An Evolutionary Algorithm with Probabilistic Annealing for Large-scale Sparse Multi-objective Optimization
This addresses a problem for researchers and practitioners in fields like adversarial attacks and signal reconstruction, offering an incremental improvement over existing evolutionary algorithms.
The paper tackles the challenge of large-scale sparse multi-objective optimization problems, where high dimensionality and sparsity make it hard for existing algorithms to find critical nonzero variables efficiently, and proposes an evolutionary algorithm with probabilistic annealing that outperforms state-of-the-art methods in convergence and diversity on benchmarks and real-world applications.
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.