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Connections between multiple-objective programming and weight restricted data envelopment analysis: The role of the ordering cone

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2025年第2期323卷 571-582页

作者： Korhonen, Pekka Soleimani-damaneh, Majid Wallenius, Jyrki Aalto Univ Sch Business POB 11000 Aalto 00076 Finland Univ Tehran Coll Sci Sch Math Stat & Comp ICOL Ind & Computat Optimizat Lab Tehran Iran

This paper explores some new, important and interesting connections between multiple-objective programming (MOP) and Data Envelopment Analysis (DEA). We show that imposing weight restrictions in DEA corresponds to changing the ordering cone in MOP in a specific way. The new ordering cone is constructed and its properties are proved, providing useful insights about the connections between MOP and DEA. After providing several theoretical results, we illustrate them on a real-world data set. In addition to their theoretical appeal, our results hold significant practical importance for several reasons which are addressed in the paper.

关键词： Data envelopment analysis (DEA) multiple-objective programming Weight restrictions Pareto solution Ordering cone Decision models

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Urban dynamics and multiple-objective programming: A case study of Beijing

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2008年第9期13卷 1998-2017页

作者： Yuan, X. H. Ji, Xi Chen, H. Chen, B. Chen, G. Q. Peking Univ Dept Engn Sci & Mech Natl Lab Complex Syst & Turbulence Beijing 100871 Peoples R China Peking Univ Coll Environm Sci Beijing 100871 Peoples R China Beijing Normal Univ Sch Environm State Key Lab Environm Simulat & Pollut Contol Beijing 100875 Peoples R China

This study serves as a primary application of the integrated system dynamics and multiple-objective programming (ISDMOP) model for strategic planning of Beijing city, which is here divided into six subsystems as population, resources, energy, economy, environment and ecosystem, with the planning horizon spanning from 2003 to 2020. Comparison between the original system dynamics (ORSD) model based on the existing economic structure of Beijing and the optimized system dynamics (OPSD) model adjusted according to the solutions of the multiple-objective programming (MOP) are conducted. The developing trend of each subsystem is simulated and illuminated, based on which constructive suggestions are provided for urban strategic planning of Beijing. The ISDMOP model is proved effective for investigating urban dynamics and realizing the multiple-objective programming. (C) 2007 Elsevier B.V. All rights reserved.

关键词： urban dynamics strategic planning multiple-objective programming

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Equivalence of balance points and Pareto solutions in multiple-objective programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1997年第1期92卷 209-212页

作者： Ehrgott, M Hamacher, HW Klamroth, K Nickel, S Schobel, A Wiecek, MM PhD Student Fachbereich Mathetnatik Universitat Kaiserslautern Kaiserslautern Germany Professor Fachbereich Mathematik Universitat Kaiserslautern Kaiserslautern Germany PhD Fachbereich Mathematik Universitat Kaiserslautern Kaiserslautern Germany PhD Fachbereich Mathematik Universitat Kaiserslautern Kaiserslautern Germany PhD Student Fachbereich Mathematik Universitat Kaiserslautern Kaiserslautern Germany Professor Fachbereich Mathematik Universitat Kaiserslautern Germany on sabbatical leave from the Department of Mathematical Sciences Clemson University Clemson South Carolina

It is shown that the concept of balance points introduced by Galperin (Ref. 1) is equivalent to the concept of Pareto optimality.

关键词： multiple-objective programming balance points balance set Pareto optimality efficient points level sets level curves

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A LINEAR-APPROXIMATION FOR CHANCE-CONSTRAINED programming

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 1987年第3期38卷 261-267页

作者： OLSON, DL SWENSETH, SR TEXAS A&M UNIV DEPT BUSINESS ANALCOLLEGE STNTX 77843 USA

Decision environments involve the need to solve problems with varying degrees of uncertainty as well as multiple, potentially conflicting objectives. Chance constraints consider the uncertainty encountered. Codes incorporating chance constraints into a mathematical programming model are not available on a widespread basis owing to the non-linear form of the chance constraints. Therefore, accurate linear approximations would be useful to analyse this class of problems with efficient linear codes. This paper presents an approximation formula for chance constraints which can be used in either the single- or multiple-objective case. The approximation presented will place a bound on the chance constraint at least as tight as the true non-linear form, thus overachieving the chance constraint at the expense of other constraints or objectives.

