Directed search domain: a method for even generation of the Pareto frontier in multiobjective optimization

Optimization is one of the most important and challenging parts of any engineering design. In real-world design, multiobjective optimization with constraints has to be considered. The optimal solution in this case is not unique because the objectives can contradict each other. Therefore, a set of optimal solutions, which forms the Pareto frontier, should be considered. There are many algorithms to generate a Pareto set. However, only a few of them are potentially capable of providing an evenly distributed set of solutions. This property is especially important in real-life design because a decision maker is usually able to analyse only a very limited number of solutions. The main objective of this article is to develop and give detailed description of an algorithm that is able to generate an evenly distributed Pareto set in a general formulation. The approach is based on shrinking a search domain to generate a Pareto optimal solution in a selected area on the Pareto frontier. The effectiveness of the algorithm is demonstrated by a number of challenging test cases. For the first time, some of these test cases are successfully solved via a classical approach. © 2011 Taylor & Francis.