An Enhanced Logic-Based Bender’s Decomposition Algorithm with Proximity Principle for Simulator-Based Distillation Process Optimization

Abstract

The optimization of distillation processes is particularly challenging due to the presence of nonlinear equations and integer variables, resulting in complex mixed-integer nonlinear programming (MINLP) problems. This work introduces an enhanced optimization algorithm, the logic-based proximity principle Bender’s decomposition (LB-PBD), to address non-convex MINLP issues in simulator-based distillation optimization. The key innovation, the proximity principle, improves lower bound predictions by prioritizing information from the closest known integer solutions. Additionally, the integration of a multi-start points strategy and a delayed convergence strategy ensures the algorithm achieves global optimality while avoiding premature convergence. The effectiveness if the proposed LB-PBD is validated through three case studies. Numerical experiments demonstrate so-called proximity principle superior ability of original algorithm to navigate local optima, making LB-PBD more versatile than traditional deterministic algorithm (logic-based outer approximation algorithm) and stochastic algorithm (adaptive superstructure-differential evolution algorithm). In a single-column distillation case, LB-PBD achieves high accuracy. In an extractive distillation case, the algorithm successfully optimizes the separation of a near-azeotropic mixture, reducing energy consumption and improving product recovery compared to previous solutions. These results highlight LB-PBD as a robust and effective tool for solving non-convex MINLLP problems, particularly in simulator-based distillation process optimization.