An Efficient Pareto Set Identification Approach for Multiobjective Optimization on Black-Box Functions

Abstract

Both multiple objectives and computation-intensive black-box functions often exist simultaneously in engineering design problems. Few of existing multi-objective optimization approaches addresses problems with expensive black-box functions. In this paper, a new method called the Pareto set pursuing (PSP) method is developed.By developing sampling guidance functions based on approximation models, this approach progressively provides a designer with a rich and evenly distributed set of Pareto optimal points. This work describes PSP procedures in detail. From testing and design application, PSP demonstrates considerable promises in efficiency, accuracy, and robustness. Properties of PSP and differences between PSP and other approximation-based methods are also discussed. It is believed that PSP has a great potential to be a practical tool for multi-objective optimization problems.

A survey on handling computationally expensive multiobjective optimization problems using surrogates: non-nature inspired methods

“…In [21], a sampling-based method called Pareto Set Pursuing (PSP) is introduced, which is an extension of the Mode Pursuing Sampling (MPS) method proposed in [88]. In Step 1 of PSP, initial points are sampled randomly.…”

“…In [89], the PSP method [21] is modified for mixed integer MOPs as the MV-PSP method. In the MV-PSP method, the basic idea of employing a surrogate problem is similar to the PSP method.…”

“…When the Pareto fitness G i is greater than 1, the corresponding feasible solution is a non-dominated solution [21].…”

Interconnected performance optimization in complex robotic systems

“…Thereby these approaches reduce the problem to a single-objective optimization problem whose solution is biased by the chosen weights. There exist recent approaches that incorporate estimation methods for those unknown functions [11], but they concentrate only on identifying the Pareto-optimal set and not on explicitly determining the functional relationships.…”

A multi-objective metamodel-assisted memetic algorithm with strength-based local refinement

“…In the literature, a considerable number of papers appeared on the use of surrogate evaluation models or metamodels to assist global search (GS ) methods, Shan and Wang (2005), such as the Evolutionary Algorithms (EAs), Madsen et al (2000), Ong et al (2000), Ulmer et al (2004Ulmer et al ( , 2003, Jin et al (2000), Buche et al (2005), Lim et al (2008). These 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 Giannakoglou (2002), Keane and Nair (2005), Jin et al (2002).…”