Dividing rectangles attack multi-objective optimization

Decomposition-based evolutionary algorithms have been applied with success to multi-objective optimization problems where they are broken into several subproblems, and solutions for the original problem are recognized in a coordinated manner. Motivated by the working principle of decomposition-based methods, viz. the “divide-and-conquer” paradigm; this paper is concerned with solving black-box multi-objective problems given a finite number of function evaluations by taking inspiration from the single-objective deterministic sampling method, DIRECT. In particular, we provide a multi-objective algorithmic instance of DIRECT, which we refer to as MO-DIRECT and investigate its performance with respect to established decomposition-based multi-objective techniques. Besides its asymptotic convergence to the Pareto front and its inherent balance between exploration and exploitation of the decision space, the proposed framework is flexible enough to incorporate indicator-based techniques, albeit at the cost of a greater space complexity when compared to the evolutionary counterpart.