An evolutionary multi-objective optimization algorithm based on LPBI with adaptive penalty value

In this paper, an adaptive localized penalty boundary intersection method is proposed and applied to MOEA/D, which is called ALPBI algorithm. In order to solve the problem that the penalty value of the penalty-based intersection (PBI) is difficult to determine, the ALPBI algorithm uses a linearly changing penalty value during operation, and uses the Subproblem-based Penalty Scheme (SPS) method to skillfully set the initial and final value of the changeable penalty value, which improves the performance of the algorithm. Experiments prove that: (1) When solving multi-objective optimization problems, the trouble of selecting a penalty value is avoided because ALPBI automatically sets the appropriate penalty value. (2) The ALPBI algorithm balances diversity and convergence metrics at the same time, so that the results have more boundary solutions and are closer to PF. (3) In early stages of operation, the ALPBI algorithm enhances the diversity of the solutions, making it perform well in diversity measurement within a small number of iterations; then, it also accelerates the convergence of the solution set in later stages, and the solutions better approximate PF.