Tensor-Based Ant Colony Optimization for Set Meal Design in Online-to-Offline Restaurants

Set meal design (SMD) for online-to-offline (O2O) restaurant services presents a complex optimization problem, requiring the simultaneous satisfaction of diverse customer preferences, operational constraints, and profit maximization objective. To address this challenge, this article proposes a comprehensive mathematical formulation for the O2O-SMD problem. This formulation integrates complex operational requirements, such as dish variety, pricing, nutritional balance, and profitability, into a unified optimization problem with well-defined objective and constraints. To efficiently solve the O2O-SMD problem, we propose a tensor-based ant colony optimization (TACO) algorithm. Distinct from traditional ant colony optimization (ACO) variants, the core of TACO lies in reformulating the fundamental ACO operations into a tensor computational structure, enabling parallel optimization over O2O-SMD tasks at the algorithmic level. Furthermore, a dedicated local search strategy is integrated to refine solutions and accelerate convergence of the algorithm. The performance of TACO is evaluated on real-world restaurant data and benchmark instances. The experimental results show that TACO significantly outperforms a wide range of comparison algorithms in terms of solution quality, scalability, and computational efficiency, confirming its effectiveness and practical value for real-world O2O-SMD problems.