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MOTGA: A multiobjective Tchebycheff based genetic algorithm for the multidimensional knapsack problem

COMPUTERS & OPERATIONS RESEARCH 2007年第11期34卷 3458-3470页

作者： Alves, Maria Joao Almeida, Marla Univ Coimbra Fac Econ INESC P-3004512 Coimbra Portugal

This paper presents a new multiobjective genetic algorithm based on the Tchebycheff scalarizing function, which aims to generate a good approximation of the nondominated solution set of the multiobjective problem. The algorithm performs several stages, each one intended for searching potentially nondominated solutions in a different part of the Pareto front. Pre-defined weight vectors act as pivots to define the weighted-Tchebycheff scalarizing functions used in each stage. Therefore, each stage focuses the search on a specific region, leading to an iterative approximation of the entire nondominated set. This algorithm, called MOTGA (multiple objective Tchebycheff based Genetic Algorithm) has been designed to the multiobjective multidimensional 0/1 knapsack problem, for which a dedicated routine to repair infeasible solutions was implemented. Computational results are presented and compared with the outcomes of other evolutionary algorithms. (C) 2006 Elsevier Ltd. All rights reserved.

关键词： genetic algorithms multiple objective programming knapsack problem

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Multi-objective optimization of a two-echelon vehicle routing problem with vehicle synchronization and 'grey zone' customers arising in urban logistics

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第3期289卷 940-958页

作者： Anderluh, Alexandra Nolz, Pamela C. Hemmelmayr, Vera C. Crainic, Teodor Gabriel WU Inst Transport & Logist Management A-1020 Vienna Austria AIT Ctr Mobil Syst Dynam Transportat Syst A-1210 Vienna Austria Univ Quebec Montreal UQAM Sch Management CP 8888 Succ Ctr Ville Montreal PQ H3C 3P8 Canada Univ Montreal CIRRELT Ctr Interuniv Rech Reseaux Entreprise Log PO 6120 Succ Ctr Ville Montreal PQ H3C 3J7 Canada

We present a multi-ob'jective two-echelon vehicle routing problem with vehicle synchronization and 'grey zone' customers arising in the context of urban freight deliveries. Inner-city center deliveries are performed by small vehicles due to access restrictions, while deliveries outside this area are carried out by conventional vehicles for economic reasons. Goods are transferred from the first to the second echelon by synchronized meetings between vehicles of the respective echelons. We investigate the assignment of customers to vehicles, i.e., to the first or second echelon, within a so-called 'grey zone' on the border of the inner city and the area around it. While doing this, the economic objective as well as negative external effects of transport, such as emissions and disturbance (negative impact on citizens due to noise and congestion), are taken into account to include objectives of companies as well as of citizens and municipal authorities. Our metaheuristic - a large neighborhood search embedded in a heuristic rectangle/cuboid splitting - addresses this problem efficiently. We investigate the impact of the free assignment of part of the customers ('grey zone') to echelons and of three different city layouts on the solution. Computational results show that the impact of a 'grey zone' and thus the assignment of these customers to echelons depend significantly on the layout of a city. Potentially pareto-optimal solutions for two and three objectives are illustrated to efficiently support decision makers in sustainable city logistics planning processes. (C) 2019 The Authors. Published by Elsevier B.V.

关键词： multiple objective programming Two-echelon VRP Vehicle synchronization City layout 'Grey zone'

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Resource allocation in multi-class dynamic PERT networks with finite capacity

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第3期247卷 879-894页

作者： Yaghoubi, Saeed Noori, Siamak Azaron, Amir Fynes, Brian Iran Univ Sci & Technol Sch Ind Engn Tehran Iran Istanbul Sehir Univ Dept Ind Engn Istanbul Turkey Univ Coll Dublin Michael Smurfit Grad Sch Business Dublin 2 Ireland Ryerson Univ Dept Mech & Ind Engn Toronto ON M5B 2K3 Canada

In this paper, the resource allocation problem in multi-class dynamic PERT networks with finite capacity of concurrent projects (COnstant Number of Projects In Process (CONPIP)) is studied. The dynamic PERT network is modeled as a queuing network, where new projects from different classes (types) are generated according to independent Poisson processes with different rates over the time horizon. Each activity of a project is performed at a devoted service station with one server located in a node of the network, whereas activity durations for different classes in each service station are independent and exponentially distributed random variables with different service rates. Indeed, the projects from different classes may be different in their precedence networks and also the durations of the activities. For modeling the multi-class dynamic PERT networks with CONPIP, we first consider every class separately and convert the queueing network of every class into a proper stochastic network. Then, by constructing a proper finite-state continuous-time Markov model, a system of differential equations is created to compute the project completion time distribution for any particular project. The problem is formulated as a multi-objective model with three objectives to optimally control the resources allocated to the service stations. Finally, we develop a simulated annealing (SA) algorithm to solve this multi-objective problem, using the goal attainment formulation. We also compare the SA results against the results of a discrete-time approximation of the original optimal control problem, to show the effectiveness of the proposed solution technique. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.

