An Evolutionary Algorithm with Probabilistic Annealing for Large-scale Sparse Multi-objective Optimization

TL;DR

This paper introduces a novel evolutionary algorithm with probabilistic annealing designed to efficiently solve large-scale sparse multi-objective optimization problems by balancing exploration and exploitation.

Contribution

It proposes a new algorithm that uses dual probability vectors with different entropy levels to adaptively transition from exploration to exploitation in high-dimensional sparse problems.

Findings

Outperforms existing algorithms on benchmark problems.

Achieves better convergence and diversity.

Effectively identifies critical sparse solutions.

Abstract

Large-scale sparse multi-objective optimization problems (LSMOPs) are prevalent in real-world applications, where optimal solutions typically contain only a few nonzero variables, such as in adversarial attacks, critical node detection, and sparse signal reconstruction. Since the function evaluation of LSMOPs often relies on large-scale datasets involving a large number of decision variables, the search space becomes extremely high-dimensional. The coexistence of sparsity and high dimensionality greatly intensifies the conflict between exploration and exploitation, making it difficult for existing multi-objective evolutionary algorithms (MOEAs) to identify the critical nonzero decision variables within limited function evaluations. To address this challenge, this paper proposes an evolutionary algorithm with probabilistic annealing for large-scale sparse multi-objective optimization. The algorithm is driven by two probability vectors with distinct entropy characteristics: a convergence-oriented probability vector with relatively low entropy ensures stable exploitation, whereas an annealed probability vector with gradually decreasing entropy enables an adaptive transition from global exploration to local refinement. By integrating these complementary search dynamics, the proposed algorithm achieves a dynamic equilibrium between exploration and exploitation. Experimental results on benchmark problems and real-world applications demonstrate that the proposed algorithm outperforms state-of-the-art evolutionary algorithms in terms of both convergence and diversity.