A global optimization algorithm and a multicriteria optimization algorithm are developed based on the genetic algorithm(GA). Firstly, a new and efficient global optimization algorithm is developed by combining the new filled function method with the GA. The GA supplies a good initial point for the local optimization procedure based on the filled function and it moves the population toward the better local minima. By introducing the penalty function in the GA step, the local minima previously found is discarded and the tunneling effect can be embodied. In the filled function procedure, the conventional local optimization algorithm is used to obtain a better point than the current minimum. The new filled function is based on the convex homotopy concept. It is a convex combination of the object function and of a special function designed for the global convexity. By minimizing the proposed filled function, we can get a point that is lower than the current minimum or that has the same value as the current minimum or that is included in the lower minimum basin.
Secondly, a new method for the generation of a Pareto optimal set is developed for multicriteria optimization problems based on the GA and the global criterion method(GCM). This method results in many Pareto optima almost uniformly distributed on the minimal space and the designer can achieve the highest design degree by selecting the solution among these Pareto solutions. Proposed algorithm utilizes the GA to improve current non-inferior solutions and finally to obtain many Pareto optima at one time. In the GA procedure, the population is separated into two groups, non-inferior points and inferior points, according to the definition of Pareto optimal solution. Non-inferior points have higher probability to survive in the next generation. The GCM is used to obtain the highly evolved points in the current generation. The solution obtained in the GCM procedure is represented as a bit string form and is included in the GA procedure. This information helps the current non-inferior points to converge to minimal space quickly. In the GCM procedure, a conventional local optimization algorithm is used. Since the GA is a global optimization algorithm, however, the presented algorithm has the global property. So the non-convex problem can also be solved by the proposed algorithm. Sharing concept of objective functions is applied to the algorithm for uniformly distributed Pareto optima.
The global optimization algorithm is tested by some test typical functions and a 4-bar link synthesis problem. The results show that the present algorithm is superior to the previous algorithms in view of efficiency and reliability. The algorithm also gives a solution suggested by MSPS and a more exact solution than that of MSPS for the 4-bar link synthesis problem. The proposed multicriteria algorithm is also tested by some test functions and a cutting problem. The results show that the proposed algorithm produces a Pareto optimal set in short time by one process. Especially, it gives an almost exact optimal set even for the non-convex test functions.