关键词： Project management Markov processes multiple objective programming Simulated annealing

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Second-Order Symmetric Duality for multiple objectives Nonlinear programming Under Generalizations of Cone-Preinvexity Functions

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JOURNAL OF SCIENTIFIC COMPUTING 2023年第1期95卷 1-15页

作者： Kassem, Mohamed Abd El-Hady Tanta Univ Fac Sci Math Dept Tanta Egypt

In this article, we present generalizations of the cone-preinvexity functions and study a pair of second-order symmetric solutions for multiple objective nonlinear programming problems under these generalizations of the cone-preinvexity functions. In addition, we establish and prove the theorems of weak duality, strong duality, strict converse duality, and self-duality by assuming the skew-symmetric functions under these generalizations of the cone-preinvexity functions. Finally, we provide four nontrivial numerical examples to demonstrate that the results of the weak and strong duality theorems are true.

关键词： multiple objective programming Second-order symmetric duality Nonlinear programming Duality theorems Cones Preinvexity functions 90-XX 90CXX

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Evaluating solutions and solution sets under multiple objectives

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第1期294卷 16-28页

作者： Karakaya, G. Koksalan, M. Middle East Tech Univ Dept Business Adm TR-06800 Ankara Turkey Univ Michigan Ross Sch Business Ann Arbor MI 48109 USA Middle East Tech Univ Dept Ind Engn TR-06800 Ankara Turkey

In this study we address evaluating solutions and solution sets that are defined by multiple objectives based on a function. Although any function can be used, we focus on mostly weighted Tchebycheff functions that can be used for a variety of purposes when multiple objectives are considered. One such use is to approximate a decision maker's preferences with a Tchebycheff utility function. Different solutions can be evaluated in terms of expected utility conditional on weight values. Another possible use is to evaluate a set of solutions that approximate a Pareto set. It is not straightforward to find the Pareto set, especially for large-size multi-objective combinatorial optimization problems. To measure the representation quality of approximate Pareto sets and to compare such sets with each other, there are some performance indicators such as the hypervolume measure, the epsilon indicator, and the integrated preference functional (IPF) measure. A Tchebycheff function based IPF measure can be used to estimate how well a set of solutions represents the Pareto set. We develop the necessary theory to practically evaluate solutions and solution sets. We develop a general algorithm and demonstrate it for two, three, and four objectives. (C) 2021 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Tchebycheff function Weight set partitioning

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An effective subgradient algorithm via Mifflin's line search for nonsmooth nonconvex multiobjective optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第2期319卷 505-516页

作者： Maleknia, Morteza Soleimani-damaneh, Majid Isfahan Univ Technol Dept Math Sci Esfahan *** Iran Univ Tehran Coll Sci Sch Math Stat & Comp Sci Tehran Iran

We propose a descent subgradient algorithm for unconstrained nonsmooth nonconvex multiobjective optimization problems. To find a descent direction, we present an iterative process that efficiently approximates the epsilon-subdifferential of each objective function. To this end, we develop a new variant of Mifflin's line search in which the subgradients are arbitrary and its finite convergence is proved under a semismooth assumption. To reduce the number of subgradient evaluations, we employ a backtracking line search that identifies the objectives requiring an improvement in the current approximation of the epsilon-subdifferential. Meanwhile, for the remaining objectives, new subgradients are not computed. Unlike bundle-type methods, the proposed approach can handle nonconvexity without the need for algorithmic adjustments. Moreover, the quadratic subproblems have a simple structure, and hence the method is easy to implement. We analyze the global convergence of the proposed method and prove that any accumulation point of the generated sequence satisfies a necessary Pareto optimality condition. Furthermore, our convergence analysis addresses a theoretical challenge in a recently developed subgradient method. Through numerical experiments, we observe the practical capability of the proposed method and evaluate its efficiency when applied to a diverse range of nonsmooth test problems.

