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A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming

APPLIED SOFT COMPUTING 2014年第0期16卷 10-19页

作者： Liefooghe, Arnaud Verel, Sebastien Hao, Jin-Kao Univ Lille 1 LIFL UMR CNRS 8022 F-59655 Villeneuve Dascq France Inria Lille Nord Europe F-59650 Villeneuve Dascq France Univ Littoral Cote dOpale LISIC F-62228 Calais France Univ Angers LERIA F-49045 Angers France

The conventional unconstrained binary quadratic programming (UBQP) problem is known to be a unified modeling and solution framework for many combinatorial optimization problems. This paper extends the single-objective UBQP to the multiobjective case (mUBQP) where multiple objectives are to be optimized simultaneously. We propose a hybrid metaheuristic which combines an elitist evolutionary multiobjective optimization algorithm and a state-of-the-art single-objective tabu search procedure by using an achievement scalarizing function. Finally, we define a formal model to generate mUBQP instances and validate the performance of the proposed approach in obtaining competitive results on large-size mUBQ Pinstances with two and three objectives. (C) 2013 Elsevier B. V. All rights reserved.

关键词： Unconstrained binary quadratic programming multiobjective combinatorial optimization Hybrid metaheuristic Evolutionary multiobjective optimization Tabu search Scalarizing functiona

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Equity metrics with risk, performance, and cost objectives for the prioritization of transportation projects

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IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT 2007年第3期54卷 539-547页

作者： Joshi, Nilesh N. Lambert, James H. Univ Virginia Ctr Risk Management Engn Syst Charlottesville VA 22904 USA

Prioritizing and selecting a few critical transportation projects from several competing projects is a multiobjective combinatorial optimization problem (MOCO). Transportation planners and managers are always interested in analyzing and visualizing the tradeoffs involved, but equity issues in distribution of resources are given much less attention. This paper develops a methodology for integrating equity metrics with traditional metrics for planning and prioritizing a large and diverse portfolio of transportation investment projects. The methodology serves to help planners, managers, and engineers to visualize and compare measures of the distributed equity of the allocation along with cost-benefit tradeoffs. It is based on incorporating network-level equity metrics along with traditional metrics in formulating a generic multiobjective combinatorial optimization (MOCO) problem and visualizing multiobjective tradeoffs on the spatial network. A case study of a region demonstrates the use of the methodology in tradeoff analysis for prioritizing and selecting transportation projects. The approach is adaptable to other manufacturing and service industries where consideration of the distributed equity of allocation is an important issue.

关键词： diversification equity metrics multiobjective combinatorial optimization network analysis transportation planning

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Pareto ant colony optimization with ILP preprocessing in multiobjective project portfolio selection

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2006年第3期171卷 830-841页

作者： Doerner, KF Gutjahr, WJ Hartl, RF Strauss, C Stummer, C Univ Vienna BWZ Dept Management Sci A-1210 Vienna Austria Univ Vienna Dept Stat & Decis Support Syst A-1010 Vienna Austria Univ Texas Dept Management Sci & Stat San Antonio TX 78249 USA

One of the most important, common and critical management issues lies in determining the "best" project portfolio out of a given set of investment proposals. As this decision process usually involves the pursuit of multiple objectives amid a lack of a priori preference information, its quality can be improved by implementing a two-phase procedure that first identifies the solution space of all efficient (i.e., Pareto-optimal) portfolios and then allows an interactive exploration of that space. However, determining the solution space is not trivial because brute-force complete enumeration only solves small instances and the underlying NP-hard problem becomes increasingly demanding as the number of projects grows. While meta-heuristics in general provide an attractive compromise between the computational effort necessary and the quality of an approximated solution space, Pareto ant colony optimization (P-ACO) has been shown to perform particularly well for this class of problems. In this paper, the beneficial effect of P-ACO's core function (i.e., the learning feature) is substantiated by means of a numerical example based on real world data. Furthermore, the original P-ACO approach is supplemented by an integer linear programming (ILP) preprocessing procedure that identifies several efficient portfolio solutions within a few seconds and correspondingly initializes the pheromone trails before running P-ACO. This extension favors a larger exploration of the search space at the beginning of the search and does so at a low cost. (c) 2004 Elsevier B.V. All rights reserved.

