Enhanced Ideal Objective Vector Estimation for Evolutionary Multi-Objective Optimization

2025-05-28

AI Summary

In multi-objective evolutionary optimization, inaccurate and poorly generalizable estimation of the ideal objective vector severely hinders convergence and diversity. Method: This paper systematically analyzes the impact mechanisms of three types of objective-space biases on estimation accuracy and proposes an plug-and-play Enhanced Ideal-point Estimation (EIE) component. EIE integrates extreme-weighted subproblem decomposition with adaptive fine-grained local search, overcoming the coarse-grained limitations of conventional population-extreme-based estimation. Contribution/Results: Evaluated on a newly constructed bias-oriented benchmark suite and standard test suites, EIE significantly improves ideal-vector estimation accuracy and consistently enhances both convergence and diversity performance of NSGA-II, MOEA/D, and SMS-EMOA.

Technology Category

• Search and Optimization: Evolutionary Computation
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

The ideal objective vector, which comprises the optimal values of the $m$ objective functions in an $m$-objective optimization problem, is an important concept in evolutionary multi-objective optimization. Accurate estimation of this vector has consistently been a crucial task, as it is frequently used to guide the search process and normalize the objective space. Prevailing estimation methods all involve utilizing the best value concerning each objective function achieved by the individuals in the current or accumulated population. However, this paper reveals that the population-based estimation method can only work on simple problems but falls short on problems with substantial bias. The biases in multi-objective optimization problems can be divided into three categories, and an analysis is performed to illustrate how each category hinders the estimation of the ideal objective vector. Subsequently, a set of test instances is proposed to quantitatively evaluate the impact of various biases on the ideal objective vector estimation method. Beyond that, a plug-and-play component called enhanced ideal objective vector estimation (EIE) is introduced for multi-objective evolutionary algorithms (MOEAs). EIE features adaptive and fine-grained searches over $m$ subproblems defined by the extreme weighted sum method. EIE finally outputs $m$ solutions that can well approximate the ideal objective vector. In the experiments, EIE is integrated into three representative MOEAs. To demonstrate the wide applicability of EIE, algorithms are tested not only on the newly proposed test instances but also on existing ones. The results consistently show that EIE improves the ideal objective vector estimation and enhances the MOEA's performance.

Problem

• Estimating ideal objective vector in multi-objective optimization
• Addressing biases hindering ideal vector estimation
• Enhancing MOEAs with plug-and-play EIE component

Innovation

• Adaptive fine-grained search for ideal vector
• Plug-and-play EIE component for MOEAs
• Extreme weighted sum subproblems optimization