Landscape-Aware Performance Prediction for Evolutionary Multiobjective Optimization

Abstract

We expose and contrast the impact of landscape characteristics on the performance of search heuristics for black-box multi-objective combinatorial optimization problems. A sound and concise summary of features characterizing the structure of an arbitrary problem instance is identified and related to the expected performance of global and local dominancebased multi-objective optimization algorithms. We provide a critical review of existing features tailored to multi-objective combinatorial optimization problems, and we propose additional ones that do not require any global knowledge from the landscape, making them suitable for large-size problem instances. Their intercorrelation and their association with algorithm performance are also analyzed. This allows us to assess the individual and the joint effect of problem features on algorithm performance, and to highlight the main difficulties encountered by such search heuristics. By providing effective tools for multiobjective landscape analysis, we highlight that multiple features are required to capture problem difficulty, and we provide further insights into the importance of ruggedness and multimodality to characterize multi-objective combinatorial landscapes.

Dominance, Indicator and Decomposition Based Search for Multi-objective QAP: Landscape Analysis and Automated Algorithm Selection

“…In terms of parameters, NSGA-II, IBEA and MOEA/D all use a population of size of 100, an exchange mutation with a rate of 0.2, and a partially-mapped crossover [10] with a rate of 0.95. Preliminary experiments revealed that using the partiallymapped crossover allows the search process to reach better quality in more than 90% of the cases, compared against the 2-point crossover used in a previous setting [15]. All the algorithms stop after 1 000 000 evaluations.…”

“…We start our analysis by characterizing mQAP instances with relevant features from the literature. We rely on the multi-objective landscape features introduced in [15], and particularly on local features, based on sampling, that do not require any prior knowledge about the solution space enumeration and/or the Pareto set. We start by recalling their definition.…”

“…1, and N : X → 2 X is a neighborhood relation based on the exchange operator, that consists in exchanging the locations of two facilities. The considered features are based on different measures computed on a sample of solutions extracted from a walk over the multi-objective landscape [15]. A walk is an ordered sequence of solutions (x 0 , x 1 , .…”

“…In a recent paper [15], we revised landscape features for multi-objective combinatorial optimization by building upon those previous studies, and by deriving additional low-cost landscape features that were revealed as highly impactful for EMO algorithms. In this paper, we are interested in analyzing the impact of mQAP instance characteristics on higher-level landscape features, such as ruggedness and multimodality.…”

“…(1) We characterize the landscape of large-scale mQAP instances with different properties by means of local multi-objective features from [15]; (2) We relate mQAP landscape features with the performance of a dominance-, an indicator-, and a decomposition-based EMO algorithm [6,29,28]; (3) We investigate the performance of feature-based automated algorithm selection by measuring its ability to discriminate between EMO algorithms, and by carefully calibrating the budget allocated to features and search.…”