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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Bibliographic Details
Published in:Processes Vol. 13; no. 4; p. 977
Main Authors: Tian, Chenshan, Zhang, Xiaodong, Lan, Yang, Sun, Jinsheng
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.04.2025
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:2227-9717
2227-9717
DOI:10.3390/pr13040977