Authors: Stanojević, Bogdana 
Glover, Fred
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: A new approach to generate pattern-efficient sets of non-dominated vectors for multi-objective optimization
Journal: Information Sciences
Volume: 530
First page: 22
Last page: 42
Issue Date: 1-Aug-2020
Rank: M21a
ISSN: 0020-0255
DOI: 10.1016/j.ins.2020.04.040
Pareto optimality is the fundamental construct employed to determine whether a given solution to a multi-criteria mathematical optimization model is preferred to another solution. In this paper we describe an approach (Pattern Efficient Set Algorithm – PESA) to generating a pattern-efficient set of non-dominated vectors to a multi-objective optimization problem. Our approach incorporates an optimization model designed to yield certain non-dominated vectors that can fill gaps between already generated non-dominated vectors, providing a way to deal with the adjacency of generated non-dominated vectors and to quantify the gaps between them. We also propose a pseudo-randomized variant of PESA (rPESA) that randomly generates hypothetical bounds for the objective functions and uses them in the optimization model.

To test our approach we selected ten problems from the literature, including bi-objective, 3-objective, 5-objective and 10-objective test instances with non-convex, disconnected or continuous Pareto. The inverted generational distance (IGD) and the hyper-volume (HV) are used as performance metrics to measure the quality of the obtained approximations. We also present graphically the numerical results from applying our method.
Keywords: Multiple objectives | Efficient frontier | Pattern efficiency | Diversified representations
Publisher: Elsevier

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