Recursive Objective Space Exploration (ROSE): A computationally efficient deterministic approach for bi-objective optimization.

Bi-objective optimization problems arise when a process needs to be optimized with respect to two conflicting objectives. Solving such problems produces a set of points called the Pareto front, where no objective can be improved without worsening at least one other objective. Existing deterministic methods for solving Multi-Objective Optimization Problems (MOOPs) include scalarization techniques, which transform the problem into a set of Single-Objective Optimization Problems (SOOPs) where each of them is to be solved independently to obtain a point on the Pareto front. In this paper, we propose an alternative strategy that tackles bi-objective optimization problems by exploring the objective space recursively at a reduced computational cost. Our approach is inspired by how plants efficiently explore physical space in search of light energy, balancing exploration and exploitation while minimizing biomass cost. The algorithm navigates the objective space without revisiting previously explored areas by solving intermediate SOOPs visualized as branches within this space. A trade-offs based stopping criterion enables the algorithm to focus on steep, information-rich segments of the Pareto front, creating denser branches to provide more detailed representation of the Pareto front. We benchmark the algorithm's performance against a standard scalarization-based solution strategy from the literature, employing five case studies. Our strategy demonstrates that a holistic approach that structures the solution process within the objective space provides significant advantages. These include a more computationally efficient method for solving bi-objective optimization problems, an adaptive representation of the Pareto front based on trade-offs, and intuitive, straightforward parameterization guided by a user-oriented, trade-offs based stopping criterion.