关键词： ant colony optimization project portfolio selection multiobjective combinatorial optimization integer linear programming preprocessing hybrid optimization method

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Design and analysis of stochastic local search for the multiobjective traveling salesman problem

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COMPUTERS & OPERATIONS RESEARCH 2009年第9期36卷 2619-2631页

作者： Paquete, Luis Stutzle, Thomas Univ Coimbra Dept Informat Engn CISUC Coimbra Portugal Univ Libre Bruxelles CoDE IRIDIA Brussels Belgium

Stochastic local search (SLS) algorithms are typically composed of a number of different components, each of which should contribute significantly to the final algorithm's performance. If the goal is to design and engineer effective SLS algorithms, the algorithm developer requires some insight into the importance and the behavior of possible algorithmic components. In this paper, we analyze algorithmic components of SLS algorithms for the multiobjective travelling salesman problem. The analysis is done using a careful experimental design for a generic class of SLS algorithms for multiobjective combinatorial optimization. Based on the insights gained, we engineer SLS algorithms for this problem. Experimental results show that these SLS algorithms, despite their conceptual simplicity, outperform a well-known memetic algorithm for a range of benchmark instances with two and three objectives. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： multiobjective combinatorial optimization Meta-heuristics

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PPLS/D: Parallel Pareto Local Search Based on Decomposition

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IEEE TRANSACTIONS ON CYBERNETICS 2020年第3期50卷 1060-1071页

作者： Shi, Jialong Zhang, Qingfu Sun, Jianyong Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Peoples R China City Univ Hong Kong Dept Comp Sci Hong Kong Peoples R China

Pareto local search (PLS) is a basic building block in many metaheuristics for a multiobjective combinatorial optimization problem. In this paper, an enhanced PLS variant called parallel PLS based on decomposition (PPLS/D) is proposed. PPLS/D improves the efficiency of PLS using the techniques of parallel computation and problem decomposition. It decomposes the original search space into L subregions and executes L parallel processes searching in these subregions simultaneously. Inside each subregion, the PPLS/D process is guided by a unique scalar objective function. PPLS/D differs from the well-known two phase PLS in that it uses the scalar objective function to guide every move of the PLS procedure in a fine-grained manner. In the experimental studies, PPLS/D is compared against the basic PLS and a recently proposed PLS variant on the multiobjective unconstrained binary quadratic programming problems and the multiobjective traveling salesman problems with, at most, four objectives. The experimental results show that regardless of whether the initial solutions are randomly generated or generated by heuristic methods, PPLS/D always performs significantly better than the other two PLS variants.

关键词： multiobjective combinatorial optimization parallel metaheuristic Pareto local search unconstrained binary quadratic programming traveling salesman problem

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Enhancing Branch-and-Bound for multiobjective 0-1 Programming

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INFORMS JOURNAL ON COMPUTING 2024年第1期36卷 1-304, C2页

作者： Forget, Nicolas Parragh, Sophie N. Aarhus Univ Sch Business & Social Sci Dept Econ & Business Econ DK-8210 Aarhus 5 Denmark Johannes Kepler Univ Linz Inst Prod & Logist Management A-4040 Linz Austria

In the biobjective branch-and-bound literature, a key ingredient is objective branching, that is, to create smaller and disjoint subproblems in the objective space, obtained from the partial dominance of the lower bound set by the upper bound set. When considering three or more objective functions, however, applying objective branching becomes more complex, and its benefit has so far been unclear. In this paper, we investigate several ingredients that allow us to better exploit objective branching in a multiobjective setting. We extend the idea of probing to multiple objectives for the 0-1 case, enhance it in several ways, and show that, when coupled with objective branching, it results in significant speedups in terms of CPU times. We also show how to adapt it to the general integer case. Furthermore, we investigate cut generation based on the objective branching constraints. Besides, we generalize the best bound idea for node selection to multiple objectives, and we show that the proposed rules outperform, in the multiobjective literature, the commonly employed depth-first and breadth-first strategies. We also analyze problem specific branching rules. We test the proposed ideas on available benchmark instances for three problem classes with three and four objectives, namely, the capacitated facility location problem, the uncapacitated facility location problem, and the knapsack problem. Our enhanced multiobjective branch-and-bound algorithm outperforms the best existing branch-and-bound-based approach and is the first to obtain competitive and even slightly better results than a state-of-the-art objective space search method on a subset of the problem classes.

关键词： multiple criteria integer programming branch and bound algorithms multiobjective combinatorial optimization probing node selection rules

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A greedy memetic algorithm for a multiobjective dynamic bin packing problem for storing cooling objects

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JOURNAL OF HEURISTICS 2019年第1期25卷 1-45页

作者： Spencer, Kristina Yancey Tsvetkov, Pavel V. Jarrell, Joshua J. Texas A&M Univ 3133 TAMU College Stn TX 77843 USA Oak Ridge Natl Lab Oak Ridge TN USA Idaho Natl Lab Idaho Falls ID USA

