HyperSPAM: A study on hyper-heuristic coordination strategies in the continuous domain

Abstract

This article proposes a simplistic algorithmic framework, namely hyperSPAM, composed of three search algorithms for addressing continuous optimisation problems. The Covariance Matrix Adaptation Evolution Strategy (CMAES) is activated at the beginning of the optimisation process as a preprocessing component for a limited budget. Subsequently, the produced solution is fed to the other two single-solution search algorithms. The first performs moves along the axes while the second makes use of a matrix orthogonalization to perform diagonal moves.Four coordination strategies, in the fashion of hyperheuristics, have been used to coordinate the two single-solution algorithms. One of them is a simple randomized criterion while the other three are based on a success based reward mechanism. The four implementations of the hyperSPAM framework have been tested and compared against each other and modern metaheuristics on an extensive set of problems including theoretical functions and real-world engineering problems.Numerical results show that the different versions of the framework display broadly a similar performance. One of the reward schemes appears to be marginally better than the others. The simplistic random coordination also displays a very good performance. All the implementations of hyperSPAM significantly outperform the other algorithms used for comparison.