Improvements of real coded genetic algorithms based on differential operators preventing premature convergence (0902.1629v1)

Abstract: This paper presents several types of evolutionary algorithms (EAs) used for global optimization on real domains. The interest has been focused on multimodal problems, where the difficulties of a premature convergence usually occurs. First the standard genetic algorithm (SGA) using binary encoding of real values and its unsatisfactory behavior with multimodal problems is briefly reviewed together with some improvements of fighting premature convergence. Two types of real encoded methods based on differential operators are examined in detail: the differential evolution (DE), a very modern and effective method firstly published by R. Storn and K. Price, and the simplified real-coded differential genetic algorithm SADE proposed by the authors. In addition, an improvement of the SADE method, called CERAF technology, enabling the population of solutions to escape from local extremes, is examined. All methods are tested on an identical set of objective functions and a systematic comparison based on a reliable methodology is presented. It is confirmed that real coded methods generally exhibit better behavior on real domains than the binary algorithms, even when extended by several improvements. Furthermore, the positive influence of the differential operators due to their possibility of self-adaptation is demonstrated. From the reliability point of view, it seems that the real encoded differential algorithm, improved by the technology described in this paper, is a universal and reliable method capable of solving all proposed test problems.

• The paper studies real-coded genetic algorithms enhanced with differential operators (DE, SADE, CERAF) to prevent premature convergence in global optimization problems.
• Empirical tests show DE and SADE methods, especially SADE with CERAF, achieve significantly higher success rates and reliability on complex functions compared to binary genetic algorithms.
• These improved real-coded methods are well-suited for high-dimensional, complex optimization challenges in scientific and engineering domains, offering a robust alternative to traditional approaches.
• The research indicates real-coded genetic algorithms with differential operators show superior precision and adaptation for multimodal problem spaces compared to binary-based methods.
• Empirical analysis across 20 objective functions demonstrated that DE and SADE methods frequently exhibited superior performance, with SADE incorporating CERAF achieving 100% success on all test problems.
• The findings suggest these enhanced real-coded methods are particularly suitable for complex, high-dimensional optimization problems in engineering and scientific computation.

Detailed Analysis of Real Coded Genetic Algorithms with Differential Operators

The paper "Improvements of Real Coded Genetic Algorithms Based on Differential Operators Preventing the Premature Convergence" presents a comprehensive paper on the application and enhancement of evolutionary algorithms (EAs) for global optimization in real domains, with a particular focus on addressing the challenges associated with multimodal problems where premature convergence is a significant issue.

Overview of Methods

The authors begin with a critique of Standard Genetic Algorithms (SGAs) that utilize binary encoding for real-value optimization. The challenges identified include slow convergence and inadequate precision, especially for problems demanding high precision. To alleviate these issues, two advanced approaches using real encoding and differential operators were examined: Differential Evolution (DE) and the Simplified Real-Coded Differential Genetic Algorithm (SADE), with an additional improvement termed CERAF.

1. Differential Evolution (DE): Originated by R. Storn and K. Price, DE is highlighted for its self-adapting differential operators which help overcome local optima. The DE operates by using real vectors instead of binary strings, providing significant adaptability via its reliance on real value differences to guide the evolutionary process.
2. Simplified Differential Genetic Algorithm (SADE): Proposed by the authors, SADE combines differential evolution principles with classical genetic algorithm features. It operates directly on real values, circumventing the pitfalls of binary encoding-based methods, with a focus on robust performance over a variety of complex functions.
3. CERAF Technology: This enhancement introduces a system to avoid being trapped in local extremas. By creating 'radioactive' zones with increased mutation rates around discovered local minima, CERAF ensures escape and continued exploration, thus improving the overall robustness and reliability of the algorithm.

Empirical Analysis

The research conducted a systematic performance evaluation of these algorithms across a set of 20 objective functions, contrasting their success rates and computational efficiency with binary genetic algorithms. Notably:

• Success Rate: The DE and SADE methods frequently exhibited superior performance, with DE achieving 100% success on several functions where binary GAs failed. SADE, particularly with CERAF, consistently achieved higher reliability, reaching 100% success on all test problems.
• Convergence Rate: DE was the fastest among the methods tested, although SADE and its CERAF-enhanced version showed remarkable convergence times relative to their reliability improvements.

Implications and Future Directions

This paper's findings underscore the potential for real-coded genetic algorithms utilizing differential operators to surpass traditional binary-based methods in precision and adaptation for multimodal problem spaces. The success rate improvements suggest these methods are particularly suited for high-dimensional, complex optimization problems faced in engineering and scientific computation domains.

Future work could focus on further refining these differential operators, exploring adaptive parameter tuning in the CERAF technique, and extending this approach to varied real-world applications with evolving constraints and dynamic objective landscapes. This aligns with the broader trend in optimization research to leverage self-adapting algorithms capable of robustly addressing the diverse and often unpredictable challenges inherent in large-scale computations.

Overall, the research presented provides substantial evidence supporting the shift towards real-coded genetic algorithms enriched with differential evolutions as a mainstream tool for global optimization problems in complex domains.