A sector-based sparse variable competition framework for large-scale many-objective optimization

Large-scale many-objective optimization problems (LSMaOPs) are simultaneously complicated by high-dimensional objective and decision spaces, which severely limits the performance of existing large-scale many-objective evolutionary algorithms (LSMaOEAs). Existing LSMaOEAs alleviate these difficulties from the perspectives of reference vectors, decomposition, indicator-based evaluation, decision variable analysis, and efficient offspring generation. However, the local information derived from these methods is primarily utilized for individual selection, subproblem optimization, or region maintenance, rather than for characterizing the update preferences of decision variables across different subregions. It remains challenging to effectively translate local search preferences from the objective space into variable-level update control within the decision space. To address this challenge, this paper proposes a Sector-Based Sparse Variable Competition Framework (SSVCF). Specifically, the SSVCF divides the population into multiple objective-space sectors according to reference vectors and constructs a sector-wise scalarized fitness within each sector, thereby transforming many-objective comparison within a sector into a one-dimensional local quality evaluation. Based on this, by selecting the best solution in each sector as a representative, SSVCF performs hierarchical decision variable block probing centered on these representatives. It identifies Sector-Specific Selected Decision Variables (SSDVs) by evaluating whether perturbations to specific decision variable blocks improve the local scalar fitness of the corresponding sector. Subsequently, the competitive update of sparse decision variables based on SSDVs within each sector is performed, enabling locally inferior individuals to learn from superior ones exclusively along the SSDVs associated with the current sector. To verify the performance of SSVCF in solving LSMaOPs, five state-of-the-art LSMaOEAs are selected as the compared algorithms. Experimental results demonstrate that SSVCF outperforms the compared algorithms on LSMOP benchmark problems with M ∈ {10, 15, 20} and D ∈ {1000, 2000, 3000, 5000}, as well as on two real-world problems and an engineering application i.e. vehicle routing planning in urban logistics. The code of SSVCF can be download from https://github.com/XinmanZhao/SSVCF .