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On the rectangular knapsack problem: approximation of a specific quadratic knapsack problem

MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2020年第1期92卷 107-132页

作者： Schulze, Britta Stiglmayr, Michael Paquete, Luis Fonseca, Carlos M. Willems, David Ruzika, Stefan Univ Wuppertal Dept Math & Nat Sci Gaussstr 20 D-42119 Wuppertal Germany Univ Coimbra Dept Informat Engn CISUC Coimbra Portugal Univ Koblenz Landau Math Inst Koblenz Germany Univ Kaiserslautern Dept Math Kaiserslautern Germany

In this article, we introduce the rectangular knapsack problem as a special case of the quadratic knapsack problem consisting in the maximization of the product of two separate knapsack profits subject to a cardinality constraint. We propose a polynomial time algorithm for this problem that provides a constant approximation ratio of 4.5. Our experimental results on a large number of artificially generated problem instances show that the average ratio is far from theoretical guarantee. In addition, we suggest refined versions of this approximation algorithm with the same time complexity and approximation ratio that lead to even better experimental results.

关键词： Quadratic knapsack problem Approximation algorithm multiobjective combinatorial optimization Hypervolume

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A Cooperative Hybrid Quantum-Inspired Salp Swarm and Differential Evolution for Solving CEC 2022 Benchmark and Controller Placement Problems in Software Defined Networks

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IEEE ACCESS 2024年 12卷 90331-90344页

作者： Pathak, Sanjai Mani, Ashish Chatterjee, Amlan Amity Univ Amity Innovat & Design Ctr Noida 201313 Uttar Pradesh India Calif State Univ Dominguez Hills Dept Comp Sci Carson CA 90747 USA

This paper introduces a Cooperative Model of Salp Swarm optimization (CMSSO), which combines four algorithms: Salp Swarm Algorithm (SSA), Elite Opposition Learning-based SSA (EOSSA), Elite Opposition Quantum-inspired SSA (EQSSA), and Individual Dependent Approach for Differential Evolution (IDA-DE). These algorithms collaborate to tackle single-objective numerical optimization benchmarks from CEC-2022. SSA is a robust population-based metaheuristic renowned for its efficacy in practical optimization tasks. EOL and Quantum-inspired evolutionary algorithms exhibit enhanced capabilities in navigating search spaces compared to standard evolutionary algorithms. The objective of this cooperative model is to preserve the diversity and computational prowess of SSA while leveraging the strengths of these advanced algorithms. The multiobjective controller placement problem in Software Defined Networks (SDN) involves assigning switches to controllers, impacting network Quality of Service (QoS). Previous studies often focused on propagation latency for this assignment. However, our paper addresses this problem considering propagation latency between switches and controllers, inter-controller latency, and load balancing as multiobjective optimization. The experimental results confirmed the effectiveness of the proposed approach and showed that CMSSO is competitive with the standard SSA approaches.

关键词： Control systems Quantum computing optimization Benchmark testing Standards Search problems Particle swarm optimization Computational intelligence multiobjective combinatorial optimization SSA computational intelligence SDN controller placement problem

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Diagramming Qualitative Goals for multiobjective Project Selection in Large-Scale Systems

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SYSTEMS ENGINEERING 2011年第1期14卷 73-86页

作者： Martinez, Lauro J. Joshi, Nilesh N. Lambert, James H. Univ Virginia Dept Syst & Informat Engn Ctr Risk Management Engn Syst Charlottesville VA 22903 USA Morehead State Univ Dept Ind & Engn Technol Morehead KY 40351 USA Inst Tecnol Monterrey Monterrey Mexico

