Efficient Noisy Optimisation with the Sliding Window Compact Genetic Algorithm

TL;DR

This paper enhances the compact Genetic Algorithm for noisy optimization by introducing variations that reuse evaluated individuals through multiple comparisons or sliding window comparisons, significantly improving performance.

Contribution

The paper proposes two simple modifications to the compact Genetic Algorithm that improve its efficiency in noisy environments by better utilizing each fitness evaluation.

Findings

Both variations outperform the standard cGA on noisy test problems.

The sliding window approach maintains simplicity while improving robustness.

Multiple comparisons per iteration lead to more reliable convergence.

Abstract

The compact genetic algorithm is an Estimation of Distribution Algorithm for binary optimisation problems. Unlike the standard Genetic Algorithm, no cross-over or mutation is involved. Instead, the compact Genetic Algorithm uses a virtual population represented as a probability distribution over the set of binary strings. At each optimisation iteration, exactly two individuals are generated by sampling from the distribution, and compared exactly once to determine a winner and a loser. The probability distribution is then adjusted to increase the likelihood of generating individuals similar to the winner. This paper introduces two straightforward variations of the compact Genetic Algorithm, each of which lead to a significant improvement in performance. The main idea is to make better use of each fitness evaluation, by ensuring that each evaluated individual is used in multiple win/loss comparisons. The first variation is to sample $n>2$ individuals at each iteration to make $n(n-1)/2$ comparisons. The second variation only samples one individual at each iteration but keeps a sliding history window of previous individuals to compare with. We evaluate methods on two noisy test problems and show that in each case they significantly outperform the compact Genetic Algorithm, while maintaining the simplicity of the algorithm.