimizing Real and Reactive Power Dispatch Using a Multi-Objective Approach Combining the ϵ-Constraint Method and Fuzzy Satisfaction." Energies 16, no. 24 (December 13, 2023): 8034. http://dx.doi.org/10.3390/en16248034.

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Optimal power dispatch is essential to improve the power system’s safety, stability, and optimal operation. The present research proposes a multi-objective optimization methodology to solve the real and reactive power dispatch problem by minimizing the active power losses and generation costs based on mixed-integer nonlinear programming (MINLP) using the epsilon constraint method and fuzzy satisficing approach. The proposed methodology was tested on the IEEE 30-bus system, in which each objective function was modeled and simulated independently to verify the results with what is obtained via Digsilent Power Factory and then combined, which no longer allows for the simulation of Digsilent Power Factory. One of the main contributions was demonstrating that the proposed methodology is superior to the one available in Digsilent Power Factory, since this program only allows for the analysis of single-objective problems.

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Cao, Huizhuo, Xuemei Li, Vikrant Vaze, and Xueyan Li. "Multi-Objective Pricing Optimization for a High-Speed Rail Network Under Competition." Transportation Research Record: Journal of the Transportation Research Board 2673, no. 7 (April 17, 2019): 215–26. http://dx.doi.org/10.1177/0361198119842817.

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Multi-objective pricing of high-speed rail (HSR) passenger fares becomes a challenge when the HSR operator needs to deal with multiple conflicting objectives. Although many studies have tackled the challenge of calculating the optimal fares over railway networks, none of them focused on characterizing the trade-offs between multiple objectives under multi-modal competition. We formulate the multi-objective HSR fare optimization problem over a linear network by introducing the epsilon-constraint method within a bi-level programming model and develop an iterative algorithm to solve this model. This is the first HSR pricing study to use an epsilon-constraint methodology. We obtain two single-objective solutions and four multi-objective solutions and compare them on a variety of metrics. We also derive the Pareto frontier between the objectives of profit and passenger welfare to enable the operator to choose the best trade-off. Our results based on computational experiments with Beijing–Shanghai regional network provide several new insights. First, we find that small changes in fares can lead to a significant improvement in passenger welfare with no reduction in profitability under multi-objective optimization. Second, multi-objective optimization solutions show considerable improvements over the single-objective optimization solutions. Third, Pareto frontier enables decision-makers to make more informed decisions about choosing the best trade-offs. Overall, the explicit modeling of multiple objectives leads to better pricing solutions, which have the potential to guide pricing decisions for the HSR operators.

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Agnoletto, Elian J., Daniel Silva de Castro, Rodolpho V. A. Neves, Ricardo Quadros Machado, and Vilma A. Oliveira. "An Optimal Energy Management Technique Using the $\epsilon$ -Constraint Method for Grid-Tied and Stand-Alone Battery-Based Microgrids." IEEE Access 7 (2019): 165928–42. http://dx.doi.org/10.1109/access.2019.2954050.

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Felfel, Houssem, Omar Ayadi, and Faouzi Masmoudi. "Pareto Optimal Solution Selection for a Multi-Site Supply Chain Planning Problem Using the VIKOR and TOPSIS Methods." International Journal of Service Science, Management, Engineering, and Technology 8, no. 3 (July 2017): 21–39. http://dx.doi.org/10.4018/ijssmet.2017070102.

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In this paper, a multi-objective, multi-product, multi-period production and transportation planning problem in the context of a multi-site supply chain is proposed. The developed model attempts simultaneously to maximize the profit and to maximize the product quality level. The objective of this paper is to provide the decision maker with a front of Pareto optimal solutions and to help him to select the best Pareto solution. To do so, the epsilon-constraint method is adopted to generate the set of Pareto optimal solutions. Then, the technique for order preference by similarity to ideal solution (TOSIS) is used to choose the best compromise solution. The multi-criteria optimization and compromise solution (VIKOR), a commonly used method in multiple criteria analysis, is applied in order to evaluate the selected solutions using TOPSIS method. This paper offers a numerical example to illustrate the solution approach and to compare the obtained results using TOSIS and VIKOR methods.