Allocating resources to competing projects is typically driven by multiple quantified objectives generated from the top-level goals of a large-scale system. Analytical tools to aid such allocations have a significant history with many existing methodologies, particularly for optimization and programming within a hierarchy of objective functions. However, the quantified objective functions are known to only partially represent the system goals, and significant challenges remain to preserve relevant considerations that resisted quantification. In particular, the patterns of allocation of resources across the goals may be important to decision-makers, since they could thereby address known, quantifiable issues with some consideration of unknown and emergent issues. This paper develops decision-aiding diagrams of top-level goals and resources that complement the existing multiobjective combinatorial optimization models, to better refine and choose among the optimization-generated portfolios of projects. Adapting existing path diagrams from the social sciences, the newly developed methodology can be subordinate to the generation of Pareto-optimal solutions via the optimization model. The application of path diagrams is demonstrated through a case study of allocating resources to a large-scale system of airports. (C) 2010 Wiley Periodicals, Inc. Syst Eng 14: 73-86, 2011

关键词： systems engineering multiobjective programming multiobjective combinatorial optimization path diagrams portfolio diversification interactive methods project selection

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multiobjective solution of the uncapacitated plant location problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2003年第3期145卷 509-529页

作者： Fernández, E Puerto, J Univ Sevilla Fac Matemat Dept Estadist & Invest Operat E-41012 Seville Spain Univ Politecn Catalunya Dept Estadist & Invest Operat E-08028 Barcelona Spain

In this paper we consider the discrete multiobjective uncapacitated plant location problem. We present an exact and an approximate approach to obtain the set of non-dominated solutions. The two approaches resort to dynamic programming to generate in an efficient way the non-dominated solution sets. The solution methods that solve the problems associated with the generated states are based on the decomposition of the problem on two nested subproblems. We define lower and upper bound sets that lead to elimination tests that have shown to have a high performance. Computational experiments on a set of test problems show the good performance of the proposal. (C) 2002 Published by Elsevier Science B.V.

关键词： multiobjective combinatorial optimization discrete location problems dynamic programming

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Using multiobjective optimization for biclustering microarray data

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APPLIED SOFT COMPUTING 2015年 33卷 239-249页

作者： Seridi, Khedidja Jourdan, Laetitia Talbi, El-Ghazali Univ Lille 1 CNRS Lab Informat Fondamentale Lille UMR Cite Sci 8022 F-59655 Villeneuve Dascq France INRIA Lille Nord Europe F-59650 Villeneuve Dascq France

Microarray data analysis is a challenging problem in the data mining field. Actually, it represents the expression levels of thousands of genes under several conditions. The analysis of this data consists on discovering genes that share similar expression patterns across a sub-set of conditions. In fact, the extracted informations are submatrices of the microarray data that satisfy a coherence constraint. These submatrices are called biclusters, while the process of extracting them is called biclustering. Since its first application to the analysis of microarray [1], many modeling and algorithms have been proposed to solve it. In this work, we propose a new multiobjective model and a new metaheuristic HMOBIibea for the biclustering problem. Results of the proposed method are compared to those of other existing algorithms and the biological relevance of the extracted information is validated. The experimental results show that our method extracts very relevant biclusters, with large sizes with respect to existing methods. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Biclustering problem Gene expression data Evolutionary algorithm multiobjective combinatorial optimization

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Finding representations for an unconstrained bi-objective combinatorial optimization problem

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optimization LETTERS 2018年第2期12卷 321-334页

作者： Jesus, Alexandre D. Paquete, Luis Figueira, Jose Rui Univ Coimbra Dept Informat Engn CISUC Polo 2 P-3030290 Coimbra Portugal Univ Lisbon Inst Super Tecn CEG IST Ave Rovisco Pais 1 P-1049001 Lisbon Portugal

Typically, multi-objective optimization problems give rise to a large number of optimal solutions. However, this information can be overwhelming to a decision maker. This article introduces a technique to find a representative subset of optimal solutions, of a given bounded cardinality for an unconstrained bi-objective combinatorial optimization problem in terms of -indicator. This technique extends the Nemhauser-Ullman algorithm for the knapsack problem and allows to find a representative subset in a single run. We present a discussion on the representation quality achieved by this technique, both from a theoretical and numerical perspective, with respect to an optimal representation.

