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An algorithm for optimizing a linear function over an integer efficient set

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2009年第1期195卷 98-103页

作者： Jorge, Jesus M. Univ La Laguna Dept Estadist IO & Computac E-38206 Tenerife Spain

Optimizing a linear function over the efficient set of a multiobjective integer linear programming (MOILP) problem is a topic of unquestionable practical as well as mathematical interest within the field of multiple criteria decision making. As known, those problems are particularly difficult to deal with due to the discrete nature of the efficient set, which is not explicitly known, nor a suitable implicit description is available. In this work an exact algorithm is presented to optimize a linear function over the efficient set of a MOILP. The approach here proposed defines a sequence of progressively more constrained single-objective integer problems that successively eliminates undesirable points from further consideration. The algorithm has been coded in C Sharp, using CPLEX solver, and computational experiments have been undertaken in order to analyze performance properties of the algorithm over different problem instances randomly generated. (c) 2008 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Optimization over the efficient set Integer programming

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Pruning Pareto optimal solutions for multi-objective portfolio asset management

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第1期297卷 203-220页

作者： Petchrompo, Sanyapong Wannakrairot, Anupong Parlikad, Ajith Kumar Univ Cambridge Inst Mfg Dept Engn 17 Charles Babbage Rd Cambridge CB3 0FS England Univ Bath Claverton Down Rd Bath BA2 7AY Avon England

Budget allocation problems in portfolio management are inherently multi-objective as they entail different types of assets of which performance metrics are not directly comparable. Existing asset management methods that either consolidate multiple goals to form a single objective ( a priori ) or populate a Pareto optimal set ( a posteriori ) may not be sufficient because a decision maker (DM) may not possess comprehensive knowledge of the problem domain. Moreover, current techniques often present a Pareto optimal set with too many options, making it counter-productive. In order to provide the DM with a diverse yet compact solution set, this paper proposes a three-step approach. In the first step, we employ different approximation functions to capture investment-performance relationships at the asset-type level. These simplified relationships are then used as inputs for the multi-objective optimisation model in the second step. In the final step, Pareto optimal solutions generated by a selected evolutionary algorithm are pruned by a clustering method. To measure the spread of representative solutions over the Pareto front, we present two novel indicators based on average Euclidean distance and cosine similarity between original Pareto solutions and representative solutions. Through numerical examples, we demonstrate that this approach can provide a set of representative solutions that maintain high integrity of the original Pareto front. We also put forward suggestions on choosing appropriate approximation functions, pruning methods, and indicators. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://***/licenses/by/4.0/ )

关键词： multiple criteria analysis multiple objective programming Pareto pruning Data clustering Asset management

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A parallel multiple reference point approach for multi-objective optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第2期205卷 390-400页

作者： Figueira, J. R. Liefooghe, A. Talbi, E. -G. Wierzbicki, A. P. Univ Lille 1 LIFL CNRS INRIA Lille Nord Europe F-59650 Villeneuve Dascq France King Saud Univ Riyadh Saudi Arabia Inst Natl Telecommun PL-04894 Warsaw Poland Univ Paris 09 LAMSADE CNRS UMR 7024 F-75775 Paris France Univ Tecn Lisboa Inst Super Tecn CEG Ctr Management Studies P-2780990 Porto Salvo Portugal

This paper presents a multiple reference point approach for multi-objective optimization problems of discrete and combinatorial nature. When approximating the Pareto Frontier, multiple reference points can be used instead of traditional techniques. These multiple reference points can easily be implemented in a parallel algorithmic framework. The reference points can be uniformly distributed within a region that covers the Pareto Frontier. An evolutionary algorithm is based on an achievement scalarizing function that does not impose any restrictions with respect to the location of the reference points in the objective space. Computational experiments are performed on a bi-objective flow-shop scheduling problem. Results, quality measures as well as a statistical analysis are reported in the paper. (C) 2010 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Parallel computing multiple reference point approach Evolutionary computations Bi-objective flow-shop scheduling

