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Examples of De-Evolution in Differential Evolution Algorithms

Introduction to Differential Evolution (DE)

Differential Evolution (DE) is a powerful optimization algorithm used for solving complex numerical problems. It operates similarly to traditional evolutionary algorithms but introduces unique mechanisms for generating offspring, which have led to its widespread adoption and numerous variants . This article explores various examples of de-evolution within DE algorithms, highlighting how different strategies and modifications have been implemented to enhance performance.

Neighborhood-Based Mutation in DE

One notable example of de-evolution in DE is the introduction of neighborhood-based mutation operators. This approach defines small neighborhoods over the index-graph of parameter vectors, inspired by particle swarm optimization (PSO) algorithms. By balancing exploration and exploitation, these neighborhood-based schemes have shown statistically significant improvements over traditional DE variants in benchmark tests.

Evolution Path in DEEP Algorithms

Another example is the DEEP (Differential Evolution with an Evolution Path) framework, which integrates cumulative correlation information from the evolutionary process. This method combines the distributed model of DE with the centralized model of evolution strategy (ES), resulting in enhanced performance. The DEEP framework allows for self-adaptation, easing the task of predetermining control parameters and demonstrating promising results in various practical problems.

Ensemble Methods in DE

Ensemble methods have also been employed to improve DE algorithms. The EDEV (Ensemble of Differential Evolution Variants) framework combines multiple efficient DE variants into a multi-population structure. By partitioning the population and rewarding the best-performing variants, EDEV ensures that the most efficient DE variant receives the most computational resources. This approach has shown superior performance in benchmark tests compared to several state-of-the-art DE variants.

Individual-Dependent Mechanisms

The introduction of individual-dependent mechanisms in DE represents another form of de-evolution. This approach includes individual-dependent parameter settings and mutation strategies based on the fitness values of individuals. By assigning different mutation operators to superior and inferior individuals at various stages of the evolution process, this method has demonstrated outstanding performance in benchmark evaluations.

Ranking-Based Mutation Operators

Ranking-based mutation operators in DE select parents proportionally according to their rankings in the current population. This method ensures that higher-ranking parents have a greater chance of being selected, thereby enhancing the performance of the DE algorithm. Experimental results have shown that ranking-based mutation operators improve both the original DE algorithm and advanced DE variants.

Collective Information-Powered DE

The CIPDE (Collective Information-Powered Differential Evolution) variant enhances DE by utilizing the collective information of the best candidates in the population. By linearly combining the evolutionary information of these candidates, CIPDE improves the mutation process and overall performance. Comparative studies have confirmed CIPDE's superiority over other DE variants in most test functions.

Multiobjective Sorting-Based Mutation Operators

Finally, multiobjective sorting-based mutation operators in DE exploit both fitness and diversity information of the population. By proportionally selecting parents based on their rankings in fitness and diversity, this approach achieves a good balance between exploration and exploitation. This method has been shown to enhance the performance of various DE algorithms in both benchmark functions and real-world application problems.

Conclusion

Differential Evolution has evolved significantly since its inception, with numerous variants and modifications enhancing its performance. Examples of de-evolution in DE, such as neighborhood-based mutation, evolution path frameworks, ensemble methods, individual-dependent mechanisms, ranking-based mutation operators, collective information-powered DE, and multiobjective sorting-based mutation operators, demonstrate the algorithm's adaptability and effectiveness in solving complex optimization problems. These advancements continue to push the boundaries of what DE can achieve in both theoretical and practical applications.