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Improved Compact Genetic Algorithms with Efficient Caching

Prasanta Dutta, Anirban Mukhopadhyay

TL;DR

This work tackles the high cost of fitness evaluations in compact genetic algorithms (cGAs) by introducing a fitness caching mechanism. A hash-based cache stores (chromosome, fitness) pairs and uses FIFO or LRU replacement to bound overhead, preserving the original algorithms’ accuracy and convergence. The approach extends to elitism-based cGAs (pe-cGA and ne-cGA), achieving substantial reductions in evaluations with asymptotically constant average cache-time and manageable space complexity. Experimental results on benchmark problems demonstrate meaningful speedups across population sizes and cache capacities, highlighting practical impact for time- and resource-intensive fitness computations.

Abstract

Compact Genetic Algorithms (cGAs) are condensed variants of classical Genetic Algorithms (GAs) that use a probability vector representation of the population instead of the complete population. cGAs have been shown to significantly reduce the number of function evaluations required while producing outcomes similar to those of classical GAs. However, cGAs have a tendency to repeatedly generate the same chromosomes as they approach convergence, resulting in unnecessary evaluations of identical chromosomes. This article introduces the concept of caching in cGAs as a means of avoiding redundant evaluations of the same chromosomes. Our proposed approach operates equivalently to cGAs, but enhances the algorithm's time efficiency by reducing the number of function evaluations. We also present a data structure for efficient cache maintenance to ensure low overhead. The proposed caching approach has an asymptotically constant time complexity on average. The proposed method further generalizes the caching mechanism with higher selection pressure for elitism-based cGAs. We conduct a rigorous analysis based on experiments on benchmark optimization problems using two well-known cache replacement strategies. The results demonstrate that caching significantly reduces the number of function evaluations required while maintaining the same level of performance accuracy.

Improved Compact Genetic Algorithms with Efficient Caching

TL;DR

This work tackles the high cost of fitness evaluations in compact genetic algorithms (cGAs) by introducing a fitness caching mechanism. A hash-based cache stores (chromosome, fitness) pairs and uses FIFO or LRU replacement to bound overhead, preserving the original algorithms’ accuracy and convergence. The approach extends to elitism-based cGAs (pe-cGA and ne-cGA), achieving substantial reductions in evaluations with asymptotically constant average cache-time and manageable space complexity. Experimental results on benchmark problems demonstrate meaningful speedups across population sizes and cache capacities, highlighting practical impact for time- and resource-intensive fitness computations.

Abstract

Compact Genetic Algorithms (cGAs) are condensed variants of classical Genetic Algorithms (GAs) that use a probability vector representation of the population instead of the complete population. cGAs have been shown to significantly reduce the number of function evaluations required while producing outcomes similar to those of classical GAs. However, cGAs have a tendency to repeatedly generate the same chromosomes as they approach convergence, resulting in unnecessary evaluations of identical chromosomes. This article introduces the concept of caching in cGAs as a means of avoiding redundant evaluations of the same chromosomes. Our proposed approach operates equivalently to cGAs, but enhances the algorithm's time efficiency by reducing the number of function evaluations. We also present a data structure for efficient cache maintenance to ensure low overhead. The proposed caching approach has an asymptotically constant time complexity on average. The proposed method further generalizes the caching mechanism with higher selection pressure for elitism-based cGAs. We conduct a rigorous analysis based on experiments on benchmark optimization problems using two well-known cache replacement strategies. The results demonstrate that caching significantly reduces the number of function evaluations required while maintaining the same level of performance accuracy.

Paper Structure

This paper contains 18 sections, 3 theorems, 10 equations, 14 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Variants of cGA
  3. Compact Genetic Algorithm (cGA)
  4. Elitism-Based cGA
  5. Proposed cGA with Efficient Caching
  6. Algorithm
  7. Data Structure for the Cache
  8. Analysis
  9. FIFO and LRU as the Cache Replacement Strategies
  10. Accuracy and Convergence
  11. Time Complexity
  12. Space Complexity
  13. Metrics for Performance Evaluation
  14. Experimental Results
  15. Experiments with Respect to Different Population Sizes
  16. ...and 3 more sections

Key Result

Lemma 1

Hitratio(%) is the measure of the percentage of reduction in the number of fitness function evaluations.

Figures (14)

  • Figure 1: Pseudocode of cGA
  • Figure 2: Modification of cGA that implements tournament selection of size $s$. This would replace steps 2-4 of the cGA code
  • Figure 3: Modification of cGA that implements a round-robin tournament. This would replace steps 2-4 of the cGA code
  • Figure 4: Modification of cGA that realizes the pe-cGA. Here only the modified steps are given, the rest of the steps are same as cGA
  • Figure 5: Modification of cGA that realizes the ne-cGA. Here only the modified steps are given, the rest of the steps are same as cGA
  • ...and 9 more figures

Theorems & Definitions (8)

  • Definition 1
  • Definition 2
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Corollary 1
  • proof