Numerical algorithms for generating an almost even approximation of the Pareto front in nonlinear multi-objective optimization problems

A multiobjective optimization problem (MOP) returns a set of non-dominated points, the so-called Pareto front. Since this set is usually infinite, it is impossible to generate it completely in practice. Therefore, a discrete approximation of the Pareto front is created. One of the most important features of this approximation is a uniform distribution of points on the full Pareto front in order to present a wide variety of solutions to the decision maker who chooses a final solution. While a few algorithms consider this property, two algorithms based on the Pascoletti-Serafini (PS) scalarization approach are proposed. In addition, six well-known test problems with convex and non-convex Pareto fronts are considered to show the effectiveness of the proposed algorithms. Their results are compared with some algorithms including Normal Constraint (NC), Benson type, Non-Dominated Sorting Genetic Algorithm-II (NSGA-II), S-Metric Selection Evolutionary Multiobjective Algorithm (SMS-EMOA), Differential Evolution (DE) with Binomial Crossover and MOEA/D-DE. The computational results on CPU time and reasonable distribution of points obtained on the Pareto front show that the presented algorithms perform better than other algorithms on these criteria. In addition, although the proposed algorithms compete closely with some algorithms in terms of CPU time, they have more non-dominated solutions and more appropriate distribution than they do in most problems.