An effective method based on the angular constraint to detect Pareto points in bi-criteria optimization problems

The most important issue in multi-objective optimization problems is to determine the Pareto points along the Pareto frontier. If the optimization problem involves multiple conflicting objectives, the results obtained from the Pareto-optimality will have the trade-off solutions that shaping the Pareto frontier. Each of these solutions lies at the boundary of the Pareto frontier, such that the improvement in one of the objectives results in the worsening of at least one of the other objectives. Usually, it is not economical to generate the entire Pareto surface due to the high computational cost for function evaluations. Therefore, it is important to get a uniform distribution at the Pareto points in the Pareto frontier.  In this paper, an efficient method based on angular constraint is presented for finding a suitable approximation of the Pareto front of bi-objective optimization problems. In order to get a better distribution of points at the Pareto front it is used a strategy following closer the main shape of the frontier. To get only the global Pareto points, this strategy sweeps the objective space just once, getting automatically rid-off the non-Pareto and local Pareto points, without any further filtering. The researcher, after proposing an algorithm for the operation of the method, compare its efficiency in one test problem with methods such as weighted sum (WS) and epsilon-constraint methods. The obtained experimental results show that the proposed method is efficient and in most situations more accurate.