Linear programming-based directed local search for expensive multi-objective optimization problems: Application to drinking water production plants

Local search (LS) is an essential module of most hybrid meta-heuristic evolutionary algorithms which are a major approach aimed to solve efficiently multi-objective optimization (MOO) problems. Furthermore, LS is specifically useful in many real-world applications where there is a need only to improve a current state of a system locally with limited computational budget and/or relying on computationally expensive process simulators. In these contexts, this paper proposes a new neighborhood-based iterative LS method, relying on first derivatives approximation and linear programming (LP), aiming to steer the search along any desired direction in the objectives space. The paper also leverages the directed local search (DS) method to constrained MOO problems. These methods are applied to the bi-objective (cost versus life cycle assessment-based environmental impact) optimization of drinking water production plants. The results obtained show that the proposed method constitutes a promising local search method which clearly outperforms the directed search approach.