关键词： multiobjective combinatorial optimization Representation problem Dynamic programming

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New multiobjective metaheuristic solution procedures for capital investment planning

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JOURNAL OF HEURISTICS 2005年第3期11卷 183-199页

作者： Stummer, C Sun, MH Univ Vienna Sch Business Econ & Comp Sci A-1210 Vienna Austria Univ Texas Coll Business San Antonio TX 78249 USA

Capital investment planning is a periodic management task that is particularly challenging in the presence of multiple objectives as trade-offs have to be made with respect to the preferences of the decision-makers. The underlying mathematical model is a multiobjective combinatorial optimization problem that is NP-hard. One way to tackle this problem is first to determine the set of all efficient. portfolios and then to explore this set in order to identify a final preferred portfolio. In this study, we developed heuristic procedures to find efficient portfolios because it is impossible to enumerate all of them within a. reasonable computation time for practical problems. We first added a neighborhood search routine to the Pareto Ant Colony optimization (P-ACO) procedure to improve its performance and then developed a Tabu Search procedure and a Variable Neighborhood Search procedure. Step-by-step descriptions of these three new procedures are provided. Computational results on benchmark and randomly generated test problems show that the Tabu Search procedure outperforms the others if the problem does not have too many objective functions and an excessively large efficient set. The improved P-ACO procedure performs better otherwise.

关键词： investment planning multiobjective combinatorial optimization ant colony optimization tabu search variable neighborhood search

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Local dominance and local recombination in MOEAs on 0/1 multiobjective knapsack problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第3期181卷 1708-1723页

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

This work studies and compares the effects on performance of local dominance and local recombination applied with different locality in multiobjective evolutionary algorithms on combinatorial 0/1 multiobjective knapsack problems. For this purpose, we introduce a method that creates a neighborhood around each individual and assigns a local dominance rank after alignment of the principle search direction of the neighborhood by using polar coordinates in objective space. For recombination a different neighborhood determined around a random principle search direction is created. The neighborhood sizes for dominance and recombination are separately controlled by two different parameters. Experimental results show that the optimum locality of dominance is different from the optimum locality of recombination. Additionally, it is shown that the performance of the algorithm that applies local dominance and local recombination with different locality is significantly better than the performance of algorithms applying local dominance alone, local recombination alone, or dominance and recombination globally as conventional approaches do. (C) 2006 Elsevier B.V. All rights reserved.

关键词： evolutionary computations multiobjective combinatorial optimization 0/1 multiobjective knapsack problems local dominance local recombination alignment of the principle search direction polar coordinates optimum locality

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On a biobjective search problem in a line: Formulations and algorithms

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THEORETICAL COMPUTER SCIENCE 2013年 507卷 61-71页

作者： Paquete, Luis Jaschob, Mathias Klamroth, Kathrin Gorski, Jochen Univ Coimbra Dept Informat Engn CISUC P-3000 Coimbra Portugal Univ Wuppertal Dept Math & Nat Sci Wuppertal Germany

In this article we describe three formulations of a multiobjective combinatorial optimization problem, as well as several complexity results and structural properties of these formulations. A multiobjective dynamic programming algorithm is proposed for each of the three formulations. Based on our theoretical and computational results we argue that a clever definition of the recursion, allowing for strong dominance criteria, is crucial in the design of a multiobjective dynamic programming algorithm. (C) 2013 Elsevier B.V. All rights reserved.

关键词： multiobjective combinatorial optimization Dynamic programming Shortest path problems Knapsack problems

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On combinatorial optimization motivated by biology

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APPLIED MATHEMATICS AND COMPUTATION 2006年第1期172卷 40-48页

作者： Ahmed, E Elettreby, MF Mansoura Univ Fac Sci Dept Math Mansoura 35516 Egypt

Some multiobjective combinatorial problems are solved using methods motivated by biology. The first method is extremal optimization which is motivated by the immune system. The second method is backward-forward greedy... 详细信息

关键词： multiobjective combinatorial optimization extremal optimization travelling salesman problem knapsack problem

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