A Performance Analysis of Basin Hopping Compared to Established Metaheuristics for Global Optimization

During the last decades many metaheuristics for global numerical optimization have been proposed. Among them, Basin Hopping is very simple and straightforward to implement, although rarely used outside its original Physical Chemistry community. In this work, our aim is to compare Basin Hopping, and two population variants of it, with readily available implementations of the well known metaheuristics Differential Evolution, Particle Swarm Optimization, and Covariance Matrix Adaptation Evolution Strategy. We perform numerical experiments using the IOH profiler environment with the BBOB test function set and two difficult real-world problems. The experiments were carried out in two different but complementary ways: by measuring the performance under a fixed budget of function evaluations and by considering a fixed target value. The general conclusion is that Basin Hopping and its newly introduced population variant are almost as good as Covariance Matrix Adaptation on the synthetic benchmark functions and better than it on the two hard cluster energy minimization problems. Thus, the proposed analyses show that Basin Hopping can be considered a good candidate for global numerical optimization problems along with the more established metaheuristics, especially if one wants to obtain quick and reliable results on an unknown problem.

Doubly Stochastic Matrix Models for Estimation of Distribution Algorithms

Problems with solutions represented by permutations are very prominent in combinatorial optimization. Thus, in recent decades, a number of evolutionary algorithms have been proposed to solve them, and among them, those based on probability models have received much attention. In that sense, most efforts have focused on introducing algorithms that are suited for solving ordering/ranking nature problems. However, when it comes to proposing probability-based evolutionary algorithms for assignment problems, the works have not gone beyond proposing simple and in most cases univariate models. In this paper, we explore the use of Doubly Stochastic Matrices (DSM) for optimizing matching and assignment nature permutation problems. To that end, we explore some learning and sampling methods to efficiently incorporate DSMs within the picture of evolutionary algorithms. Specifically, we adopt the framework of estimation of distribution algorithms and compare DSMs to some existing proposals for permutation problems. Conducted preliminary experiments on instances of the quadratic assignment problem validate this line of research and show that DSMs may obtain very competitive results, while computational cost issues still need to be further investigated.