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On the structure of multiobjective combinatorial search space: MNK-landscapes with correlated objectives

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2013年第2期227卷 331-342页

作者： Verel, Sebastien Liefooghe, Arnaud Jourdan, Laetitia Dhaenens, Clarisse Univ Nice Sophia Antipolis CNRS I3S F-06903 Sophia Antipolis France Univ Lille 1 LIFL CNRS F-59655 Villeneuve Dascq France INRIA Lille N Europe F-59655 Villeneuve Dascq France

The structure of the search space explains the behavior of multiobjective search algorithms, and helps to design well-performing approaches. In this work, we analyze the properties of multiobjective combinatorial search spaces, and we pay a particular attention to the correlation between the objective functions. To do so, we extend the multiobjective NK-landscapes in order to take the objective correlation into account. We study the co-influence of the problem dimension, the degree of non-linearity, the number of objectives, and the objective correlation on the structure of the Pareto optimal set, in terms of cardinality and number of supported solutions, as well as on the number of Pareto local optima. This work concludes with guidelines for the design of multiobjective local search algorithms, based on the main fitness landscape features. (C) 2012 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Combinatorial optimization Local search Fitness landscape analysis Pareto optimal set Pareto local optima

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An additive achievement scalarizing function for multiobjective programming problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2008年第3期188卷 683-694页

作者： Ruiz, Francisco Luque, Mariano Miguel, Francisca del Mar Munoz, Maria Univ Malaga Dept Appl Econ Math E-29071 Malaga Spain

The success of the reference point scheme within interactive techniques for multiobjective programming problems is unquestionable. However, so far, the different achievement scalarizing functions are, more or less, extensions of the Tchebychev distance. The reason for this is the ability of this function to determine efficient solutions and to support every efficient solution of the problem. For the same reasons, no additive scheme has yet been used in reference point-based interactive methods. In this paper, an additive achievement scalarizing function is proposed. Theoretical results prove that this function supports every efficient solution, and conditions are given under which the efficiency of each solution is guaranteed. Some examples and computational tests show the different behaviours of the Tchebychev and additive approaches, and an additive reference point interactive algorithm is proposed. (C) 2007 Elsevier B.V. All rights reserved.

关键词： multiple objective programming achievement scalarizing functions interactive methods

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Graphical exploration of the weight space in three-objective mixed integer linear programs

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2016年第1期248卷 72-83页

作者： Alves, Maria Joao Costa, Joao Paulo Univ Coimbra INESC Coimbra Fac Econ P-3000 Coimbra Portugal

In this paper we address the computation of indifference regions in the weight space for multiobjective integer and mixed-integer linear programming problems and the graphical exploration of this type of information for three-objective problems. We present a procedure to compute a subset of the indifference region associated with a supported nondominated solution obtained by the weighted-sum scalarization. Based on the properties of these regions and their graphical representation for problems with up to three objective functions, we propose an algorithm to compute all extreme supported nondominated solutions adjacent to a given solution and another one to compute all extreme supported nondominated solutions to a three-objective problem. The latter is suitable to characterize solutions in delimited nondominated areas or to be used as a final exploration phase. A computer implementation is also presented. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.

关键词： multiple objective programming Mixed integer linear programming Weighted-sum scalarization Weight space Extreme supported nondominated solutions

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A multi-objective decision model for investment in energy savings and emission reductions in coal mining

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第1期260卷 335-347页

作者： Yu, Shiwei Zheng, Shuhong Gao, Shiwei Yang, Juan China Univ Geosci Sch Econ & Management Wuhan 430074 Peoples R China Eastern Kentucky Univ Dept Accounting Finance & Informat Syst Richmond KY 40475 USA Shandong Inst Business & Technol Sch Management Sci & Engn Yantai 264005 Peoples R China

