A parallel multiple reference point approach for multi-objective optimization

Figueira, José Rui; Liefooghe, Arnaud; Talbi, El‐Ghazali; Wierzbicki, Andrzej P.

doi:10.1016/j.ejor.2009.12.027

Cited by 60 publications

(20 citation statements)

References 31 publications

(37 reference statements)

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“…Thiele et al [47] proposed a modification of the Indicator Based Evolutionary Algorithm (IBEA) [52] called the Preference Based Evolutionary Algorithm (PBEA), where the binary quality indicator of IBEA is redefined using an achievement scalarizing function and one or several reference points. Later, Figueira et al [22] made use of PBEA in the Parallel Multiple Reference Point Evolutionary Algorithm (PMRPEA). In this method, the area between the worst and the best (preferred) objective values given by the DM is explored by solving multiple PBEAs in parallel.…”

Section: Introductionmentioning

confidence: 99%

A preference-based evolutionary algorithm for multiobjective optimization: the weighting achievement scalarizing function genetic algorithm

2014

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When solving multiobjective optimization problems, preference-based evolutionary multiobjective optimization (EMO) algorithms introduce preference information into an evolutionary algorithm in order to focus the search for objective vectors towards the region of interest of the Pareto optimal front. In this paper, we suggest a preference-based EMO algorithm called weighting achievement scalarizing function genetic algorithm (WASF-GA), which considers the preferences of the decision maker (DM) expressed by means of a reference point. The main purpose of WASF-GA is to approximate the region of interest of the Pareto optimal front determined by the reference point, which contains the Pareto optimal objective vectors that obey the preferences expressed by the DM in the best possible way. The proposed approach is based on the use of an achievement scalarizing function (ASF) and on the classification of the individuals into several fronts. At each generation of WASF-GA, this classification is done according to the values that each solution takes on the ASF for the reference point and using different weight vectors. These vectors of weights are selected so that the vectors formed by their inverse components constitute a well-distributed representation of the weight vectors space. The efficiency and usefulness of WASF-GA is shown in several test problems in comparison to other preference-based EMO algorithms. Regarding a metric based on the hypervolume, we can say that WASF-GA has outperformed the other algorithms considered in most of the problems.

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Section: Introductionmentioning

confidence: 99%

A preference-based evolutionary algorithm for multiobjective optimization: the weighting achievement scalarizing function genetic algorithm

2014

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“…They are simpler and require less expert effort than a priori methods, need moderate computational requirements, and the decision maker can effectively control the search process (Branke et al 2008). As already stated, one of the most extended methods to introduce preferences interactively in MOMHs is using reference points (Molina et al 2009;Ben Said et al 2010;Figueira et al 2010). The advantage of this approach is that it can return an approximation to the Pareto set and not simply projected solutions.…”

Section: The Need For Modelling Interactive Preferencesmentioning

confidence: 99%

Interactive preferences in multiobjective ant colony optimisation for assembly line balancing

et al. 2014

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In this contribution, we propose an interactive multicriteria optimisation framework for the time and space assembly line balancing problem. The framework allows decision maker interaction by means of reference points to obtain the most interesting non-dominated solutions. The principal components of the framework are the g-dominance preference scheme and a state-of-the-art memetic multiobjective ant colony optimisation approach. In addition, the framework includes a novel adaptive multi-colony mechanism to be able to handle the preferences in an interactive way. Results show how the multiobjective framework can interactively obtain the most useful solutions with higher convergence than previous a priori methods. The experimentation also makes use of original data of the Nissan Pathfinder engine and practical bounds to define industrially feasible solutions in a set of scenarios. By solving the problem in these scenarios, we show the search guidance advantages of Communicated by V. Loia.

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“…On the contrary, the achievement scalarizing function potentially enables the identification of both supported and non-supported Pareto optimal solutions [40]. Successful integrations of the achievement scalarizing function into evolutionary multiobjective optimization algorithms can be found elsewhere [44,45,46]. However, in existing approaches, the parameters of the achievement scalarizing function are usually kept static or randomly chosen throughout the search process, whereas they are adapted to appropriate values according to the current state of the search process in the HM proposed in the paper, as will be detailed in Section 3.5.…”

Section: Achievement Scalarizing Functionmentioning

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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A parallel multiple reference point approach for multi-objective optimization

Cited by 60 publications

References 31 publications

A preference-based evolutionary algorithm for multiobjective optimization: the weighting achievement scalarizing function genetic algorithm

A preference-based evolutionary algorithm for multiobjective optimization: the weighting achievement scalarizing function genetic algorithm

Interactive preferences in multiobjective ant colony optimisation for assembly line balancing

A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming

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