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Dwijendra, Ngakan Ketut Acwin, Muhaned Zaidi, I. Gusti Ngurah Kerta Arsana, Samar Emad Izzat, Abduladheem Turki Jalil, Ming-Hung Lin, Untung Rahardja, Iskandar Muda, A. Heri Iswanto, and Surendar Aravindhan. "A Multi-Objective Optimization Approach of Smart Autonomous Electrical Grid with Active Consumers and Hydrogen Storage System." Environmental and Climate Technologies 26, no. 1 (January 1, 2022): 1067–79. http://dx.doi.org/10.2478/rtuect-2022-0080.

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Abstract In this paper, a multi objective optimization approach is studied for optimal energy scheduling of the smart autonomous electrical grid with participation of active consumers (ACs) and hydrogen storage system (HSS). The objective functions consist of: 1) minimizing the costs and 2) maximizing reliability. The ACs participation are modelled through demand reduction approach based on offer price to peak demand management. The proposed optimization is solved by epsilon-constraint method and LINMAP decision making strategy. The 21-node test system is employed to analyse the efficiency of the proposed approach at two case studies. The obtained results shown the high effectiveness of smart autonomous electrical grid with participation of ACs and HSS to supply the demand.

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Khalilzadeh, Mohammad, Sayyid Ali Banihashemi, and Darko Božanić. "A Step-By-Step Hybrid Approach Based on Multi-Criteria Decision-Making Methods And A Bi-Objective Optimization Model To Project Risk Management." Decision Making: Applications in Management and Engineering 7, no. 1 (January 10, 2024): 442–72. http://dx.doi.org/10.31181/dmame712024884.

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Project success and achieving project objectives and goals highly depend on effective and thorough risk management implementation. This study provides a comprehensive and practical methodology for project risk management. In this paper, firstly, the risks were collected by analyzing the historical documents and literature. Then, the collected risks were screened using brainstorming and categorized into five groups. Subsequently, a questionnaire was made and the identified risks were validated using the Fuzzy Delphi technique. Also, the relationships between risks were determined using the Interpretive Structural Modelling (ISM) method. Moreover, the weights of the criteria used to rank the risks were calculated through the Fuzzy Best-Worst Method. Subsequently, the major risks were determined using the fuzzy WASPAS method. Furthermore, a novel bi-objective mathematical programming model was developed and solved using the Augmented Epsilon-Constraint (AEC) method to choose the optimal risk response strategies for each critical risk. The results demonstrated that the proposed framework is effective in dealing with construction project risks.

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Vaisi, Bahareh, Hiwa Farughi, and Sadigh Raissi. "Schedule-Allocate and Robust Sequencing in Three-Machine Robotic Cell under Breakdowns." Mathematical Problems in Engineering 2020 (October 30, 2020): 1–24. http://dx.doi.org/10.1155/2020/4597827.

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The purpose of this paper is to model two problems comprising schedule-allocate (in case of producing identical parts) and sequencing of parts (in case of producing different parts). The first model is used for minimizing the cycle time and operational cost, and the second one for minimizing both the mean and standard deviation of the total production cost as well the cycle time, in an unreliable three-machine robotic cell which confronted with many uncertainty factors. In the current article, mathematical modelling and simulation-based optimization method have been presented to schedule-allocate similar parts and trace the optimal sequence of different parts. Several solution procedures, including epsilon-constraint method and multiobjective particle swarm optimization algorithm, for identical parts case and response surface methodology for different parts case are applied. The results derived from solving numerical examples revealed some advantages in terms of time to attain the optimal solution.

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Bıçakcı, İsmail, Yusuf Tansel İç, Esra Karasakal, and Berna Dengiz. "A Multi-Objective Mathematical Model for Level of Repair Analysis with Lead Times and Multi-Transportation Modes." International Journal of Information Technology & Decision Making 21, no. 01 (September 30, 2021): 423–40. http://dx.doi.org/10.1142/s0219622021500632.

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In the event of failure of the product, level of repair analysis (LORA) is used to determine (1) whether the defective component should be discarded or repaired and (2) where this repair is made. In the literature, these repair operations are made with the aim of minimizing the total life cycle cost of the product. In this paper, we develop a multi-objective decision model that minimizes both the repair time (affected by lead times) and the repair costs. Our proposed model also considers the movement of the defective components to be performed by multiple transportation modes such as highway, railway, and airway. We use the epsilon constraint method to generate the Pareto frontier and analyze the trade-off between total repair costs and total repair time. We demonstrate the approach on an example problem.