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Estimating the form of a decision maker's preference function and converging towards preferred solutions

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IISE TRANSACTIONS 2020年第6期52卷 651-664页

作者： Karakaya, Gulsah Koksalan, Murat Middle East Tech Univ Dept Business Adm Ankara Turkey Middle East Tech Univ Dept Ind Engn Ankara Turkey Univ Michigan Ross Sch Business Ann Arbor MI 48109 USA

Preference functions have been widely used to scalarize multiple objectives. Various forms such as linear, quasiconcave, or general monotone have been assumed. In this article, we consider a general family of functions that can take a variety of forms and has properties that allow for estimating the form efficiently. We exploit these properties to estimate the form of the function and converge towards a preferred solution(s). We develop the theory and algorithms to efficiently estimate the parameters of the function that best represent a decision maker's preferences. This in turn facilitates fast convergence to preferred solutions. We demonstrate on a variety of experiments that the algorithms work well both in estimating the form of the preference function and converging to preferred solutions.

关键词： multiple objective programming interactive algorithm preference function form

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A shift scheduling model for employees with different seniority levels and an application in healthcare

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2009年第3期198卷 943-957页

作者： Topaloglu, Seyda Dokuz Eylul Univ Dept Ind Engn TR-35160 Izmir Turkey

This paper addresses the problem of scheduling medical residents that arises in different clinical settings of a hospital. The residents are grouped according to different seniority levels that are specified by the number of years spent in residency training. It is required from the residents to participate in the delivery of patient care services directly by working weekday and weekend day shifts in addition to their regular daytime work. A monthly shift schedule is prepared to determine the shift duties of each resident considering shift coverage requirements, seniority-based workload rules, and resident work preferences. Due to the large number of constraints often conflicting, a multi-objective programming model has been proposed to automate the schedule generation process. The model is implemented on a real case in the pulmonary unit of a local hospital for a 6-month period using sequential and weighted methods. The results indicate that high quality solutions can be obtained within a few seconds compared to the manually prepared schedules expending considerable effort and time. It is also shown that the employed weighting procedure based on seniority levels performs much better compared to the preemptive method in terms of computational burden. (C) 2008 Elsevier B.V. All rights reserved.

关键词： OR in manpower planning OR in health services multiple objective programming Shift scheduling Resident physicians Seniority

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Multi-objective branch and bound

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第3期260卷 856-872页

作者： Przybylski, Anthony Gandibleux, Xavier Univ Nantes IRCCyN UMR CNRS 6597 Fac Sci & Technol Bldg 112 Rue Houssiniere BP 92208 F-44322 Nantes 03 France

Branch and bound is a well-known generic method for computing an optimal solution of a single objective optimization problem. Based on the idea "divide to conquer", it consists in an implicit enumeration principle viewed as a tree search. Although the branch and bound was first suggested by Land and Doig (1960), the first complete algorithm introduced as a multi-objective branch and bound that we identified was proposed by Kiziltan and Yucaoglu (1983). Rather few multi-objective branch and bound algorithms have been proposed. This situation is not surprising as the contributions on the extensions of the components of branch and bound for multi-objective optimization are recent. For example, the concept of bound sets, which extends the classic notion of bounds, has been mentioned by Villarreal and Karwan (1981). But it was only developed for the first time in 2001 by Ehrgott and Gandibleux, and fully defined in 2007. This paper describes a state-of-the-art of multi-objective branch and bound, which reviews concepts, components and published algorithms. It mainly focuses on the contributions belonging to the class of optimization problems who has received the most of attention in this context from 1983 until 2015: the linear optimization problems with zero-one variables and mixed 0-1/continuous variables. Only papers aiming to compute a complete set of efficient solutions are discussed. (C) 2017 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Branch and bound Bound sets

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On highly robust efficient solutions to uncertain multiobjective linear programs

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第1期273卷 20-30页

作者： Dranichak, Garrett M. Wiecek, Margaret M. Clemson Univ Dept Math Sci Clemson SC 29634 USA

