Benchmarking of GPU-optimized Quantum-Inspired Evolutionary Optimization Algorithm using Functional Analysis

TL;DR

This paper benchmarks GPU-optimized quantum-inspired evolutionary optimization (QIEO) against GPU-optimized genetic algorithm (GA) on three challenging benchmark functions to address data-efficiency and convergence reliability when function evaluations are expensive. QIEO uses a single-parameter Ry rotation in a quantum-inspired representation to maintain exploration while guiding exploitation, implemented on CUDA for NVIDIA A100 GPUs, and is compared to a generational GA with binary tournament selection, crossover, and mutation. On Ackley, Rosenbrock, and Rastrigin, QIEO achieved the target fitness with far smaller population sizes and fewer total function evaluations, yielding speedups of about 2.9×, 3.9×, and 3.84×, respectively, and lower variance across 30 trials. These results suggest QIEO can substantially reduce computation time in engineering optimization where each evaluation is costly, making it a promising alternative to GA for non-linear, multi-modal objectives, with tolerances of $1e^{-3}$ for Ackley/Rosenbrock and $1e^{-6}$ for Rastrigin.

Abstract

This article presents a comparative analysis of GPU-parallelized implementations of the quantum-inspired evolutionary optimization (QIEO) approach and one of the well-known classical metaheuristic techniques, the genetic algorithm (GA). The study assesses the performance of both algorithms on highly non-linear, non-convex, and non-separable function optimization problems, viz., Ackley, Rosenbrock, and Rastrigin, that are representative of the complex real-world optimization problems. The performance of these algorithms is checked by varying the population sizes by keeping all other parameters constant and comparing the fitness value it reached along with the number of function evaluations they required for convergence. The results demonstrate that QIEO performs better for these functions than GA, by achieving the target fitness with fewer function evaluations and significantly reducing the total optimization time approximately three times for the Ackley function and four times for the Rosenbrock and Rastrigin functions. Furthermore, QIEO exhibits greater consistency across trials, with a steady convergence rate that leads to a more uniform number of function evaluations, highlighting its reliability in solving challenging optimization problems. The findings indicate that QIEO is a promising alternative to GA for these kind of functions.

Figures (10)

• Figure 1: Ackley: Distribution of achieved fitness values across 30 trials for different population sizes.
• Figure 2: Ackley: Distribution of convergence rates across 30 trials for different population sizes.
• Figure 3: Ackley: Comparison of GA and QIEO, showing the distribution of the total number of function evaluations across 30 trials to achieve the same fitness and the evolution of the average fitness over time across 30 trials.
• Figure 4: Rosenbrock: Distribution of achieved fitness values across 30 trials for different population sizes.
• Figure 5: Rosenbrock: Distribution of convergence rates across 30 trials for different population sizes.