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Dwijendra, Ngakan Ketut Acwin, Wongchai Anupong, Ahmed Majed Althahabi, Sabah Auda Abdulameer, Waleed Khalid Al-Azzawi, Mustafa Musa Jaber, Musaddak Maher Abdul Zahra, and Zuhair I. Al Mashhadani. "Optimal Dispatch of the Energy Demand in Electrical Distribution Grid with Reserve Scheduling." Environmental and Climate Technologies 27, no. 1 (January 1, 2023): 80–91. http://dx.doi.org/10.2478/rtuect-2023-0007.

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Abstract The operation of the electrical systems is a major problem for electrical companies’ subject to uncertainties threatening. In this study, the optimal management of the energy demand in the electrical distribution grid is done by interval optimization approach under electrical price uncertainty. The management of the energy demand is implemented via incentive-based modelling of the demand response programs (DRPs). The incentive-based modelling as reserve, and based on bid price for reduction of the electrical demand at peak hours is proposed. The interval optimization approach is used for the minimization of the electrical price uncertainty effects. The main objective in the proposed approach is minimizing operation cost; epsilon-constraint method is utilized to solve the problem. Finally, an electrical distribution grid has been used at various case studies to numerical simulation results and positive effects of the proposed modelling under uncertainties.

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Li, Jiajia, Kaifeng Duan, Quanwei Xu, Xuefei Sun, Yanwei Zhang, and Changhua Hua. "Efficiency of tourism development in China’s major cities under the constraint of PM2.5." PLOS ONE 16, no. 8 (August 11, 2021): e0255508. http://dx.doi.org/10.1371/journal.pone.0255508.

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Climate / weather factors are important factors for tourists to choose tourist destinations. With the public’s attention to the influence of haze, air quality will have a profound impact on the development of tourism in tourist destinations. Based on the Epsilon-based Measure (EBM) super-efficiency model and Global Malmquist–Luenberger index analysis method, this paper aims to study the tourism development efficiency of 58 major cities in China from 2001 to 2016 and analyse the total factor productivity in the development of urban tourism and the changing driving factors in consideration of the undesirable output of haze characterised by PM2.5 emission concentration. The study findings show that the overall efficiency of tourism development of 58 cities is not high in 2001–2016, but the tourism development efficiency of all cities is increasing year by year. Under the constraint of haze, the efficiency of urban tourism development is not directly proportional to the degree of urban development. The overall redundancy rate of each input index is slightly high, and the redundancy of PM2.5 emission concentration has a considerable effect on the efficiency of urban tourism development. The overall change trend in total factor productivity in the development of urban tourism is improved, mainly due to the improvement of technological progress factors. On this basis, the corresponding policy implications are concluded according to high-efficiency and high-quality development of tourism in 58 major cities.

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Praneetpholkrang, Panchalee, and Sarunya Kanjanawattana. "A Novel Approach for Determining Shelter Location-Allocation in Humanitarian Relief Logistics." International Journal of Knowledge and Systems Science 12, no. 2 (April 2021): 52–68. http://dx.doi.org/10.4018/ijkss.2021040104.

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This study proposes a methodology that integrates the epsilon constraint method (EC) and artificial neural network (ANN) to determine shelter location-allocation. Since shelter location-allocation is a critical part of disaster response stage, fast decision-making is very important. A multi-objective optimization model is formulated to simultaneously minimize total cost and minimize total evacuation time. The proposed model is solved by EC because it generates the optimal solutions without intervention of decision-makers during the solution process. However, EC requires intensive computational time, especially when dealing with large-scale data. Thus, ANN is combined with EC to facilitate prompt decision-making and address the complexity. Herein, ANN is supervised by the optimal solutions generated by EC. The applicability of the proposed methodology is demonstrated through a case study of shelter allocation in response to flooding in Surat Thani, Thailand. It is plausible to use this proposed methodology to improve disaster response for the benefit of victims and decision-makers.

