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

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 princ...

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Vydané v:	Processes Ročník 13; číslo 4; s. 977
Hlavní autori:	Tian, Chenshan, Zhang, Xiaodong, Lan, Yang, Sun, Jinsheng
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Basel MDPI AG 01.04.2025
Predmet:	Adaptive algorithms Algorithms Approximation Case studies Complex variables Convergence Convex analysis Decomposition Design Distillation Effectiveness Energy conservation Energy consumption Evolution Evolutionary algorithms Evolutionary computation Heat exchangers Linear programming Logic Lower bounds Mathematical optimization Mathematical programming Methods Mixed integer Nonlinear equations Nonlinear programming Optimization Superstructures Variables
ISSN:	2227-9717, 2227-9717
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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.
AbstractList	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.
Audience	Academic
Author	Zhang, Xiaodong Lan, Yang Sun, Jinsheng Tian, Chenshan
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SubjectTerms	Adaptive algorithms Algorithms Approximation Case studies Complex variables Convergence Convex analysis Decomposition Design Distillation Effectiveness Energy conservation Energy consumption Evolution Evolutionary algorithms Evolutionary computation Heat exchangers Linear programming Logic Lower bounds Mathematical optimization Mathematical programming Methods Mixed integer Nonlinear equations Nonlinear programming Optimization Superstructures Variables
Title	An Enhanced Logic-Based Bender’s Decomposition Algorithm with Proximity Principle for Simulator-Based Distillation Process Optimization
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