Advanced shelf space allocation in brick-and-mortar stores: A multi-population differential evolution approach for high-impact planogram design

Shelf space is one of a retailer’s most valuable assets, yet designing profitable planograms remains a high-stakes, NP-hard challenge. Small layout changes can shift consumer attention, trigger substitution effects, and swing category profits, but conventional heuristics and single-population metaheuristics often collapse under tight spatial and demand constraints. This paper advances a Multi-Population Differential Evolution (MP–DE) framework that redefines retail shelf optimization. The model embeds two-dimensional geometry, contiguous facings, and nonlinear space elasticity, while the algorithm enforces feasibility by design, maintains diversity through island sub-swarms, and triggers adaptive restarts to avoid stagnation. Across sixty benchmark scenarios, MP–DE outperforms Genetic Algorithms, Particle Swarm Optimization, and classical Differential Evolution—delivering profit gains above 15 %, variance reductions exceeding 50 %, and statistically significant superiority on all tests. The results establish MP–DE as a scalable, reliable, and profit-driven optimization engine for modern retailers, bridging cutting-edge evolutionary computation with actionable planogram design.