关键词： chance-constrained programming goal programming multiple-objective programming

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Geometric compromise programming: application in portfolio selection

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2023年第5期30卷 2571-2594页

作者： Salas-Molina, Francisc Pla-Santamaria, David Vercher-Ferrandiz, Maria Luisa Garcia-Bernabeu, Ana Univ Politecn Valencia Ferrandiz & Carbonell S-N Alcoy 03801 Alicante Spain

Compromise programming (CP) aims to find solutions by minimising distances to an ideal point with maximum achievement which is usually infeasible. A common assumption in CP is that it is highly unlikely that the optimum decision will lie out of the bounds of the compromise set given by metrics p=1$p=1$ and p=infinity$p=\infty$ of the Minkowski distance function. This assumption excludes the use of multiplicative functions as a measure of achievement. We propose geometric CP (GCP) to provide alternative solutions based on multiplicative functions to overcome this limitation. This methodology is an extension of CP that allows to incorporate the principle of limited compensability. An additional interesting feature of GCP is that, under reasonable assumptions, characterises extreme seekers' behaviour with non-concave utility functions (expressing no preference for any of the extremes). We discuss the practical implications of our approach and present three numerical illustrations in the context portfolio selection.

关键词： multiple-objective programming multiplicative utility functions extreme seekers compromise set

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A multi-objective stochastic programming approach for supply chain design considering risk

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2008年第1期116卷 129-138页

作者： Azaron, A. Brown, K. N. Tarim, S. A. Modarres, M. Dalhousie Univ Dept Ind Engn Halifax NS Canada Univ Coll Cork Dept Comp Sci Cork Constraint Computat Ctr Cork Ireland Hacettepe Univ Dept Management Ankara Turkey Sharif Univ Technol Dept Ind Engn Tehran Iran

In this paper, we develop a multi-objective stochastic programming approach for supply chain design under uncertainty. Demands, supplies, processing, transportation, shortage and capacity expansion costs are all considered as the uncertain parameters. To develop a robust model, two additional objective functions are added into the traditional comprehensive supply chain design problem. So, our multi-objective model includes (i) the minimization of the sum of current investment costs and the expected future processing, transportation, shortage and capacity expansion costs, (ii) the minimization of the variance of the total cost and (iii) the minimization of the financial risk or the probability of not meeting a certain budget. The ideas of unreliable suppliers and capacity expansion, after the realization of uncertain parameters, are also incorporated into the model. Finally, we use the goal attainment technique to obtain the Pareto-optimal solutions that can be used for decision-making. (c) 2008 Elsevier B.V. All rights reserved.

关键词： Supply chain management Stochastic programming multiple-objective programming Risk management

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A mathematical programming approach for generating alternatives in discrete structural optimization

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ENGINEERING OPTIMIZATION 1997年第1-2期28卷 1-31页

作者： Baugh, JW Caldwell, SC Brill, ED Department of Civil Engineering North Carolina State University Raleigh NC 27695-7908 United States

Structural design, like other complex decision problems, involves many tradeoffs among competing criteria. While mathematical programming models are increasingly realistic, there are often relevant issues that cannot be easily captured, if at all, in a formal system. This paper describes an approach to modelling that recognizes these limitations and allows a designer to explore unmodelled issues in a joint human-computer cognitive system. A prototype based on this approach is presented for topological truss optimization, and three modelling techniques are contrasted for their effectiveness in producing ''different'' alternatives. The results show that alternatives produced using these techniques are good with respect to modelled objectives, and yet are different, and often better, with respect to interesting objectives not present in the model.

