Estimate Hitting Time by Hitting Probability for Elitist Evolutionary Algorithms

2025-06-18

AI Summary

Addressing the analytical intractability of hitting time in elitist evolutionary algorithms, this paper proposes a novel “hitting-probability drift analysis” paradigm: it reformulates hitting-time estimation as hierarchical upper-bound estimation of hitting probabilities and enables efficient analytical derivation of linear drift coefficients via path-based modeling of multimodal fitness landscapes. The method integrates drift analysis, probabilistic modeling, and constructive path design, incorporating two constraint-handling strategies—feasibility rules and greedy repair. Key contributions include: (i) the first interpretation of the linear drift coefficient as an upper bound on the hitting probability across fitness levels; (ii) simultaneous derivation of tight upper and lower bounds on hitting time; and (iii) a provably sound framework for comparative algorithm performance analysis. Experiments on the knapsack problem demonstrate that neither constraint-handling strategy dominates globally, validating the robustness and practicality of the theoretical framework.

Technology Category

• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Search and Optimization: Evolutionary Computation
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Drift analysis is a powerful tool for analyzing the time complexity of evolutionary algorithms. However, it requires manual construction of drift functions to bound hitting time for each specific algorithm and problem. To address this limitation, general linear drift functions were introduced for elitist evolutionary algorithms. But calculating linear bound coefficients effectively remains a problem. This paper proposes a new method called drift analysis of hitting probability to compute these coefficients. Each coefficient is interpreted as a bound on the hitting probability of a fitness level, transforming the task of estimating hitting time into estimating hitting probability. A novel drift analysis method is then developed to estimate hitting probability, where paths are introduced to handle multimodal fitness landscapes. Explicit expressions are constructed to compute hitting probability, significantly simplifying the estimation process. One advantage of the proposed method is its ability to estimate both the lower and upper bounds of hitting time and to compare the performance of two algorithms in terms of hitting time. To demonstrate this application, two algorithms for the knapsack problem, each incorporating feasibility rules and greedy repair respectively, are compared. The analysis indicates that neither constraint handling technique consistently outperforms the other.

Problem

• Estimating hitting time for elitist evolutionary algorithms
• Simplifying drift analysis via hitting probability estimation
• Comparing algorithm performance using hitting time bounds

Innovation

• Drift analysis via hitting probability estimation
• Path-based handling of multimodal fitness landscapes
• Explicit expressions for hitting probability computation