Multiobjective Combinatorial Optimization — Theory, Methodology, and Applications

Ehrgott, Matthias; Gandibleux, Xavier

doi:10.1007/0-306-48107-3_8

Cited by 78 publications

(58 citation statements)

References 273 publications

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“…(2). Existing multiobjective formulations of classical combinatorial optimization problems with binary variables include multiobjective linear assignment problems [24,28], multiobjective knapsack problems [29,30], multiobjective maxcut problems [31], or multiobjective set covering and partitioning problems [28], just to mention a few. Nevertheless, the objective functions of such formulations are linear, and not quadratic as in mUBQP.…”

Section: Links With Existing Problem Formulationsmentioning

confidence: 99%

A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming

Liefooghe

Vérel

Hao

2014

Applied Soft Computing

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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 mUBQP instances with two and three objectives.

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Section: Links With Existing Problem Formulationsmentioning

confidence: 99%

A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming

Liefooghe

Vérel

Hao

2014

Applied Soft Computing

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“…5 and 6, and OF s are described in scenario details, the tool generates multi-objective optimized enactment plans which consider both maximizing profit and minimizing waiting time. In this way, the tool suggests: a resource for executing each activity, the start and end time of the activities, and the services which will be offered to each client (i.e., services which were not booked by the client) 9 . The generated optimized plans are then used to support the salon director in managing the working day in an optimized way.…”

Section: Condec-r Specificationmentioning

confidence: 99%

“…5) can be found. To solve multi-objective optimization problems (for more information, the reader is referred to [9]), there are, basically, three approaches: (i) defining a new objective function (i.e., combining the original objective functions) which can be optimized with single objective solvers (e.g., the weighted-sum method [1]), (ii) optimizing one of the objective functions constraining the other ones (e.g., ε-constraint method [13]), and (iii) working with a set of Pareto optimal solutions (e.g., evolutionary multi-objective optimization [6]). In this work, the ε-constraint method [13] is applied since it appeared well suited for our purposes and typically provides good results.…”

Section: Introductionmentioning

confidence: 99%

Generating Multi-objective Optimized Business Process Enactment Plans

Jiménez-Ramírez

Barba

Valle

et al. 2013

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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Abstract. Declarative business process (BP) models are increasingly used allowing their users to specify what has to be done instead of how. Due to their flexible nature, there are several enactment plans related to a specific declarative model, each one presenting specific values for different objective functions, e.g., completion time or profit. In this work, a method for generating optimized BP enactment plans from declarative specifications is proposed to optimize the performance of a process considering multiple objectives. The plans can be used for different purposes, e.g., providing recommendations. The proposed approach is validated through an empirical evaluation based on a real-world case study.

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“…Epsilon Constraint Method is one of the common approaches for dealing with multiobjective problems, which solves such problems by considering all objective functions as constraints and retaining only one of them in each phase as the main objective function (Ehrgott & Gandibleux, 2002). In this case, Pareto Border can be constructed by ε constraint method (Bérubé et al 2009).…”

Section: Solution Proceduresmentioning

confidence: 99%

A multi-objective model for locating distribution centers in a supply chain network considering risk and inventory decisions

Hamedani¹,

Jabalameli²,

Bozorgi-Amiri³

2013

10.5267/j.msl

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This paper presents a multi-objective location problem in a three level supply chain network under uncertain environment considering inventory decisions. The proposed model of this paper considers uncertainty for different parameters including procurement, transportation costs, supply, demand and the capacity of various facilities. The proposed model presents a robust optimization model, which specifies locations of distribution centers to be opened, inventory control parameters (r, Q), and allocation of supply chain components, concurrently. The resulted mixed-integer nonlinear programming minimizes the expected total cost of such a supply chain network comprising location, procurement, transportation, holding, ordering, and shortage costs. The model also minimizes the variability of the total cost of relief chain and minimizes the financial risk or the probability of not meeting a certain budget. We use the ε-constraint method, which is a multi-objective technique with implicit trade-off information given, to solve the problem and using a couple of numerical instances, we examine the performance of the proposed approach.

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Multiobjective Combinatorial Optimization — Theory, Methodology, and Applications

Cited by 78 publications

References 273 publications

A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming

A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming

Generating Multi-objective Optimized Business Process Enactment Plans

A multi-objective model for locating distribution centers in a supply chain network considering risk and inventory decisions

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