Heterogeneous multi-agent evolutionary system for solving parametric interval linear systems

Abstract

The problem of computing the hull, that is the tightest interval enclosure of the solution set for linear systems with parameters being nonlinear functions of interval parameters, is an NP-hard problem. However, since the problem of computing the hull can be considered as a combinatorial or as a constrained optimisation problem, metaheuristic techniques might be helpful. Alas, experiments performed so far show that they are time consuming and their performance may depend on the problem size and structure, therefore some acceleration and stabilisation techniques are required. In this paper, a new approach which rely on a multi-agent system is proposed. The idea is to apply evolutionary method and differential evolution for different agents working together to solve constrained optimisation problems. The results obtained for several examples from structural mechanics involving many parameters with large uncertainty ranges show that some synergy effect of the metaheuristics can be achieved, especially for problems of a larger size. © 2013 Springer-Verlag.