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Solving the linear multiple choice knapsack problem with two objectives: profit and equity

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2009年第2期43卷 261-294页

作者： Kozanidis, George Univ Thessaly Syst Optimizat Lab Dept Mech & Ind Engn Volos 38334 Greece

In this paper, we study an extension of the linear Multiple Choice Knapsack (LMCK) Problem that considers two objectives. The problem can be used to find the optimal allocation of an available resource to a group of disjoint sets of activities, while also ensuring that a certain balance on the resource amounts allocated to the activity sets is attained. The first objective maximizes the profit incurred by the implementation of the considered activities. The second objective minimizes the maximum difference between the resource amounts allocated to any two sets of activities. We present the mathematical formulation and explore the fundamental properties of the problem. Based on these properties, we develop an efficient algorithm that obtains the entire nondominated frontier. The algorithm is more efficient than the application of the general theory of multiple objective linear programming (MOLP), although there is a close underlying relationship between the two. We present theoretical findings which provide insight into the behavior of the algorithm, and report computational results which demonstrate its efficiency for randomly generated problems.

关键词： linear multiple choice knapsack Balanced resource allocation Equity multiobjective linear programming Nondominated frontier

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Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2008年第2期68卷 257-276页

作者： Shao, Lizhen Ehrgott, Matthias Univ Auckland Dept Engn Sci Auckland 1 New Zealand Univ Nantes Lab Informat Nantes Atlantique Nantes France

In this paper, we propose a modification of Benson's algorithm for solving multiobjective linear programmes in objective space in order to approximate the true nondominated set. We first summarize Benson's original algorithm and propose some small changes to improve computational performance. We then introduce our approximation version of the algorithm, which computes an inner and an outer approximation of the nondominated set. We prove that the inner approximation provides a set of epsilon-nondominated points. This work is motivated by an application, the beam intensity optimization problem of radiotherapy treatment planning. This problem can be formulated as a multiobjective linear programme with three objectives. The constraint matrix of the problem relies on the calculation of dose deposited in tissue. Since this calculation is always imprecise solving the MOLP exactly is not necessary in practice. With our algorithm we solve the problem approximately within a specified accuracy in objective space. We present results on four clinical cancer cases that clearly illustrate the advantages of our method.

关键词： multiobjective linear programming radiotherapy treatment planning epsilon-efficient solution

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NEGO - GROUP DECISION SUPPORT SYSTEM

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INFORMATION & MANAGEMENT 1985年第5期8卷 237-246页

作者： KERSTEN, GE MANAGEMENT ORG & DEV INST DEPT MANAGEMENT SYSTWARSAWPOLAND

Formulating the policy of a plan for an organization by its members can be called group decision making (GDM). A combination of 2 major decision-making frameworks, maximizing and satisficing, may be used to describe GDM. In the satisficing approach, decision makers (DM) formulate demands in the form of constraints, then they take into account preferences or wants, which take the form of objective functions, when choosing from among different decisions. GDM has 2 stages: 1. The DM makes a decision. 2. DMs negotiate to reach a compromise decision. Negotiating is an iterative process that is completed when all demands have been met. NEGO is a group decision support system that assists DMs in finding a compromise. An example is presented to illustrate how NEGO can be used to help solve GDM problems that can be modeled as multiobjective linear programming problems. NEGO is not helpful to solving problems in which 2 decision makers have the same objective but different criteria.

关键词： Decision Support System Negotiations Group Decision Making multiobjective Decision Making multiobjective linear programming Goal programming

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A multiobjective based approach for mathematical programs with linear flexible constraints

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APPLIED MATHEMATICAL MODELLING 2012年第12期36卷 6264-6274页

作者： Yaghoobi, M. A. Pourkarimi, L. Mashinchi, M. Razi Univ Dept Math Kermanshah 67149 Iran Shahid Bahonar Univ Kerman Fac Math & Comp Dept Math Kerman Iran Shahid Bahonar Univ Kerman Fac Math & Comp Dept Stat Kerman Iran

In this paper a mathematical problem with linear flexible constraints is considered. In order to solve the problem an approach is proposed based on multiobjective linear programming. Indeed, allowing violations for the constraints, and using multiobjective linear programming to minimize these violations, a subset of solution set which has less violations, namely efficiently feasible set, is obtained. Then, the corresponding objective function is optimized over efficiently feasible set in order to obtain an optimal solution. An application of the proposed approach in pattern classification is introduced. (C) 2012 Elsevier Inc. All rights reserved.

