A square lattice probability model for optimising the Graph Partitioning Problem

Abstract

Estimation of Distribution Algorithms have proved to be very competitive for solving combinatorial and continuous optimisation problems. However, there are problems for which they have not been extensively developed: we refer to constrained optimisation problems. Existing proposals approach these problems by (i) modifying the sampling strategy of the probabilistic model to allow feasible solutions or (ii) adopting general approaches used in the context of heuristic optimisation such as penalisation. Nonetheless, from a theoretical point of view, little progress have been given in the context of EDAs when developing algorithms designed specifically to solve constrained problems. In this paper, we propose developing EDAs by introducing probability models defined exclusively on the space of feasible solutions. In this sense, we give a first approach by taking the Graph Partitioning Problem (GPP) as a case of study, and present a probabilistic model defined exclusively on the feasible region of solutions: a square lattice probability model. The experiments conducted on a benchmark of 22 artificial instances confirm the effectiveness of the proposal in terms of quality of solutions and execution time.