关键词： multiple-objective programming decision-support systems mathematical modelling design

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PROJECT Method for Multiobjective Optimization Based on Gradient Projection and Reference Points

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IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART A-SYSTEMS AND HUMANS 2009年第4期39卷 864-879页

作者： Luque, Mariano Yang, Jian-Bo Wong, Brandon Yu Han Univ Malaga Dept Appl Econ Math E-29071 Malaga Spain Univ Manchester Manchester Business Sch Manchester M15 6PB Lancs England Citi Private Bank Singapore 049481 Singapore

In this paper, we propose a new interactive method for multiobjective programming (MOP) called the PROJECT method. Interactive methods in MOP are techniques that can help the decision maker (DM) to generate the most preferred solution from a set of efficient solutions. An interactive method should be capable of capturing the preferences of the DM in a pragmatic and comprehensive way. In certain decision situations, it may be easier and more reliable for DMs to follow an interactive process for providing local tradeoffs than other kinds of preferential information like aspiration levels, objective function classification, etc. The proposed PROJECT method belongs to the class of interactive local tradeoff methods. It is based on the projection of utility function gradients onto the tangent hyperplane of an efficient set and on a new local search procedure that inherits the advantages of the reference-point method to search for the best compromise solution within a local region. Most of the interactive methods based on local tradeoffs assume convexity conditions in a MOP problem, which is too restrictive in many real-life applications. The use of a reference-point procedure makes it possible to generate any efficient solutions, even the nonsupported solutions or efficient solutions located in the nonconvex part of the efficient frontier of a nonconvex MOP problem. The convergence of the proposed method is investigated. A nonlinear example is examined using the new method, as well as a case study on efficiency analysis with value judgements. The proposed PROJECT method is coded in Microsoft Visual C++ and incorporated into the software PROMOIN (Interactive MOP).

关键词： Interactive methods local tradeoffs multiple-objective programming reference-point methods utility functions

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Humanitarian relief supply chain: a multi-objective model and solution

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SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES 2017年第7期42卷 1167-1174页

作者： Jha, Aditya Acharya, Damodar Tiwari, M. K. Indian Inst Technol Kharagpur Dept Mech Engn Kharagpur 721302 W Bengal India Indian Inst Technol Kharagpur Dept Ind & Syst Engn Kharagpur 721302 W Bengal India

This paper models a humanitarian relief chain that includes a relief goods supply chain and an evacuation chain in case of a natural disaster. Optimum network flow is studied for both the chains by considering three conflicting objectives, namely demand satisfaction in relief chain, demand satisfaction in evacuation chain and overall logistics cost. The relief goods supply chain consists of three echelons: suppliers, relief camps and affected areas. The evacuation chain consists of two echelons: evacuation camps and affected areas. The model has been made more resilient by considering multiple paths between any two locations and disruption of camps and paths due to natural factors. The Mixed Integer programming problem has been solved using NSGA-III and results have been compared to those from benchmark algorithms. The model has been successfully tested on generated real-life-like data.

关键词： Humanitarian logistics supply chain resilience multiple-objective programming evolutionary algorithms

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Metaheuristics for solving the biobjective single-path multicommodity communication flow problem

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2019年第2期26卷 589-614页

作者： Masri, Hela Krichen, Saoussen Guitouni, Adel Univ Tunis Tunis Business Sch Tunis Tunisia Univ Tunis Inst Super Gest Tunis Tunis Tunisia Univ Victoria Peter B Gustavson Sch Business Victoria BC Canada

Single-path multicommodity flow problem (SMCFP) is a well-known combinatorial optimization problem, in which the flow of each commodity can be transmitted using only one path linking its destination to an appropriate origin within the addressed network. In this paper, we study the SMCFP in a multiobjective context by considering the simultaneous optimization of paths' delay and average reliability. The network is modeled as a finite set of nodes that can communicate using preestablished connections where each connection is characterized by a capacity, a lead time, and a reliability. A node can be an information producer or/and information consumer. The contention problem is solved by assigning a path and a dedicated bandwidth to each flow. The problem is formulated as a biobjective nonlinear optimization problem. This biobjective problem has not been considered in the literature. We design three alternative procedures for approximating the Pareto front. We proposed an MGA based on NSGA-II, a multiobjective variable neighborhood search and a new distance-based hybrid metaheuristic. The hybridization integrates a local search into the framework of genetic algorithm to effectively drive the search toward a better approximating of the Pareto front. The propounded algorithms' efficiencies are experimentally investigated on a test bed of instances applied to a planar and a grid network. A comparative study is conducted based on different multiobjective performance indicators.

关键词： multiple-objective programming metaheuristics network flows nonlinear programming

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