Coal-mining companies should clearly be investing in energy savings and treatment technologies aimed at reducing both their energy consumption and their pollution levels in order to meet the requirements of government regulations relating to environmental protection;however, when considering the types of technical equipment to use and the timing of their investment, these companies also need to consider their profits and the costs of such investment. We therefore propose a "multi-objective mixed integer non-linear programming" (MMINLP) model of investment in energy savings and emission reductions designed to handle this type of decision-making problem. Given three objectives (maximum profits, minimal energy consumption and minimal pollution), we develop a hybrid mixed-coding "particle swarm optimization and multi-objective non-dominated sorting genetic algorithm-II" (PSO-NSGA-II) to optimize the continuous and discrete decision variables as a means of helping companies to reach the optimum decision. We also integrate the subtractive clustering-multi-criteria tournament decision-gain analysis method (SC-MTD-GAM) to select the best trade-off solutions on the optimal Pareto fronts. Finally, we carry out a case study of investment decisions on energy savings and emission reductions in the Zhenzhou Coal Industry (Group) Co., Ltd., China, with the results revealing that the proposed model can support decision making for energy savings and emission reductions in coal mining areas. As compared with the NSGA-II and "non-dominated sorting particle swarm optimization" (NSPSO) algorithms, the proposed PSO-NSGA-II is found to have better convergence, coverage and uniformity. (C) 2016 Elsevier B.V. All rights reserved.

关键词： multiple objective programming PSO-NSGA-II Investment decision making Coal mining

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Quality recovering of university timetables

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第2期276卷 422-435页

作者： Lindahl, Michael Stidsen, Thomas Sorensen, Matias Tech Univ Denmark Dept Management Engn Lyngby Denmark MaCom AS Copenhagen Denmark

At universities, the timetable plays a large role in the daily life of students and staff, showing when and where lectures are given. But whenever a schedule is executed in a dynamic environment, disruptions will occur. It is then desirable to find a new timetable similar to the old one, so only a few people will be affected. This leads to a minimum perturbation problem, where the goal is to find a feasible timetable by changing as few assignments as possible. This solution will, however, often lead to timetables of low quality as it can have many undesired features that will cause much inconvenience for effected parties. In this paper we show that minimum perturbation solutions often have low quality and how using additional perturbations results in timetables with significantly higher quality while still keeping the number of perturbations low, so the solutions can be practically implemented. We formulate a bi-objective model and propose a method to solve it by using mixed integer programming. We test the method on standard instances of the Curriculum-based Course Timetabling Problem with four different types of disruptions. The use of bi-objective optimization enables us to generate multiple solutions whereby we provide the decision makers with multiple choices for handling the disruption. This allows the decision makers to determine the best trade-off between the number of perturbations and the quality, ultimately leading to better timetables for students and staff when disruptions occur. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Timetabling Disruptions multiple objective programming Minimum perturbation Integer programming

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Finding preferre d solutions under weighte d Tchebycheff preference functions for multi-objective integer programs

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第1期308卷 215-228页

作者： Karakaya, G. Koksalan, M. Middle East Tech Univ Dept Business Adm TR-06800 Ankara Turkiye Univ Michigan Ross Sch Business Ann Arbor MI 48109 USA Middle East Tech Univ Dept Ind Engn TR-06800 Ankara Turkiye

Many interactive approaches in multi-objective optimization assume the existence of an underlying pref-erence function that represents the preferences of a decision maker (DM). In this paper, we develop the theory and an exact algorithm that guarantees finding the most preferred solution of a DM whose pref-erences are consistent with a Tchebycheff function for multi-objective integer programs. The algorithm occasionally presents pairs of solutions to the DM and asks which one is preferred. It utilizes the prefer-ence information together with the properties of the Tchebycheff function to generate solutions that are candidates to be the most preferred solution. We test the performance of the algorithm on a set of three and four-objective combinatorial optimization problems.(c) 2022 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Tchebycheff function Interactive approach Preferred solution

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Multi-objective optimization of two-echelon vehicle routing problem: Vaccines distribution as a case study

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COMPUTERS & INDUSTRIAL ENGINEERING 2024年 187卷

作者： Al Theeb, Nader Abu-Aleqa, Mohammed Diabat, Ali Jordan Univ Sci & Technol Dept Ind Engn Irbid 22110 Jordan New York Univ Abu Dhabi Div Engn Abu Dhabi 129188 Saadiyat Isl U Arab Emirates NYU Tandon Sch Engn Dept Civil & Urban Engn Brooklyn NY 11201 USA

During pandemics, the efficiency of the vaccine supply chain may be compromised, especially the last-mile distribution, due to poor infrastructure that is unable to support the urgent need for vaccination. In developing countries, this becomes even more challenging due to limited vehicles, road conditions, and inadequate cold storage. Since it is impractical to construct permanent warehouses when pandemics occur, vaccine distribution would be extravagant both environmentally and financially. In this study, a new multi-objective MILP model combining two-echelon vehicle routing problem (2E-VRP) and vaccine supply chain (VSC) is presented to minimize the number of unsatisfied doses undelivered to customers. A heuristic solution based on the greedy random search is proposed to solve the model, as it is classified as NP-hard model. The model is solved using the commercial solver CPLEX for different datasets. Then the heuristic is used to solve the same datasets, and the results are compared based on the solution's quality and computation efforts. Moreover, Pareto fronts were constructed to demonstrate the trade-offs between the conflicting objective functions. Finally, a real case study is solved using the proposed model to demonstrate its effectiveness compared to the original VRP, and the results showed an improvement of average 11.97% in the number of doses delivered.

