A Box-constrained Multi-Objective Derivative Free Optimization Algorithm Based on Global Search Strategy of Sparse Surrogate Model

In practical applications, it is common to have optimization problems that have multiple conflicting objective functions which are computationally expensive or do not have analysis formulas. These functions present the application of traditional derivative-based techniques. This paper proposes a new box-constrained multi-objective derivative free optimization (DFO) algorithm for solving such kind problems, which inspired by the search/poll paradigm of direct multisearch and utilized the concept of Pareto dominance to obtain a list of non-dominated points. The purpose of this paper is to generate a better approximation of the Pareto front with a reduced number of function evaluations. To achieve this, a global search strategy based on surrogate model is devised for the search step. Within this strategy, a high-dimensional statistical approach is employed to address the modeling challenges posed by insufficient samples. Moreover, the NP-hard parameter optimization model is approximately transformed into a linear programming one for formulating the surrogate model, upon which the non-dominated points within the entire feasible region are computed. In addition, the surrogate model is built and updated dynamically in the iteration process. Finally, the numerical experiments demonstrate that the proposed algorithm is comparable and competitive.