.png){kind=icon}
Return
Enhanced Ideal Objective Vector Estimation for Evolutionary Multi-Objective Optimization
.png){kind=icon}
PRE
AI
DOI：10.1109/tetci.2026.3722244.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
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 well on relatively 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 show that EIE generally improves the ideal objective vector estimation and enhances the MOEA’s performance across most biased scenarios.
Keywords:
Multi-objective optimization
evolutionary computation
ideal objective vector
test problems
bias feature
Journal
I
IF:
6.5
Papers:
1.4K
Citations:
4.5K
Organization
View more organizations
Cited Papers
No cited papers available