Evolutionary Algorithms for Solving Unconstrained, Constrained and Multi-objective Noisy Combinatorial Optimisation Problems

TL;DR

This paper empirically evaluates various evolutionary algorithms on noisy combinatorial optimization problems, demonstrating that UMDA and PCEA are robust and effective, especially on complex and multi-objective problems.

Contribution

It provides a comprehensive empirical comparison showing UMDA and PCEA outperform others on noisy combinatorial problems, including multi-objective cases.

Findings

UMDA and PCEA handle noise robustly in toy problems.

UMDA outperforms PCEA on complex problems.

UMDA variants excel in noisy multi-objective optimization.

Abstract

We present an empirical study of a range of evolutionary algorithms applied to various noisy combinatorial optimisation problems. There are three sets of experiments. The first looks at several toy problems, such as OneMax and other linear problems. We find that UMDA and the Paired-Crossover Evolutionary Algorithm (PCEA) are the only ones able to cope robustly with noise, within a reasonable fixed time budget. In the second stage, UMDA and PCEA are then tested on more complex noisy problems: SubsetSum, Knapsack and SetCover. Both perform well under increasing levels of noise, with UMDA being the better of the two. In the third stage, we consider two noisy multi-objective problems (CountingOnesCountingZeros and a multi-objective formulation of SetCover). We compare several adaptations of UMDA for multi-objective problems with the Simple Evolutionary Multi-objective Optimiser (SEMO) and NSGA-II. We conclude that UMDA, and its variants, can be highly effective on a variety of noisy combinatorial optimisation, outperforming many other evolutionary algorithms.