Andrei Lissovoi;Pietro S. Oliveto;John Alasdair Warwicker
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引用次数: 31
Abstract
Selection hyper-heuristics (HHs) are randomised search methodologies which choose and execute heuristics during the optimisation process from a set of low-level heuristics. A machine learning mechanism is generally used to decide which low-level heuristic should be applied in each decision step. In this article, we analyse whether sophisticated learning mechanisms are always necessary for HHs to perform well. To this end we consider the most simple HHs from the literature and rigorously analyse their performance for the LeadingOnes benchmark function. Our analysis shows that the standard Simple Random, Permutation, Greedy, and Random Gradient HHs show no signs of learning. While the former HHs do not attempt to learn from the past performance of low-level heuristics, the idea behind the Random Gradient HH is to continue to exploit the currently selected heuristic as long as it is successful. Hence, it is embedded with a reinforcement learning mechanism with the shortest possible memory. However, the probability that a promising heuristic is successful in the next step is relatively low when perturbing a reasonable solution to a combinatorial optimisation problem. We generalise the “simple” Random Gradient HH so success can be measured over a fixed period of time τ, instead of a single iteration. For LeadingOnes we prove that the Generalised Random Gradient (GRG) HH can learn to adapt the neighbourhood size of Randomised Local Search to optimality during the run. As a result, we prove it has the best possible performance achievable with the low-level heuristics (Randomised Local Search with different neighbourhood sizes), up to lower-order terms. We also prove that the performance of the HH improves as the number of low-level local search heuristics to choose from increases. In particular, with access to k low-level local search heuristics, it outperforms the best-possible algorithm using any subset of the k heuristics. Finally, we show that the advantages of GRG over Randomised Local Search and Evolutionary Algorithms using standard bit mutation increase if the anytime performance is considered (i.e., the performance gap is larger if approximate solutions are sought rather than exact ones). Experimental analyses confirm these results for different problem sizes (up to n=108) and shed some light on the best choices for the parameter τ in various situations.
期刊介绍:
Evolutionary Computation is a leading journal in its field. It provides an international forum for facilitating and enhancing the exchange of information among researchers involved in both the theoretical and practical aspects of computational systems drawing their inspiration from nature, with particular emphasis on evolutionary models of computation such as genetic algorithms, evolutionary strategies, classifier systems, evolutionary programming, and genetic programming. It welcomes articles from related fields such as swarm intelligence (e.g. Ant Colony Optimization and Particle Swarm Optimization), and other nature-inspired computation paradigms (e.g. Artificial Immune Systems). As well as publishing articles describing theoretical and/or experimental work, the journal also welcomes application-focused papers describing breakthrough results in an application domain or methodological papers where the specificities of the real-world problem led to significant algorithmic improvements that could possibly be generalized to other areas.