Random search optimization approach for highly multi-modal nonlinear problems

The paper addresses a random search optimization method for nonlinear problems with continuous variables. The approach called LJ-MM algorithm, deals with both unconstrained and constrained optimization problems. The algorithm was developed (in the basis of the so called Luus-Jaakola (LJ) one, which was successfully used by several researchers to solve chemical and process engineering problems. The LJ-MM approach is aimed at highly multi-modal problems with sharp peaks, The major change in comparison with the LJ algorithm consists in different scheme of search space reduction rate. The tests carried out for several unconstrained and constrained problems proved its high performance for multi-modal problems with sharp peaks in particular. Also, they showed that it is the robust solver even in cases of problems with a smoother function. In all cases the performance of the LJ-MM approach depends only slightly on starting points and parameter setting. The detailed analysis of the test results and the comparison with the original LJ algorithm and others stochastic solvers is given in the paper. (c) 2005 Elsevier Ltd. All rights reserved.