The sequential optimization-constraint multi-objective problem and its applications for robust planning of robot paths

In this paper a new approach to search for diverse solutions for a multi-objective problem is presented. Commonly, a search for solutions for a multi-objective problem, which is aimed at optimization, results in a set of Pareto optimal solutions. There are cases where more solutions should be also considered, nonetheless preserving the optimization inspiration. These solutions should not resemble the Pareto set, so as to provide diversity within the design space, and therefore they might not always be found by taking an epsilon-Pareto approach. With this motivation in mind, an already established method, which searches for diverse solutions, which are not all necessarily optimal, is herewith discussed and its shortages are highlighted. In contrast to the already established design method, the approach taken in this paper is to solve the multi-objective problem repeatedly, adding (automatically or interactively) at each run constraints, which are constructed, based on the obtained Pareto set. The motivation for the introduced approach comes from the need to generate a set of robot paths, which allow a mobile robot operator, flexibility in complying with different planning demands and a rapid response to a developing scenario. The methodology and the applicability of the approach are explained and demonstrated by utilizing multi-objective path planning problems.