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Mavalizadeh, Hani, Abdollah Ahmadi, and H. A. Shayanfar. "Corrigendum to “Hybrid expansion planning considering security and emission by augmented epsilon-constraint method” [Int. J. Electr. Power Energy Syst. 61 (2014) 90–100]." International Journal of Electrical Power & Energy Systems 83 (December 2016): 601. http://dx.doi.org/10.1016/j.ijepes.2016.06.009.

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Nouri, Alireza, Hossein Khodaei, Ayda Darvishan, Seyedmehdi Sharifian, and Noradin Ghadimi. "RETRACTED: Optimal performance of fuel cell-CHP-battery based micro-grid under real-time energy management: An epsilon constraint method and fuzzy satisfying approach." Energy 159 (September 2018): 121–33. http://dx.doi.org/10.1016/j.energy.2018.06.141.

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Arab Momeni, Mojtaba, Vipul Jain, and Mehdi Bagheri. "A Multi-Objective Model for Designing a Sustainable Closed-Loop Supply Chain Logistics Network." Logistics 8, no. 1 (March 13, 2024): 29. http://dx.doi.org/10.3390/logistics8010029.

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Background: The growing concern for environmental and social issues has led to a focus on designing sustainable supply chains and increasing industrial responsibility towards society. In this paper, a multi-objective mixed-integer programming model is presented for designing a sustainable closed-loop supply chain. The model is aimed at the minimization of the total cost with the total used facilities, the negative environmental impacts, and the maximization of the positive social impacts. Methods: The epsilon-constraint method is utilized for solving the model and further extracting the Pareto solutions. Results: The result of the research clearly shows an optimal trade-off between the conflicting objectives, where, by paying more attention to the social and environmental aspects of sustainability, the total costs are increased or by optimizing the number of facilities, a better balance between the dynamics associated with the short-term and long-term goals is reached. The results of the sensitivity analysis also show that increasing the demand of the supply chain has the greatest impact on the supply chain costs compared to other objectives. Conclusions: Consequently, investigating such comprehensive sustainable objectives provides better insights into the impact of design variables on the expectations of stakeholders.

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Daoud, Malika. "Role of combinatorial optimization problems for the efficient decision making of a company- Case study-." les cahiers du cread 39, no. 3 (February 10, 2024): 275–301. http://dx.doi.org/10.4314/cread.v39i3.11.

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All company seeks to improve their performance through achieving several objectives to stay in the labor market and increase competitiveness. The problem lies in the fact that it often relies on traditional methods for efficient decision-making, causing a waste of time and effort. The paper aims to find the best car service stations among several proposed stations by the Naftal Company, which seeks to achieve the two most important objectives; maximizing lubricants and tires revenues, and maximizing fuel and LPG revenues for the year 2019. The new applied case study was done with the help of the binary multi-objective knapsack problem, which is considered one of the most important problems in multi-objective combinatorial optimization problems. The problem was solved by the epsilon constraint method using MATLAB and CPLEX software. The study results confirmed that the proposed efficient solution set (Pareto optimal solutions) provides the decision maker with a comprehensive view of how to make their decision in a scientific, thoughtful, logical, and convincing manner that suits his situation and puts him at ease, away from trial and error or relying on self-experience.

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Arango González, Daniela S., Elias Olivares-Benitez, and Pablo A. Miranda. "Insular Biobjective Routing with Environmental Considerations for a Solid Waste Collection System in Southern Chile." Advances in Operations Research 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/4093689.

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This paper presents a biobjective problem for a solid waste collection system in a set of islands in southern Chile. The first objective minimizes transportation cost and the second one reduces the environmental impact caused by the accumulation of solid waste at the collection points. To solve this problem, biobjective mixed integer linear programming is used. In the model, an itinerary scheme is considered for the visit to the islands. The model decides which collection points are visited per island, the collection pattern, and quantity of solid waste to be collected at each site. The quantity of solid waste is obtained dividing the solid waste generated in the island by the number of collection points selected in that same island and the frequency of visits. For this problem, we considered that the environmental impact function varies through the days during which solid waste is accumulated at each collection point. We present an instance based on real data for a set of islands in Chiloe and Palena regions in southern Chile, in which the deposit node is Dalcahue. We used the epsilon-constraint method and the weighted sum method to obtain the Pareto front, using commercial optimization software.

