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Improving genetic algorithms performance via deterministic population shrinkage

Juan Luis Jiménez Laredo, Carlos Fernandes, Juan Julián Merelo, Christian Gagné

TL;DR

This work investigates whether a fixed population size is optimal for genetic algorithms and proposes a deterministic Simple Variable Population Sizing (SVPS) framework. It uses a bisection-based method to compute the minimum initial population $P_{init}'$ needed to supply enough building blocks, refines this to $P_{init}$, and then applies a deterministic shrinking schedule governed by $\tau$ (speed) and $\rho$ (severity) to reduce the population during the run. Empirical results on trap functions show SVPS can improve performance by reducing the number of evaluations while maintaining a 0.98 success rate, with larger gains on harder problem instances. The study provides a general framework for evaluating variable population schemes and highlights the potential of deterministic shrinkage to balance exploration and exploitation in GAs, along with directions for extending the approach to include mutation and broader parameter tuning.

Abstract

Despite the intuition that the same population size is not needed throughout the run of an Evolutionary Algorithm (EA), most EAs use a fixed population size. This paper presents an empirical study on the possible benefits of a Simple Variable Population Sizing (SVPS) scheme on the performance of Genetic Algorithms (GAs). It consists in decreasing the population for a GA run following a predetermined schedule, configured by a speed and a severity parameter. The method uses as initial population size an estimation of the minimum size needed to supply enough building blocks, using a fixed-size selectorecombinative GA converging within some confidence interval toward good solutions for a particular problem. Following this methodology, a scalability analysis is conducted on deceptive, quasi-deceptive, and non-deceptive trap functions in order to assess whether SVPS-GA improves performances compared to a fixed-size GA under different problem instances and difficulty levels. Results show several combinations of speed-severity where SVPS-GA preserves the solution quality while improving performances, by reducing the number of evaluations needed for success.

Improving genetic algorithms performance via deterministic population shrinkage

TL;DR

This work investigates whether a fixed population size is optimal for genetic algorithms and proposes a deterministic Simple Variable Population Sizing (SVPS) framework. It uses a bisection-based method to compute the minimum initial population needed to supply enough building blocks, refines this to , and then applies a deterministic shrinking schedule governed by (speed) and (severity) to reduce the population during the run. Empirical results on trap functions show SVPS can improve performance by reducing the number of evaluations while maintaining a 0.98 success rate, with larger gains on harder problem instances. The study provides a general framework for evaluating variable population schemes and highlights the potential of deterministic shrinkage to balance exploration and exploitation in GAs, along with directions for extending the approach to include mutation and broader parameter tuning.

Abstract

Despite the intuition that the same population size is not needed throughout the run of an Evolutionary Algorithm (EA), most EAs use a fixed population size. This paper presents an empirical study on the possible benefits of a Simple Variable Population Sizing (SVPS) scheme on the performance of Genetic Algorithms (GAs). It consists in decreasing the population for a GA run following a predetermined schedule, configured by a speed and a severity parameter. The method uses as initial population size an estimation of the minimum size needed to supply enough building blocks, using a fixed-size selectorecombinative GA converging within some confidence interval toward good solutions for a particular problem. Following this methodology, a scalability analysis is conducted on deceptive, quasi-deceptive, and non-deceptive trap functions in order to assess whether SVPS-GA improves performances compared to a fixed-size GA under different problem instances and difficulty levels. Results show several combinations of speed-severity where SVPS-GA preserves the solution quality while improving performances, by reducing the number of evaluations needed for success.
Paper Structure (9 sections, 2 equations, 5 figures, 2 tables, 3 algorithms)

This paper contains 9 sections, 2 equations, 5 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Methodology
  4. Bisection Method
  5. Refining Initial Supply of Building Blocks
  6. Varying Population Size
  7. Experimental Setup
  8. Results
  9. Conclusions

Figures (5)

  • Figure 1: SVPS shapes for different values of $\tau$-$\rho$.
  • Figure 2: Generalized l-trap function.
  • Figure 3: Improvement in the number of evaluations of the SVPS-GA with respect to the fixed-size GA. Results are depicted as a function of the initial population size used by the different problem instances of 2-trap, 3-trap, and 4-trap functions.
  • Figure 4: Scalability with trap functions. Optimal population size ( top) and Average Evaluations to Solution (AES) ( bottom) values for a fixed-size GA and the SVPS-GA.
  • Figure 5: SVPS-GA combinations of $\tau$-$\rho$ converging to a SR of 0.98. From left to right, 2-trap, 3-trap, and 4-trap are represented for sub-functions values of $m=4$, $m=16$, and $m=64$. The area of the circles stands for the AES improvement with respect to the fixed-size GA.