On the Performance of Multi-Objective Estimation of Distribution Algorithms for Combinatorial Problems

Abstract

Fitness landscape analysis investigates features with a high influence on the performance of optimization algorithms, aiming to take advantage of the addressed problem characteristics. In this work, a fitness landscape analysis using problem features is performed for a Multi-objective Bayesian Optimization Algorithm (mBOA) on instances of MNK-landscape problem for 2, 3, 5 and 8 objectives. We also compare the results of mBOA with those provided by NSGA-III through the analysis of their estimated runtime necessary to identify an approximation of the Pareto front. Moreover, in order to scrutinize the probabilistic graphic model obtained by mBOA, the Pareto front is examined according to a probabilistic view. The fitness landscape study shows that mBOA is moderately or loosely influenced by some problem features, according to a simple and a multiple linear regression model, which is being proposed to predict the algorithms performance in terms of the estimated runtime. Besides, we conclude that the analysis of the probabilistic graphic model produced at the end of evolution can be useful to understand the convergence and diversity performances of the proposed approach.

A regression analysis of the impact of routing and packing dependencies on the expected runtime

“…Cost models are őtness landscapes methods that can help predicting the performance of algorithms by identifying features that make a problem more or less difficult to solve. These models can can be expressed as linear, multiple regression models [20], decision trees [24], or other models of features and search cost; also, some models are more amendable to human interpretation than others. To aid interpretability, the features are extracted from the problem structure and the model can at times explain their inŕuence in the difficulty level during the search [9].…”