Multi-start Optimization Method via Scalarization based on Target Point-based Tchebycheff Distance for Multi-objective Optimization

2025-05-01

AI Summary

To address inadequate coverage of inverted triangular or highly nonlinear Pareto fronts and performance degradation of algorithms like NSGA-III caused by variable interdependencies in multi-objective optimization, this paper proposes a scalarization-based multi-start optimization framework leveraging Target-Point-adaptive Tchebycheff Distance (TPTD). The method introduces a novel target-point-driven dynamic TPTD scalarization mechanism that adaptively conforms to the geometric characteristics of the Pareto front. It seamlessly integrates with single-objective optimizers such as Natural Evolution Strategies (NES). On inverted triangular benchmark problems, the proposed approach significantly outperforms NSGA-II, NSGA-III, and MOEA/D-DE: it achieves substantial improvements in Hypervolume and attains up to 474× speedup in computational efficiency.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Multi-objective optimization is crucial in scientific and industrial applications where solutions must balance trade-offs among conflicting objectives. State-of-the-art methods, such as NSGA-III and MOEA/D, can handle many objectives but struggle with coverage issues, particularly in cases involving inverted triangular Pareto fronts or strong nonlinearity. Moreover, NSGA-III often relies on simulated binary crossover, which deteriorates in problems with variable dependencies. In this study, we propose a novel multi-start optimization method that addresses these challenges. Our approach introduces a newly introduced scalarization technique, the Target Point-based Tchebycheff Distance (TPTD) method, which significantly improves coverage on problems with inverted triangular Pareto fronts. For efficient multi-start optimization, TPTD leverages a target point defined in the objective space, which plays a critical role in shaping the scalarized function. The position of the target point is adaptively determined according to the shape of the Pareto front, ensuring improvement in coverage. Furthermore, the flexibility of this scalarization allows seamless integration with powerful single-objective optimization methods, such as natural evolution strategies, to efficiently handle variable dependencies. Experimental results on benchmark problems, including those with inverted triangular Pareto fronts, demonstrate that our method outperforms NSGA-II, NSGA-III, and MOEA/D-DE in terms of the Hypervolume indicator. Notably, our approach achieves computational efficiency improvements of up to 474 times over these baselines.

Problem

• Improves coverage for inverted triangular Pareto fronts
• Handles variable dependencies via single-objective optimization integration
• Enhances computational efficiency in multi-objective optimization

Innovation

• Target Point-based Tchebycheff Distance scalarization method
• Adaptive target point for improved coverage
• Integration with natural evolution strategies