Two-stage multi-objective optimization based on knowledge-driven approach: A case study on production and transportation integration

The multi-objective evolutionary algorithm (MOEA) has been widely applied to solve various optimization problems. Existing search models based on dominance and decomposition are extensively used in MOEAs to balance convergence and diversity during the search process. In this paper, we propose for the first time a two-stage MOEA based on a knowledge-driven approach (TMOK). The first stage aims to find a rough Pareto front through an improved nondominated sorting algorithm, whereas the second stage incorporates a dynamic learning mechanism into a decomposition-based search model to reasonably allocate computational resources. To further speed up the convergence of TMOK, we present a Markov chain-based TMOK (MTMOK), which can potentially capture variable dependencies. In particular, MTMOK employs a marginal probability distribution of single variables and an N-state Markov chain of two adjacent variables to extract valuable knowledge about the problem solved. Moreover, a simple yet effective local search is embedded into MTMOK to improve solutions through variable neighborhood search procedures. To illustrate the potential of the proposed algorithms, we apply them to solve a distributed production and transportation-integrated problem encountered in many industries. Numerical results and comparisons on 54 test instances with different sizes verify the effectiveness of TMOK and MTMOK. We have made the 54 instances and the source code of our algorithms publicly available to support future research and real-life applications. © 2024 Elsevier B.V.