An Improved Weighted Sum Algorithm For Multi-objectie Optimization Problems

In the real world problems, many have more than one objective under consideration. For example, invest problems, not only the lowest cost of investment but also the highest revenue is expected. This results in a multi-objective optimization problem (MOP).With the development of computer science, MOP is widely used in engineering design, economics, finance, management and so on. But, by far MOP has not been solved perfectly yet. In recent years, genetic algorithm (GA) is widely used in MOP, and has a good performance. But GA usually needs large computation cost and is lack of complete theory.Among these algorithms, the weighed sum method is still one of the most widely used algorithms, which are simple, easy to understand and efficient. But it has two disadvantages:(1) the solutions found usually can not be uniformly distributed; (2) it can't find solutions that lie in the nonconvex regions of the Pareto front.An improved weighted sum method is proposed in this paper and it can overcome the shortcomings mentioned above. In fact, some new constraints are added in the weighted sum method and they can limit the range of the search area and force the search in the nonconvex regions of the Patreto front. At the same time, the added constraints guarantee the distance between the solutions. As a result, the solutions found will have a better distribution. The simulations on standard benchmark problems are made and the results indicate that the proposed algorithm can find good distributed solutions along the Pareto front.