关键词： multiple objective programming Nonlinear optimization Nonsmooth optimization Nonconvex programming Subgradient

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A practical multi-objective auction design and optimization framework for sponsored search

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OPERATIONS RESEARCH LETTERS 2023年第6期51卷 541-547页

作者： Li, Qian Wang, Liang Xia, Lirong Zheng, Wenxun Zhou, Yuxuan Shenzhen Res Inst Big Data Shenzhen Int Ctr Ind & Appl Math Shenzhen 518172 Peoples R China Alibaba Grp Hangzhou Peoples R China Rensselaer Polytech Inst New York NY USA Ant Grp Hangzhou Peoples R China

We propose a simple, flexible, efficient, and general framework for running large-scale highly-dynamic sponsored search auctions. Our framework aims at exploring optimal tradeoffs among various objectives of three parties: platform, advertisers, and users. We model the optimal tradeoffs as an online linear program problem, which can be addressed by a simple approach based on semi-Lagrangian duality. Experimental results conducted on large-scale real-world traffic show that the proposed framework can significantly improve all objectives considered, as well as the platform's revenue.(c) 2023 Elsevier B.V. All rights reserved.

关键词： Sponsored search multiple objective programming Online algorithm Semi-Lagrangian duality

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A multiple criteria decision making approach to manure management systems in the Netherlands

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2014年第3期232卷 643-653页

作者： Gebrezgabher, Solomie A. Meuwissen, Miranda P. M. Lansink, Alfons G. J. M. Oude PMB Int Water Management Inst Cantonments Accra Ghana Wageningen Univ NL-6706 KN Wageningen Netherlands

The intensification of livestock operations in the last few decades has resulted in an increased social concern over the environmental impacts of livestock operations and thus making appropriate manure management decisions increasingly important. A socially acceptable manure management system that simultaneously achieves the pressing environmental objectives while balancing the socio-economic welfare of farmers and society at large is needed. Manure management decisions involve a number of decision makers with different and conflicting views of what is acceptable in the context of sustainable development. This paper developed a decision-making tool based on a multiple criteria decision making (MCDM) approach to address the manure management problems in the Netherlands. This paper has demonstrated the application of compromise programming and goal programming to evaluate key trade-offs between socio-economic benefits and environmental sustainability of manure management systems while taking decision makers' conflicting views of the different criteria into account. The proposed methodology is a useful tool in assisting decision makers and policy makers in designing policies that enhance the introduction of economically, socially and environmentally sustainable manure management systems. (C) 2013 Elsevier B.V. All rights reserved.

关键词： multiple criteria decision making multiple objective programming Compromise programming Goal programming Analytical hierarchy process

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Solving the biobjective zero-one knapsack problem by an efficient LP-based heuristic

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第3期159卷 545-557页

作者： Zhang, CW Ong, HL Natl Univ Singapore Dept Ind & Syst Engn Singapore 119260 Singapore

In this paper, we propose a simple and useful method, the core of which is an efficient LP-based heuristic, for solving biobjective 0-1 knapsack problems. Extensive computational experiments show that the proposed method is able to generate a good approximation to the nondominated set very efficiently. We also suggest three qualitative criteria to evaluate such an approximation. In addition, the method can be extended to other problems having properties similar to the knapsack problem. (C) 2003 Elsevier B.V. All rights reserved.

关键词： integer programming multiple objective programming epsilon-nondominated solution LP-based heuristic Knapsack problem

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A multi-objective optimization model of component selection in enterprise information system integration

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COMPUTERS & INDUSTRIAL ENGINEERING 2018年 115卷 278-289页

作者： Mu, Lifeng Kwong, C. K. Shanghai Univ SHU UTS SILC Business Sch 20 Chengzhong Rd Shanghai 201899 Peoples R China Hong Kong Polytech Univ Hung Hom Dept Ind & Syst Engn Hong Kong Polytech Univ Kowloon Hong Kong Peoples R China

Integrating legacy IT assets and new commercial software components together into a flexible IT architecture is one of open challenges facing modern enterprises today. Most of previous studies focused on using re-engineering to improve the flexibility of IT architectures, rather than employing optimization theory in architecture design problem, especially the problem of component selection and re-allocation in IT architecture. Moreover, a scant amount of literature is available on considering the architectural flexibility and integration cost simultaneously. To fill in this gap, based on a modified quantitative method of measuring the relationship between couplings and cohesions in architecture, we devise a nonlinear multi-objective binary integer programming to select components from legacy candidates and commercial candidates, and to group them into services under the service-oriented architecture (SOA) environment. The customized SPEA2 algorithm is further used to solve the problem, and some managerial insights are provided based on experiments and sensitivity analysis with the model.

关键词： OR in software engineering Flexible IT architecture Enterprise information technologies Component selection multiple objective programming

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