(203v) Efficient Algorithm for Simultaneous Synthesis of Heat Exchanger Networks

As traditional energy supplies dwindle and their environmental effects are of increasing concerns, energy conservation is our first line of defense. Process/energy integration has been important for the chemical and related industries, and heat exchanger network synthesis (HENS) has been studied extensively over the last 50 years. The first approach for HENS uses a sequential strategy (Linnhoff and Hindmarsh, 1983). It decomposes the problem into a series of smaller subproblems based on the concept of pinch and with differing objectives. This enables it to solve the large industry-scale problems relatively faster, which appeals to the practitioner. However, this approach cannot accurately trade-off between utility and exchanger costs. In contrast, the simultaneous approach for HENS uses no decomposition and aims to minimize directly the total annualized cost (TAC) of heat exchanger network (HEN). Although it has the potential to yield better and more holistic solutions, it involves solving a complex non-convex NP-hard mixed-integer nonlinear programming (MINLP) problem (Furman and Sahinidis, 2001), for which finding even a good solution becomes a challenge especially for larger problems. Thus, it would be desirable to develop more efficient and superior algorithms for the simultaneous approach for HENS. This is the aim of this work.

Several advances in optimization have been applied to handle large complex MINLPs. These include generalized benders decomposition, branch and bound, outer approximation, extended cutting plane, branch and reduce, and branch-and-cut. However, most of these face significant difficulty in case of large non-convex MINLP models. Two most common problems are infeasible solutions and premature termination. These have naturally prompted the researchers to make simplifications and assumptions.

An alternate and popular approach has been to simply use one of several evolutionary methods such as simulated annealing, genetic algorithm, differential evolution, tabu search, harmony search, or particle swarm optimization. These methods are largely empirical, but impervious to nonlinearity, discontinuity, and non-convexity. While they can get good solutions, they employ many tunable parameters and demand long computational times. Only recently, Fieg and his coworkers (Brandt et al., 2012; Ernst et al., 2010) have shown that specially tailored genetic algorithms are capable of obtaining good solutions for large-scale HENS problems. 

HENS models become even more complex and their solutions even more challenging, when one considers various enhancements to the basic HENS problem. These include non-isothermal mixing, non-isothermal phase changes, multiple utilities, and more complex superstructures. The presence of nonlinear area cost terms and bilinear energy balances make the generalized HENS models nonconvex. Its speedy solution to global optimality is a challenge. Commercial optimization solvers such as BARON and DICOPT fail to solve even medium-size test problems. For such problems, the outer-approximation with equality relaxation and augmented penalty (OA/ER/AP) algorithm proposed by Viswanathan and Grossmann (1990) offers some hope, although it also fails to give good solutions in its original form and cannot guarantee global solutions for nonconvex problems. However, as Tavallali et al. (2013) have demonstrated, a heuristic local search to revive the algorithm periodically can improve its performance and solution quality significantly. This provides us the motivation for using the OA/ER/AP as the underlying algorithm in our proposed solution strategy.

In this work, we present a tailor-made heuristic search strategy that repeatedly revives the OA algorithm, which in its original form is mostly ineffective for solving large HENS problems due to its critical reliance on initial feasible solution, while our approach does not need a feasible starting point. We illustrate the application of our strategy to two recent HENS models, namely those of Huang et al. (2012) and Huang & Karimi (2013). Both are large, complex, non-convex MINLP models that are difficult to solve and require substantial computational effort, but yield demonstrated novel and superior HENs than reported solutions. The former is based on an improved stagewise superstructure that allows non-isothermal mixing and stage bypasses. The latter reports a new multistage superstructure that allows cross flows, cyclic matching, series matches on a substream, multiple utilities, and utility placement at any stage. We use several test examples to demonstrate the relative effectiveness and efficiency of our proposed solution strategy as compared to some existing models or algorithms.

References

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