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Shafiee Moghadam, Shayan, Amir Aghsami, and Masoud Rabbani. "A hybrid NSGA-II algorithm for the closed-loop supply chain network design in e-commerce." RAIRO - Operations Research 55, no. 3 (May 2021): 1643–74. http://dx.doi.org/10.1051/ro/2021068.

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Designing the supply chain network is one of the significant areas in e-commerce business management. This concept plays a crucial role in e-commerce systems. For example, location-inventory-pricing-routing of an e-commerce supply chain is considered a crucial issue in this field. This field established many severe challenges in the modern world, like maintaining the supply chain for returned items, preserving customers’ trust and satisfaction, and developing an applicable supply chain with cost considerations. The research proposes a multi-objective mixed integer nonlinear programming model to design a closed-loop supply chain network based on the e-commerce context. The proposed model incorporates two objectives that optimize the business’s total profits and the customers’ satisfaction. Then, numerous numerical examples are generated and solved using the epsilon constraint method in GAMS optimization software. The validation of the given model has been tested for the large problems via a hybrid two-level non-dominated sort genetic algorithm. Finally, some sensitivity analysis has been performed to provide some managerial insights.

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Nadeem, Diallo, Nguyen-Quang, Venkatadri, and Havard. "Optimizing a Bi-Objective Mathematical Model for Minimizing Spraying Time and Drift Proportion." AgriEngineering 1, no. 3 (August 12, 2019): 418–33. http://dx.doi.org/10.3390/agriengineering1030031.

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The global agriculture sector faces many challenges in its mission to meet the increasing demand for food and fiber. Climate change, increasing population growth, emergence of crop diseases, damage to crops from rodents and critters, and shrinking farming land in some regions are among these challenges. Application of agrochemicals has proven to be an efficient answer to some of these challenges. However, the impacts of these products on human health and the environment combined with the increased requirement for sustainable farming requires the development of optimal spraying practices that would balance out all interests and concerns. In this paper, a mathematical model is developed to jointly minimize spraying time and drift losses. The obtained bi-objective mixed integer nonlinear programming model is solved for a case study example published in the crop protection literature. Optimal solutions are obtained using the weighted sum method and the epsilon-constraint approach. The results showed that valid and reasonable solutions can be obtained by selecting the appropriate combination of boom height, nozzle spacing, nozzle type, and tractor travel speed. Useful insights are obtained through various computational experiments.

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Dastani, Mehdi, Sayyed Mohammad Reza Davoodi, Mehdi Karbassian, and Shahram Moeini. "Developing a Mathematical Model for a Green Closed-Loop Supply Chain with a Multi-Objective Gray Wolf Optimization Algorithm." Foundations of Computing and Decision Sciences 47, no. 2 (June 1, 2022): 127–50. http://dx.doi.org/10.2478/fcds-2022-0007.

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Abstract Intense competition in today’s market and quick change in customer preferences, along with the rapid development of technology and globalization, have forced companies to work as members of a supply chain instead of individual companies. The success of the supply chain depends on the integration and coordination of all its institutions to form an efficient network structure. An efficient network leads to cost savings throughout the supply chain and helps it respond to customer needs faster. Accordingly, and with respect to the importance of the supply chain, in this study a developed mathematical model for the design of a green closed-loop supply chain is presented. In this mathematical model, the economic and environmental objectives are simultaneously optimized. In order to tackle this mathematical model, two methods of epsilon constraint and multi-objective gray wolf optimization (MOGWO) algorithm have been applied. The results of comparisons between the two mentioned methods show that MOGWO reduce the average solving time from about 1300 seconds to 88 seconds. In the last step of this research, in order to show the application of the proposed mathematical model and the method of solving the research problem, it was implemented in the supply chain of Dalan Kouh diary product and the Pareto optimal solutions were analyzed.

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Soon, Amirhossein, Ali Heidari, Mohammad Khalilzadeh, Jurgita Antucheviciene, Edmundas Kazimieras Zavadskas, and Farbod Zahedi. "Multi-Objective Sustainable Closed-Loop Supply Chain Network Design Considering Multiple Products with Different Quality Levels." Systems 10, no. 4 (July 2, 2022): 94. http://dx.doi.org/10.3390/systems10040094.

