MAAPO-E: an entropy-guided, constraint-aware membrane protozoa optimizer for high-dimensional numerical and engineering optimization
摘要
Recent progress in metaheuristic optimization has shown that biologically inspired algorithms could be useful for solving hard numerical and engineering design issues. The Artificial Protozoa Optimizer (APO) is one of them. It uses a bio-inspired exploration technique, although it has problems with convergence efficiency, handling constraints, and scaling up in high-dimensional or confined environments. Also, current APO variations do not perform considering the balance between exploration and exploitation or supporting dynamic membrane-based parallelism. This paper suggests MAAPO-E, an Entropy-Guided, Constraint-Aware Membrane Protozoa Optimizer, to fill in these gaps. It is meant to help with large-scale numerical and constrained engineering optimization issues. MAAPO-E adds a number of important new features: (1) a self-adaptive membrane-computing framework that uses entropy-based diversity metrics to dynamically control communication between membranes; (2) an improved Roulette Fitness–Distance Balance (RFDB⁺) mechanism to keep a strong trade-off between exploration and exploitation; (3) a hybrid local search module that starts when stagnation is detected to speed up fine-tuning near optima; and (4) a multi-stage constraint-handling strategy that combines Deb’s feasibility rules with adaptive penalty functions. These changes make MAAPO-E more powerful, allowing it to reach steady convergence and stay feasible in engineering problems in both the real world and in numbers. The approach is compared to ten of the best optimizers in the CEC 2017 high-dimensional numerical test suite (D = 50, 100) and six classic restricted engineering design problems. The results reveal that MAAPO-E beats other approaches in 83% of benchmark cases when it comes to the best, mean, and standard deviation of fitness values. MAAPO-E usually finds solutions that are viable and do not break any rules across all engineering benchmarks. It also improves the best-case fitness by 9.7% and lowers the standard deviation by 32%. Statistical tests like the Wilcoxon signed-rank and Friedman ranking show that these gains are important. The suggested MAAPO-E framework is a powerful and scalable tool for optimizing things in the real world. It has been shown to be durable, adaptable, and able to find good solutions that are good enough for use in engineering design automation. Finally, we outline how the membrane/entropy/RFDB⁺ design extends to constrained multi-objective problems and point to recent real-world MOO benchmarks as a natural next step.
Highlights Introduces MAAPO-E: an enhanced membrane-based protozoa optimizer Uses entropy to adapt membrane interaction and boost diversity Hybrid local search improves fine-tuning and convergence speed Novel RFDB⁺ balances exploration and exploitation adaptively Solves high-dimensional and constrained engineering problems Outperforms ten optimizers on CEC benchmarks and real case studies