关键词： multiobjective linear programming Efficiency Maximal efficient face Flexible constraint

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Optimization of environmental management strategies through a dynamic stochastic possibilistic multiobjective program

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JOURNAL OF HAZARDOUS MATERIALS 2013年第Feb.15期246卷 257-266页

作者： Zhang, Xiaodong Huang, Gordon Univ Texas Austin Jackson Sch Geosci Bur Econ Geol Austin TX 78713 USA Univ Regina Inst Energy Environm & Sustainable Communities Regina SK S4S 0A2 Canada

Greenhouse gas (GHG) emissions from municipal solid waste (MSW) management facilities have become a serious environmental issue. In MSW management, not only economic objectives but also environmental objectives should be considered simultaneously. In this study, a dynamic stochastic possibilistic multiobjective programming (DSPMP) model is developed for supporting MSW management and associated GHG emission control. The DSPMP model improves upon the existing waste management optimization methods through incorporation of fuzzy possibilistic programming and chance-constrained programming into a general mixed-integer multiobjective linear programming (MOP) framework where various uncertainties expressed as fuzzy possibility distributions and probability distributions can be effectively reflected. Two conflicting objectives are integrally considered, including minimization of total system cost and minimization of total GHG emissions from waste management facilities. Three planning scenarios are analyzed and compared, representing different preferences of the decision makers for economic development and environmental-impact (i.e. GHG-emission) issues in integrated MSW management. Optimal decision schemes under three scenarios and different pi levels (representing the probability that the constraints would be violated) are generated for planning waste flow allocation and facility capacity expansions as well as GHG emission control. The results indicate that economic and environmental tradeoffs can be effectively reflected through the proposed DSPMP model. The generated decision variables can help the decision makers justify and/or adjust their waste management strategies based on their implicit knowledge and preferences. (c) 2012 Elsevier B.V. All rights reserved.

关键词： Municipal solid waste management Greenhouse gas emission control Fuzzy possibilistic programming multiobjective linear programming

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Optimal Planning of University Technology Transfer Measures With FDANP-F-FlowSort and an Extended multiobjective PROMETHEE V

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IEEE ACCESS 2022年 10卷 56629-56651页

作者： Tibay, Edgar Quinones, Renissa Quinones, Hubert Selerio, Egberto, Jr. Shane Evangelista, Samantha Lourdes Aro, Joerabell Maturan, Fatima May Atibing, Nadine Yamagishi, Kafferine Ocampo, Lanndon Cebu Technol Univ Prod Extens & Resource Generat Cebu Philippines Cebu Technol Univ Ctr Appl Math & Operat Res Cebu Philippines Cebu Technol Univ Dept Tourism Management Cebu 6000 Philippines

This work offers an integrated methodological framework for decision support in planning the implementation of measures that address the barriers to university technology transfer (UTT). The planning problem consists of two parts: 1) identifying the high priority measures;2) optimally implementing these measures over a specified planning horizon subject to resource constraints. Treated as a multi-criteria sorting problem under uncertainty, the high priority measures are determined via fuzzy DEcision MAking Trial and Evaluation Laboratory (DEMATEL) and analytic network process (ANP) for evaluating the barriers, and the fuzzy FlowSort (F-FlowSort) for classifying the priority of the various measures. Then, an extended multi-objective extension of the Preference Ranking Organization METHod for Enrichment Evaluations V (PROMETHEE V) is offered to determine the degree of implementation of the high priority measures over multiple periods. Demonstrated in an actual case study with 29 identified measures under 24 previously known barriers, findings reveal six high priority measures, which include designing a sustained partnership, engaging in joint research ventures, establishing partnerships from international financial institutions, streamlining objectives to full support of the technology readiness levels, establishing a holistic system approach towards technology readiness levels, and establishing agreements to have access to the industry laboratory facilities. The implementation plan, represented as a set of Pareto optimal solutions, is obtained through the augmented epsilon -constraint (AUGMECON) algorithm for the epsilon -constrained multi-objective linear programming formulation of the extended PROMETHEE V. Layers of sensitivity analysis were performed to test the robustness of the results to changes in the parameters. Finally, policy insights are provided to key decision-makers for advancing UTT.

关键词： University technology transfer multi-period planning analytic network process fuzzy FlowSort PROMETHEE V multiobjective linear programming

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A new hybrid algorithm of simulated annealing and simplex downhill for solving multiple-objective aggregate production planning on fuzzy environment

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NEURAL COMPUTING & APPLICATIONS 2019年第6期31卷 1823-1834页

作者： Zaidan, A. A. Atiya, Bayda Abu Bakar, M. R. Zaidan, B. B. Univ Pendidikan Sultan Idris Dept Comp Fac Arts Comp & Creat Ind Tanjong Malim Malaysia Univ Putra Malaysia Dept Math Fac Sci Serdang Malaysia

