Push and Pull Search Embedded in an M2M Framework for Solving Constrained Multi-objective Optimization Problems

In dealing with constrained multi-objective optimization problems (CMOPs), a key issue of multi-objective evolutionary algorithms (MOEAs) is to balance the convergence and diversity of working populations.

Embedding Push and Pull Search in the Framework of Differential Evolution for Solving Constrained Single-objective Optimization Problems

This paper proposes a push and pull search method in the framework of differential evolution (PPS-DE) to solve constrained single-objective optimization problems (CSOPs). More specifically, two sub-populations, including the top and bottom sub-populations, are collaborated with each other to search global optimal solutions efficiently. The top sub-population adopts the pull and pull search (PPS) mechanism to deal with constraints, while the bottom sub-population use the superiority of feasible solutions (SF) technique to deal with constraints. In the top sub-population, the search process is divided into two different stages --- push and pull stages.An adaptive DE variant with three trial vector generation strategies is employed in the proposed PPS-DE. In the top sub-population, all the three trial vector generation strategies are used to generate offsprings, just like in CoDE. In the bottom sub-population, a strategy adaptation, in which the trial vector generation strategies are periodically self-adapted by learning from their experiences in generating promising solutions in the top sub-population, is used to choose a suitable trial vector generation strategy to generate one offspring. Furthermore, a parameter adaptation strategy from LSHADE44 is employed in both sup-populations to generate scale factor $F$ and crossover rate $CR$ for each trial vector generation strategy. Twenty-eight CSOPs with 10-, 30-, and 50-dimensional decision variables provided in the CEC2018 competition on real parameter single objective optimization are optimized by the proposed PPS-DE. The experimental results demonstrate that the proposed PPS-DE has the best performance compared with the other seven state-of-the-art algorithms, including AGA-PPS, LSHADE44, LSHADE44+IDE, UDE, IUDE, $\epsilon$MAg-ES and C$^2$oDE.