A Large-Scale Sparse Multiobjective Optimization Algorithm Based on Optimal Performance Scores

Jul 16, 2026

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Large-scale sparse multiobjective optimization problems (LSSMOPs) feature many decision variables but only a few nonzero variables determine most Pareto-optimal solutions. As dimensionality increases, detecting the nonzero variables becomes harder and overall optimization performance degrades. An evolutionary algorithm is developed to address these issues by introducing a score-based initialization that estimates variable importance, a mask template for targeting nonzero variables, and variable-wise mutation plus Pareto-guided normal-distribution updates to avoid local traps and accelerate global convergence, validated on eight benchmarks and three real applications.

LanguageEnglish

CategoryResearch & Report

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Pages21

Reading Time53 min

Introduction

Contributions and Proposed Approach

A Large-Scale Sparse Multiobjective Optimization Algorithm Based on Optimal Performance Scores Jia-Lin Maia , Min-Rong Chena,∗ , Guo-Qiang Zengb , Xiang Liuc,∗∗ and Jian Wengd a School of Computer Science, South China Normal University, Guangzhou, 510631, China b National-local Joint Engineering Laboratory for Digitalize Eletrical Design Technology, Wenzhou University, Wenzhou, 325035, China c Institute of Science and Technology Innovation, Dongguan University of Technology, Dongguan, 523808, China d College of Cyber Security, Guangzhou University, Guangzhou, 510006, China ARTICLE INFO ABSTRACT arXiv :2607 .04765v 1 [ cs .NE] 6 Jul 2026 Keywords: Multiobjective optimization Sparse optimization Evolutionary algorithm Optimal performance scores Large-scale sparse multiobjective optimization problems (LSSMOPs) involve a large number of decision variables and Pareto optimal solutions with only a few nonzero variables. However, asthe number of decision variables grows, it becomes increasingly challenging to accurately identify the nonzero variables, and optimization performance is adversely affected. To address these issues, this paper proposes an evolutionary algorithm for LSSMOPs. Specifically, we propose anew initialization method capable of generating scores that accurately reflect the importance of variables, and an initial mask vector template that can locate nonzero variables. This leads to the generation of a high-quality initial population. Additionally, this paper introduces a new strategy to calculate the mutation probability for each variable and a novel optimization for real variables based on the Pareto-guided normal distribution, enabling the population to avoid being trapped in local optima and quickly converge to the global optimum. Experimental results from eight benchmark problems and three real-world applications demonstrate that the proposed algorithm achieves superior performance compared with state-of-the-art algorithms. 1. Introduction Multiobjective optimization plays a central role in many fields [1], such as machine learning [2, 3], data mining [4], and financial decision making [5], aiming to optimize multiple (often conflicting) performance criteria simultaneously and to obtain the Pareto front (PF) . Pareto optimal solutions of sparse multiobjective optimization problems (SMOPs) contain only a few nonzero variables. SMOPs have direct engineering relevance in a variety of applications [6], including feature selection [7], where one seeks a compact subset of informative features to improve model interpretability and predictive performance; sparse signal reconstruction [8], which aims to recover an accurate signal from limited or noisy measurements by exploiting its inherent sparsity; and sparse neural network training [9], which enforces weight sparsity so that most network parameters become zero and the resulting model is smaller to store. In SMOPs, we seek solutions that are both close to the PF and as sparse as possible, to satisfy practical constraints like interpretability, storage, and computational cost. With the rapid growth of data scale and system complexity, large-scale sparse multiobjective optimization algorithms (LSSMOOAs) have become increasingly common: decision-variable dimensionality can be extremely high, but in many practical problems, only a small subset of variables dominantly affects objectives (i.e., solutions are sparse). This sparsity is both a challenge and an opportunity – exploiting sparse structure can dramatically reduce the search space and evaluation cost, while ignoring it often leads conventional algorithms to suffer from the curse of dimensionality or poor efficiency [10] . Conventional multiobjective evolutionary algorithms (MOEAs) perform well on small-scale benchmark problems but encounter three major bottlenecks on large-scale SMOPs [11, 12, 13] . First, random variation and standard crossover make it difficult to find key variable combina

FAQs

What makes large-scale sparse multiobjective optimization problems difficult?

They have high-dimensional decision variables while only a few nonzero variables matter, making it challenging to accurately identify key variables and maintain strong optimization performance as dimensionality grows.

How does the algorithm determine which variables are important?

It calculates variable scores from performance across intervals of the decision space, enabling construction of an initial mask template that guides the population toward nonzero variables.

What strategies are used to improve search efficiency and avoid local optima?

The method introduces variable-wise mutation probabilities and real-variable optimization using a Pareto-guided normal distribution, improving the population’s ability to escape local optima and converge to global optima.

Jul 16, 2026

Upload by Violet