Multiobjective optimization techniques

Abstract

In this dissertation, multiobjective simulated annealing method is introduced and discussed with the evolutionary approach. There have been many researches of using evolutionary algorithms to solve multiobjective problems and many efficient algorithms have been developed. However, though the simulated annealing is also very powerful search algorithm and has shown good results in various optimization fields, it has been seldom used for the multiobjective optimization because it conventionally uses only one search agent, which is inadequate in finding all the solutions of the Pareto set. With the idea that simulated annealing has a uniform state probability over global optima, a new multiobjective simulated annealing method is suggested. The suggested algorithm uses the Pareto-based cost and the mathematical convergence of the algorithm to the global optimum is proved. The preliminary results of the developed algorithms are compared with multiobjective evolutionary algorithms and shows that simulated annealing has good properties in many cases. The first test in the finite state test-beds shows that simulated annealing has a tendency of finding the Pareto optimal solutions with nearly uniform probability. This property was tested on the more complex real-valued continuous problems. For the comparison, multiobjective metrics to test the performances are surveyed and developed. Four categories of metrics are suggested to measure various properties of multiobjective optimization algorithms. The accuracy, coverage, uniformity, and speed metrics are used in the experiment. Also a practical application of voltage reference circuit design is introduced for the real world test problem. The results show that multiobjective simulated annealing outperforms the multiobjective evolutionary algorithms in many times and suggest that simulated annealing can be a good candidate algorithm in solving the real-world multiobjective optimization problems.