关键词： multiple objective programming Two-echelon vehicle routing problem Vaccine distribution

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A multi-objective integrated facility location-hardening model: Analyzing the pre- and post-disruption tradeoff

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2014年第1期237卷 257-270页

作者： Medal, Hugh R. Pohl, Edward A. Rossetti, Manuel D. Mississippi State Univ Dept Ind & Syst Engn Starkville MS 39762 USA Univ Arkansas Dept Ind Engn Fayetteville AR 72701 USA

Two methods of reducing the risk of disruptions to distribution systems are (1) strategically locating facilities to mitigate against disruptions and (2) hardening facilities. These two activities have been treated separately in most of the academic literature. This article integrates facility location and facility hardening decisions by studying the minimax facility location and hardening problem (MFLHP), which seeks to minimize the maximum distance from a demand point to its closest located facility after facility disruptions. The formulation assumes that the decision maker is risk averse and thus interested in mitigating against the facility disruption scenario with the largest consequence, an objective that is appropriate for modeling facility interdiction. By taking advantage of the MELHP's structure, a natural three-stage formulation is reformulated as a single-stage mixed-integer program (MIP). Rather than solving the MIP directly, the MFLHP can be decomposed into sub-problems and solved using a binary search algorithm. This binary search algorithm is the basis for a multi-objective algorithm, which computes the Pareto-efficient set for the pre- and post-disruption maximum distance. The multi-objective algorithm is illustrated in a numerical example, and experimental results are presented that analyze the tradeoff between objectives. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Location Interdiction multiple objective programming Catastrophe planning and management Discrete optimization

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Min-ordering and max-ordering scalarization methods for multi-objective robust optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第2期275卷 446-459页

作者： Schmidt, M. Schoebel, Anita Thom, Lisa Erasmus Univ Rotterdam Sch Management Dept Technol & Operat Management POB 1738 NL-3000 DR Rotterdam Netherlands Univ Gottingen Inst Numer & Angew Math Lotzestr 16-18 D-37083 Gottingen Germany

Several robustness concepts for multi-objective uncertain optimization have been developed during the last years, but not many solution methods. In this paper we introduce two methods to find min-max robust efficient solutions based on scalarizations: the min-ordering and the max-ordering method. We show that all point-based min-max robust weakly efficient solutions can be found with the max-ordering method and that the min-ordering method finds set-based min-max robust weakly efficient solutions, some of which cannot be found with formerly developed scalarization based methods. We then show how the scalarized problems may be approached for multi-objective uncertain combinatorial optimization problems with special uncertainty sets. We develop compact mixed-integer linear programming formulations for multi-objective extensions of bounded uncertainty (also known as budgeted or Gamma-uncertainty). For interval uncertainty, we show that the resulting problems reduce to well-known single-objective problems. (C) 2018 The Authors. Published by Elsevier B.V.

关键词： multiple objective programming Robust optimization Multi-objective robust optimization Combinatorial optimization Scalarization

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A new algorithm for linearly constrained c-convex vector optimization with a supply chain network risk application

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第2期247卷 359-365页

作者： Qu, Shaojian Goh, Mark Ji, Ying De Souza, Robert Shanghai Univ Sci & Technol Sch Business Shanghai 200093 Peoples R China Harbin Inst Technol Ctr Nat Sci Harbin Heilongjiang Peoples R China Natl Univ Singapore Logist Inst Asia Pacific Singapore 117548 Singapore Natl Univ Singapore NUS Business Sch Singapore 117548 Singapore

We study a class of vector optimization problems with a C-convex objective function under linear constraints. We extend the proximal point algorithm used in scalar optimization to vector optimization. We analyze both the global and local convergence results for the new algorithm. We then apply the proximal point algorithm to a supply chain network risk management problem under bi-criteria considerations. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.

关键词： multiple objective programming Pareto optimum C-convex Proximal point algorithm Supply chain network risk management

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