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International laws and increasing consumer awareness have led to drastic changes in traditional supply chain network designs. Moreover, because of environmental and social requirements, traditional supply chain networks have changed to sustainable supply chain networks. On the other hand, reverse logistics can be effective in terms of environmental and economic aspects, so the design of the supply chain network as a closed loop is necessary. In addition, customers have a demand for different products with different quality levels. Considering different types of customers with a variety of consumption trends can be a challenging issue, and is addressed in this study. The main contributions of this research are considering different quality levels for products as well as different tendencies of customers towards environmental issues. In this study, a sustainable closed-loop supply chain model is designed that seeks to balance economic, environmental, and social responsibilities. In this paper, costs and customer demands for different types of products at different quality levels are considered under uncertain conditions using a robust possibilistic programming method. The proposed multi-objective model is solved using the Augmented Epsilon Constraint (AEC) method that provides an efficient set of solutions for all decision-making levels. The results show that the robust possibilistic programming method is more effective in dealing with uncertainties than the possibilistic programming method.

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Majumder, Saibal, Partha Sarathi Barma, Arindam Biswas, Pradip Banerjee, Bijoy Kumar Mandal, Samarjit Kar, and Paweł Ziemba. "On Multi-Objective Minimum Spanning Tree Problem under Uncertain Paradigm." Symmetry 14, no. 1 (January 8, 2022): 106. http://dx.doi.org/10.3390/sym14010106.

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Minimum spanning tree problem (MSTP) has allured many researchers and practitioners due to its varied range of applications in real world scenarios. Modelling these applications involves the incorporation of indeterminate phenomena based on their subjective estimations. Such phenomena can be represented rationally using uncertainty theory. Being a more realistic variant of MSTP, in this article, based on the principles of the uncertainty theory, we have studied a multi-objective minimum spanning tree problem (MMSTP) with indeterminate problem parameters. Subsequently, two uncertain programming models of the proposed uncertain multi-objective minimum spanning tree problem (UMMSTP) are developed and their corresponding crisp equivalence models are investigated, and eventually solved using a classical multi-objective solution technique, the epsilon-constraint method. Additionally, two multi-objective evolutionary algorithms (MOEAs), non-dominated sorting genetic algorithm II (NSGAII) and duplicate elimination non-dominated sorting evolutionary algorithm (DENSEA) are also employed as solution methodologies. With the help of the proposed UMMSTP models, the practical problem of optimizing the distribution of petroleum products was solved, consisting in the search for symmetry (balance) between the transportation cost and the transportation time. Thereafter, the performance of the MOEAs is analyzed on five randomly developed instances of the proposed problem.

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Cao, Zhichao, Yuqing Wang, Zihao Yang, Changjun Chen, and Silin Zhang. "Timetable Rescheduling Using Skip-Stop Strategy for Sustainable Urban Rail Transit." Sustainability 15, no. 19 (October 5, 2023): 14511. http://dx.doi.org/10.3390/su151914511.

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Unanticipated events inevitably occur in daily urban rail transit operations, disturbing the scheduled timetable. Despite the mild delay, the busy operation system probably tends to worsen a larger disturbance and even lead to a knock-on disruption if no rescheduling is timely carried out. We propose a bi-objective mixed-integer linear programming model (MILP) that employs the skip-stop operation strategy to eliminate unscheduled delays. This model addresses two distinct, yet interconnected objectives. Firstly, it aims to minimize the difference between the plan and the actual operation. Secondly, it strives to minimize the number of left-behind passengers. In order to resolve this MILP problem, we devised a Pareto-based genetic algorithm (GA). Based on the case study, we certify the superior effectiveness with comparisons to the whale optimization algorithm and the epsilon constraint method. The outcomes affirm that our model has the potential to reduce the total delay time of the line by 44.52% at most compared with the traditional all-stop running adjustment model. The optimal scheme saved 6.08% of the total costs based on a trade-off between operators’ interests and passenger satisfaction.

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Keshavarz Ziarani, Hasan, Seyed Hossein Hosseinian, and Ahmad Fakharian. "Providing a New Multiobjective Two-Layer Approach for Developing Service Restoration of a Smart Distribution System by Islanding of Faulty Area." International Transactions on Electrical Energy Systems 2024 (January 2, 2024): 1–14. http://dx.doi.org/10.1155/2024/9687002.