Aggregate production planning (APP) is a significant level that seeks efficient production systems. In actual condition, APP decisions, production inputs, and relevant planning parameters are intrinsically imprecise, which results in significant complexities in the generation of master production schedules. Thus, this paper proposes a hybridization of a fuzzy programming, simulated annealing (SA), and simplex downhill (SD) algorithm called fuzzy-SASD to establish multiple-objective linear programming models and consequently resolve APP problems in a fuzzy environment. The proposed strategy is dependent on Zimmerman's approach for handling all inexact operating costs, data capacities, and demand variables. The SD algorithm is employed to balance exploitation and exploration in SA, thereby efficient and effective (speed and quality) solution for the APP model. The proposed approach produces rates for efficient solutions of APP in large-scale problems that are 33, 83, and 89% more efficient than those of particle swarm optimization (PSO), standard algorithm (SA), and genetic algorithm (GA), respectively. Moreover, the proposed approach produces a significantly low average rate for computational time at only 64, 77, and 24% compared with those of GA, PSO, and SA, respectively. Experimental results indicate that the fuzzy-SASD is the most effectual of all approaches.

关键词： Aggregate production planning Simulated annealing multiobjective linear programming Simplex downhill approach

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An interactive fuzzy satisficing method for multiobjective optimal control problems in linear distributed-parameter systems

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FUZZY SETS AND SYSTEMS 1999年第2期102卷 237-246页

作者： Sakawa, M Inuiguchi, M Kato, K Ikeda, T Hiroshima Univ Fac Engn Dept Ind & Syst Engn Higashihiroshima 739 Japan

In this paper, we propose an interactive fuzzy satisficing method for the solution of a multiobjective optimal control problem in a linear distributed-parameter system governed by a heat conduction equation. In order to reduce the control problem of this distributed-parameter system to an approximate multiobjective linear programming problem, we use a numerical integration formula and introduced the suitable auxiliary variables. By considering the vague nature of human judgements, we assume that the decision maker may have fuzzy goals for the objective functions. Having elicited the corresponding linear membership functions through the interaction with the decision maker, if the decision maker specifies the reference membership values, the corresponding Pareto optimal solution can be obtained by solving the minimax problems. Then a linear programming-based interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker efficiently from a Pareto optimal solution set is presented. An illustrative numerical example is worked out to indicate the efficiency of the proposed method. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： linear distributed-parameter systems multiobjective optimal control multiobjective linear programming fuzzy programming fuzzy goals fuzzy satisficing methods

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linear bilevel programs with multiple objectives at the upper level

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2010年第4期234卷 950-959页

作者： Calvete, Herminia I. Gale, Carmen Univ Zaragoza Dpto Metodos Estadist E-50009 Zaragoza Spain Univ Zaragoza Dpto Metodos Estadist Zaragoza 50018 Spain

Bilevel programming has been proposed for dealing with decision processes involving two decision makers with a hierarchical structure. They are characterized by the existence of two optimization problems in which the constraint region of the upper level problem is implicitly determined by the lower level optimization problem. Focus of the paper is on general bilevel optimization problems with multiple objectives at the upper level of decision making. When all objective functions are linear and constraints at both levels define polyhedra, it is proved that the set of efficient solutions is non-empty. Taking into account the properties of the feasible region of the bilevel problem, some methods of computing efficient solutions are given based on both weighted sum scalarization and scalarization techniques. All the methods result in solving linear bilevel problems with a single objective function at each level. (C) 2008 Elsevier B.V. All rights reserved.

关键词： Bilevel programming multiobjective linear programming Efficient Non-dominated

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Adjacency-based local top-down search method for finding maximal efficient faces in multiple objective linear programming

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NAVAL RESEARCH LOGISTICS 2018年第3期65卷 203-217页

作者： Tohidi, G. Hassasi, H. Islamic Azad Univ Cent Tehran Branch Dept Math Tehran Iran Islamic Azad Univ Cent Tehran Branch Fac Management Sci Tehran Iran

It is well-known that the efficient set of a multiobjective linear programming (MOLP) problem can be represented as a union of the maximal efficient faces of the feasible region. In this paper, we propose a method for finding all maximal efficient faces for an MOLP. The new method is based on a condition that all efficient vertices (short for the efficient extreme points and rays) for the MOLP have been found and it relies on the adjacency, affine independence and convexity results of efficient sets. The method uses a local top-down search strategy to determine maximal efficient faces incident to every efficient vertex for finding maximal efficient faces of an MOLP problem. To our knowledge, the proposed method is the first top-down search method that uses the adjacency property of the efficient set to find all maximal efficient faces. We discuss this and other advantages and disadvantages of the algorithm. We also discuss some computational experience we have had with our computer code for implementing the algorithm. This computational experience involved solving several MOLP problems with the code.

关键词： adjacency affine independence efficient face multiobjective linear programming top-down search strategy

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