In this paper, a multiobjective dynamic bin packing problem for storing cooling objects is introduced along with a metaheuristic designed to work well in mixed-variable environments. The dynamic bin packing problem is based on cookie production at a bakery, where cookies arrive in batches at a cooling rack with limited capacity and are packed into boxes with three competing goals. The first is to minimize the number of boxes used. The second objective is to minimize the average initial heat of each box, and the third is to minimize the maximum time until the boxes can be moved to the storefront. The metaheuristic developed here incorporated greedy heuristics into an adaptive evolutionary framework with partial decomposition into clusters of solutions for the crossover operator. The new metaheuristic was applied to a variety benchmark bin packing problems and to a small and large version of the dynamic bin packing problem. It performed as well as other metaheuristics in the benchmark problems and produced more diverse solutions in the dynamic problems. It performed better overall in the small dynamic problem, but its performance could not be proven to be better or worse in the large dynamic problem.

关键词： Dynamic bin packing problem multiobjective combinatorial optimization Metaheuristics Memetic algorithms

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Solving the musical orchestration problem using multiobjective constrained optimization with a genetic local search approach

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JOURNAL OF HEURISTICS 2010年第5期16卷 681-714页

作者： Carpentier, Gregoire Assayag, Gerard Saint-James, Emmanuel IRCAM F-75004 Paris France LIP6 F-75252 Paris 5 France

In this paper a computational approach of musical orchestration is presented. We consider orchestration as the search of relevant sound combinations within large instruments sample databases and propose two cooperating metaheuristics to solve this problem. Orchestration is seen here as a particular case of finding optimal constrained multisets on a large ensemble with respect to several objectives. We suggest a generic and easily extendible formalization of orchestration as a constrained multiobjective search towards a target timbre, in which several perceptual dimensions are jointly optimized. We introduce Orchid,e, a time-efficient evolutionary orchestration algorithm that allows the discovery of optimal solutions and favors the exploration of non-intuitive sound mixtures. We also define a formal framework for global constraints specification and introduce the innovative CDCSolver repair metaheuristic, thanks to which the search is led towards regions fulfilling a set of musical-related requirements. Evaluation of our approach on a wide set of real orchestration problems is also provided.

关键词： Orchestration Computer-aided composition Computer music Compositional algorithms multiobjective combinatorial optimization Evolutionary algorithms Global constraints Local search CDCSolver

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Working principles, behavior, and performance of MOEAs on MNK-landscapes

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第3期181卷 1670-1690页

作者： Aguirre, Hernan E. Tanaka, Kiyoshi Shinshu Univ Fac Engn Nagano 3808553 Japan

This work studies the working principles, behavior, and performance of multiobjective evolutionary algorithms (MOEAs) on multiobjective epistatic fitness functions with discrete binary search spaces by using MNK-landscapes. First, we analyze the structure and some of the properties of MNK-landscapes under a multiobjective perspective by using enumeration on small landscapes. Then, we focus on the performance and behavior of MOEAs on large landscapes. We organize our study around selection, drift, mutation, and recombination, the four major and intertwined processes that drive adaptive evolution over fitness landscapes. This work clearly shows pros and cons of the main features of MOEAs, gives a valuable guide for the practitioner on how to set up his/her algorithm, enhance MOEAs, and presents useful insights on how to design more robust and efficient MOEAs. (C) 2006 Elsevier B.V. All rights reserved.

关键词： evolutionary computations multiobjective evolutionary algorithms multiobjective combinatorial optimization MNK-landscapes epistasis non-linear multiobjective fitness functions discrete binary search spaces selection drift mutation recombination

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Solving a multiobjective location routing problem with a metaheuristic based on tabu search.: Application to a real case in Andalusia

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第3期177卷 1751-1763页

作者： Caballero, Rafael Gonzalez, Mercedes Guerrero, Flor M. Molina, Julian Paralera, Concepcion Univ Malaga Fac Econ Dept Appl Econ Math Malaga 29007 Spain Univ Pablo Olavide Dept Econ & Business Seville 41013 Spain

In this work we present a multiobjective location routing problem and solve it with a multiobjective metaheuristic procedure. In this type of problem, we have to locate some plants within a set of possible locations to meet the demands of a number of clients with multiple objectives. This type of model is used to solve a problem with real data in the region of Andalusia (Spain). Thus, we study the location of two incineration plants for the disposal of solid animal waste from some preestablished locations in Andalusia, and design the routes to serve the different slaughterhouses in this region. This must be done while taking into account certain economic objectives (start-up, maintenance, and transport costs) and social objectives (social rejection by towns on the truck routes, maximum risk as an equity criterion, and the negative implications for towns close to the plant). (c) 2005 Elsevier B.V. All rights reserved.

关键词： location routing problems multiobjective combinatorial optimization metaheuristics

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