Two-Archive Evolutionary Algorithm for Constrained Multi-Objective Optimization (1711.07907v1)

Abstract: When solving constrained multi-objective optimization problems, an important issue is how to balance convergence, diversity and feasibility simultaneously. To address this issue, this paper proposes a parameter-free constraint handling technique, two-archive evolutionary algorithm, for constrained multi-objective optimization. It maintains two co-evolving populations simultaneously: one, denoted as convergence archive, is the driving force to push the population toward the Pareto front; the other one, denoted as diversity archive, mainly tends to maintain the population diversity. In particular, to complement the behavior of the convergence archive and provide as much diversified information as possible, the diversity archive aims at exploring areas under-exploited by the convergence archive including the infeasible regions. To leverage the complementary effects of both archives, we develop a restricted mating selection mechanism that adaptively chooses appropriate mating parents from them according to their evolution status. Comprehensive experiments on a series of benchmark problems and a real-world case study fully demonstrate the competitiveness of our proposed algorithm, comparing to five state-of-the-art constrained evolutionary multi-objective optimizers.

• The paper presents a dual-archive approach where the convergence archive drives solutions toward the Pareto front while the diversity archive explores under-exploited regions.
• It implements a restricted mating selection strategy that combines high-quality solutions from both archives to enhance overall search performance.
• Experimental results demonstrate that C-TAEA outperforms state-of-the-art methods on IGD and Hypervolume metrics across synthetic benchmarks and real-world applications like water distribution optimization.

Two-Archive Evolutionary Algorithm for Constrained Multi-Objective Optimization

The paper introduces a novel evolutionary algorithm designed for constrained multi-objective optimization (CMOP), addressing the trio of challenges: convergence, diversity, and feasibility. This algorithm, termed the Constrained Two-Archive Evolutionary Algorithm (C-TAEA), operates with a parameter-free constraint handling mechanism and leverages two co-evolving archives to guide the optimization process effectively.

Core Concepts and Methodology

In C-TAEA, the two archives play distinct yet complementary roles:

1. Convergence Archive (CA): This archive focuses primarily on pushing the population towards the Pareto front. It ensures convergence and maintains feasibility within the evolutionary process. The CA effectively applies selection pressure to consistently drive solutions to feasible and optimal regions.
2. Diversity Archive (DA): This archive is designed to maintain and enhance the diversity of the solutions without being confined to the feasible regions alone. By exploring the under-exploited areas, including infeasible regions, the DA provides a broader set of candidate solutions, which enhances the exploration capability of the algorithm across the search space.

The algorithm implements a restricted mating selection strategy, selecting mating parents from both archives based on their evolutionary status. This mechanism ensures that the complementary strengths of the CA and DA are harnessed to produce high-quality offspring.

Experimental Evaluation and Results

The paper evaluates the performance of C-TAEA on several benchmark problems including classic DTLZ test functions and real-world scenarios such as water distribution network optimization. These problems present various constraint types, including complex feasibility landscapes and multi-modal feasible regions.

Key findings include:

• Performance Metrics: C-TAEA consistently outperforms existing state-of-the-art methodologies in terms of both IGD (Inverted Generational Distance) and HV (Hypervolume), particularly on problems with intricate feasible regions or when feasible regions are separated by infeasible barriers.
• Algorithmic Efficacy: The DA notably aids in escaping local optima by providing diverse solutions, thereby enabling the CA to explore more effectively and maintain broad coverage of the Pareto front.
• Real-World Application: In practical scenarios such as the optimization of water distribution networks, C-TAEA demonstrates superior ability to balance cost efficiency with resilience, demonstrating its potential applicability in complex engineered systems.

Implications and Future Directions

From a theoretical standpoint, the introduction of a dual-archive framework offers new avenues for enhancing EMO algorithms' capability to handle complex constraints. The separation and specialization of convergence and diversity tasks between two archives may prompt future exploration into adaptive and hybrid strategies in evolutionary computation.

Practically, the algorithm shows promise for real-world applications where multi-objective trade-offs are constrained by non-trivial feasibility requirements. In scenarios with evolving systems or dynamic constraints, extensions of the current framework could be developed to maintain algorithm efficiency.

Future research could explore enhancing the theoretical foundation of dual-archive systems, exploring adaptive strategies that modify the interplay between the CA and DA dynamically, or extending the approach to include other optimization paradigms beyond evolutionary algorithms.

In conclusion, C-TAEA serves as a significant contribution to the field of constrained multi-objective optimization, showcasing the potential benefits of using specialized archives to manage complex problem landscapes efficiently. Its robust performance on both synthetic and real-world problems reflects its utility and adaptability as a sophisticated tool in evolutionary computation.