Decision making in the presence of uncertainty and multiple conflicting objectives is a real-life issue in many areas of human activity. To address this type of problem, we study highly robust (weakly) efficient solutions to uncertain multiobjective linear programs (UMOLPs) with objective-wise uncertainty in the objective function coefficients. We develop properties of the highly robust efficient set, characterize highly robust (weakly) efficient solutions using the cone of improving directions associated with the UMOLP, derive several upper and lower bound sets on the highly robust (weakly) efficient set, and present a robust counterpart for a class of UMOLPs. As various results rely on the acuteness of the cone of improving directions, we also propose methods to verify this property. (C) 2018 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Robust multiobjective optimization objective-wise uncertainty Polar cones Acute cones

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Dynamic parametric bounds on efficient outcomes in interactive multiple criteria decision making problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2003年第1期147卷 94-107页

作者： Kaliszewski, I Polish Acad Sci Syst Res Inst PL-01447 Warsaw Poland

Bounds on efficient outcomes in interactive multiple criteria decision making problems are derived. Bounds are dynamic, i.e., they become stronger with the growing number of explicitly identified outcomes. They are also parametric with respect to weighting coefficients. Computational cost to calculate bounds is negligible. Bounds of the sort offer a breakthrough for prohibitive size and/or solution time bottlenecks by allowing a decision maker to interact with an approximation of the underlying mathematical model rather the model itself. Possible applications of bounds to existing interactive decision making algorithms are discussed. Illustrative numerical examples are given. (C) 2002 Published by Elsevier Science B.V.

关键词： multiple objective programming interactive multiple criteria decision making nonconvex programming efficiency large-scale models

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A combined scalarizing method for multiobjective programming problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2014年第1期236卷 229-237页

作者： Rastegar, Narges Khorram, Esmaile Amirkabir Univ Technol Fac Math & Comp Sci Dept Appl Math Tehran Iran

In this paper, a new general scalarization technique for solving multiobjective optimization problems is presented. After studying the properties of this formulation, two problems as special cases of this general formula are considered. It is shown that some well-known methods such as the weighted sum method, the epsilon-constraint method, the Benson method, the hybrid method and the elastic epsilon-constraint method can be subsumed under these two problems. Then, considering approximate solutions, some relationships between epsilon-(weakly, properly) efficient points of a general (without any convexity assumption) multiobjective optimization problem and epsilon-optimal solutions of the introduced scalarized problem are achieved. (C) 2013 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Scalarization method Approximate solutions Properly efficient solutions epsilon-Properly efficient solutions

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A new hybrid memetic multi-objective optimization algorithm for multi-objective optimization

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INFORMATION SCIENCES 2018年 448卷 164-186页

作者： Luo, Jianping Yang, Yun Liu, Qiqi Li, Xia Chen, Minrong Gao, Kaizhou Guangdong Key Lab Intelligent Informat Proc Shenzhen Peoples R China Shenzhen Key Lab Media Secur Shenzhen Peoples R China Shenzhen Univ Coll Informat Engn Shenzhen 518060 Peoples R China

To deal with the multi-objective optimization problems (MOPS), a meta-heuristic based on an improved shuffled frog leaping algorithm (ISFLA) which belongs to memetic evolution is presented. For the MOPs, both diversity maintenance and searching effectiveness are crucial for algorithm evolution. In this work, modified calculation of crowding distance to evaluate the density of a solution, memeplex clustering analyses based on a grid to divide the population, and new selection measure of global best individual are proposed to ensure the diversity of the algorithm. A multi-objective extremal optimization procedure (MEOP) is also introduced and incorporated into ISFLA to enable the algorithm to evolve more effectively. Finally, the experimental tests on thirteen unconstrained MOPs and DTLZ many-objective problems show that the proposed algorithm is flexible to handle MOPs and many-objective problems. The effectiveness and robustness of the proposed algorithm are also analyzed in detail. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Evolutionary computing Hybrid computing multiple objective programming Algorithm diversity Shuffled frog leaping algorithm Extremal optimization

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