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One of the essential capabilities of a smart distribution network is to improve network restoration performance using the postfault islanding method. Islanding of the faulty area can be done offline and online. Online islanding will decrease load shedding and operation cost. In this study, a novel two-step mathematical method for system restoration after the fault is presented. A new mathematical model for the optimal arrangement of the system for the faulty area in the first layer is proposed. In this layer, the main objective is to decrease the distribution system’s load shedding and operational costs. In this regard, after the fault event, the boundary of the islanded MGs is determined. Then, in the second layer, the problem of unit commitment in the smart distribution network is addressed. In addition to the load shedding, optimal planning of energy storage systems (ESSs) and nondispatchable distributed generation (DG) resource rescheduling are also determined in this layer. The important advantages of the proposed approach are low execution time and operational costs. A demand response (DR) program has also been used for optimal system restoration. Solving the problem using the multiobjective method with the epsilon-constraint method is another goal of the paper, which simultaneously minimizes the cost and the emissions of the smart distribution network. The proposed model has been tested on an IEEE 33-bus system. Better performance of the proposed model compared to the techniques in the literature has been proven.

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Liu, Xuemin, Guozhong Huang, Shengnan Ou, Xingyu Xiao, Xuehong Gao, Zhangzhou Meng, Youqiang Pan, and Ibrahim M. Hezam. "Biobjective Optimization Model Considering Risk and Profit for the Multienterprise Layout Design in Village-Level Industrial Parks in China." Sustainability 15, no. 4 (February 16, 2023): 3623. http://dx.doi.org/10.3390/su15043623.

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With the advent and development of Industry 4.0 and 5.0, manufacturing modes have changed and numerous newly complicated and integrated village-level industrial parks have emerged in the Southeast of China, where several enterprises are gathered in the same multistory building. The number of floors and surrounding enterprises can have an impact on accident risk. To reduce the overall risk level of industrial parks, the layout of enterprises with different risks needs to be well designed and optimized. However, to date, limited studies have been conducted to emphatically consider safety and optimize the enterprise layout at an industrial area level, and most studies focus on the cost of the layout. Therefore, this study proposed three biobjective mathematical optimization models to obtain the trade-off between minimizing risk and maximizing rental profit. Risk factors include the enterprise location and the association risk; the enterprise inherent safety risks are not considered. To solve this problem, a specific linearization strategy was proposed and an epsilon-constraint method was applied to obtain Pareto-optimal solutions. Subsequently, an industrial park in Shunde, China, was considered as a case study to verify the performance of the proposed models and methods. Finally, a sensitivity analysis of critical parameters was conducted. The critical factors influencing the objective functions were also analyzed to provide valuable managerial insights.

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Lu, Hanyu, and Lufei Huang. "Optimization of Shore Power Deployment in Green Ports Considering Government Subsidies." Sustainability 13, no. 4 (February 3, 2021): 1640. http://dx.doi.org/10.3390/su13041640.

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Shipping trade and port operations are two of the primary sources of greenhouse gas emissions. The emission of air pollutants brings severe problems to the marine environment and coastal residents’ lives. Shore power technology is an efficient CO2 emission reduction program, but it faces sizeable initial investment and high electricity prices. For shipping companies, energy such as low-sulfur fuels and liquefied natural gas has become an essential supplementary means to meet emission reduction requirements. This research considers the impact of government subsidies on port shore power construction and ship shore power use. It constructs a multi-period dual-objective port shore power deployment optimization model based on minimizing operating costs and minimizing CO2 emissions. Multi-combination subsidy strategies, including unit subsidy rate and subsidy demarcation line, are quantitatively described and measured. The proposed Epsilon constraint method is used to transform and model the dual-objective optimization problem. Numerical experiments verify the effectiveness of the model and the feasibility of the solution method. By carrying out a “cost-environment” Pareto trade-off analysis, a model multi-period change analysis, and a subsidy efficiency analysis, this research compares the decision-making results of port shore power construction, ship berthing shore power use, and ship berthing energy selection. Government subsidy strategy and operation management enlightenment in the optimization of port shore power deployment are discussed.

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Journal articles on the topic 'Epsilon constraint method'

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