Search Space Analysis in Work and Heat Exchange Networks Synthesis using MINLP Models

Superstructure-based optimization models have been used as important approaches in solving process systems engineering problems. Despite its promising results, mixed-integer nonlinear programming (MINLP) optimization models are usually complex, once they involve integer and continuous variables, and nonlinear, non-convex functions. For work and heat exchange networks (WHEN) synthesis, even in problems of few process streams, the derived MINLP models have large combinatorial and continuous search spaces. In the present paper, the search spaces of two equivalents MINLP models for WHEN synthesis are analyzed to test their influence on optimization performance. The models are derived from the same superstructure, but one of those uses strategies to reduce the number of decision variables that provides a considerable diminution of combinatorial problem. The same bi-level meta-heuristic optimization approach in which Simulated Annealing deals with the combinatorial level and Particle Swarm Optimization with the continuous one is used to solve both MINLP problems. The mean values of total annualized cost and elapsed time from several optimization runs of both models are compared. The results show that the decision-variable-reduced model is more efficient and consistent than the standard-decision-variable one. It can be concluded that combinatorial search space reduction is important for optimization performance of highly complex decision-making problems such as WHEN synthesis and should be addressed in WHEN modeling because the problem’s complexity increases exponentially with the number of the model binary variables.