A Branching Strategy for Exploring the Objective Space in Bi-objective Optimization Problems

The process of optimization of chemical/ biochemical processes can often involve multiple conflicting objectives. This gives rise to a class of problems called multi-objective optimization problems. Solving such problems results in an infinite set of points, the Pareto set, which includes all the solutions in which no objective can be improved without worsening at least one other objective. In this paper, we propose a new strategy that is inspired by branching phenomena in nature for exploring the objective space to obtain a representation of the Pareto set. The algorithm starts from a single point in the objective space, and systematically constructs branches towards the Pareto front by solving correspondingly-modified subproblems. This process continues till points that lie at the Pareto front are obtained. This way, it ensures that no region in the objective space gets explored more than a single time. Additionally, using a proximity parameter, the branches density can be controlled, consequently leading to controlling the resolution of the Pareto front. The proposed method has been applied to a numerical bi-objective optimization problem as well as the problem of the bi-objective control of a William-Otto reactor. Results show that the new algorithm has managed to obtain a Pareto front with adaptive resolution where the areas with high trade-offs are represented with higher points density. Copyright (c) 2022 The Authors. This is an open access article under the CC BY-NC-ND license(https://creativecommons.org/licenses/by-nc-nd/4.0/)