On heuristic hybrid methods and structured point sets in global continuous optimization

Abstract

Heikki Maaranen tutki väitöskirjassaan kuinka globaalin optimoinnin menetelmiä jatkuvien muuttujien tehtäville voidaan parantaa hybridisointia ja strukturaalisia pistejoukkoja käyttämällä.

In this work, we concentrate on improving the performance of global methods for continuous optimization via hybridization and the use of structured point sets. Optimization is an important part of solving real-life problems. The problem solving process involves modeling, simulation and optimization of the simulated model, after which the results can be applied into practice, for example, in product manufacturing. Many of the real-life problems can be formulated as global continuous optimization problems. Efficient global optimization methods are needed because realistic mathematical models are often very complex with nonconvex objective functions.Hybridization is widely recognized to be one of the most attractive areas of method development. By hybridization we mean a combination of different methods or elements. Through hybridization, it is possible to form new methods that posses the strengths, but not the weaknesses of the original elements. Here, we construct new hybrid methods based on popular metaheuristics. We combine a simulated annealing with the proximal bundle method and a real-coded genetic algorithm with the Nelder-Mead simplex method and are able to improve both the efficiency and the reliability of the original algorithms. In addition, we form interdisciplinary hybrids by using structured point sets such as quasi random sequences and spatial point processes in initial populations of a real-coded genetic algorithm. We study the properties of the point generators and test what effects the different initial populations have on the objective function value. We also point out some difficulties in method comparison. We show that the change of test problems or other test settings may strongly affect the outcome of the comparison.The efficiency of all the methods developed is evaluated through numerical experiments. In general, we show that hybridization, in its different forms, may be a very useful tool for improving the performance of existing methods.