Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

Abstract

This manuscript reviews recent advances in deterministic global optimization for Mixed-Integer Nonlinear Programming (MINLP), as well as Constrained DerivativeFree Optimization (CDFO). This work provides a comprehensive and detailed literature review in terms of significant theoretical contributions, algorithmic developments, software implementations and applications for both MINLP and CDFO. Both research areas have experienced rapid growth, with a common aim to solve a wide range of real-world problems. We show their individual prerequisites, formulations and applicability, but also point out possible points of interaction in problems which contain hybrid characteristics. Finally, an inclusive and complete test suite is provided for both MINLP and CDFO algorithms, which is useful for future benchmarking.

Deterministic global flowsheet optimization: Between equation‐oriented and sequential‐modular methods

“…38 Flash for Reduced-Space Global Optimization. A fully equation-oriented flash model like (1)(2)(3)(4)(5)(6)(7)(8)(9), where (6-9) are replaced with suitable submodels, can be directly included in formulation (FS) for global optimization by considering all equations of the flash model as equality constraints and all variables occurring therein as optimization variables.…”

“…For a reduced-space flash model to be used in (RS), we instead seek to construct a function that contains as much as possible of the model variables and equations, thus moving them out of the optimization problem, while still admitting explicit evaluation. The extent to which such an elimination of optimization variables is possible depends on the submodels in (6)(7)(8)(9).…”

“…3 Therefore, there have been increasing efforts to develop efficient solution strategies and apply deterministic global optimization to various problems in process engineering including heat exchanger network synthesis, pooling problems, and process design. [4][5][6] However, application of deterministic global methods is expensive in terms of computational time, which has so far limited tractability with respect to the size or complexity of the models. This is partly because of the fact that the worstcase runtime of global methods is exponential, and that stateof-the-art global solvers 7,8 have mostly been used with modeling environments that essentially require fully equationoriented modeling approaches, which lead to very large problems (in terms of the number of optimization variables and equality constraints) for realistic flowsheets.…”

Model-based multi-parametric programming strategies towards the integration of design, control and operational optimization

“…For example, the approximation of a non-linear neural network can be in some cases very appealing and fitting to the data set at hand but the purpose of the approximation is defeated as the complexity reduction compared to the original model is very little. Similarly for gray and black box approaches mentioned earlier [49,50]. Given the application of receding horizon multi-parametric programming based techniques that follow the approximation step, the model structure choice becomes very limited.…”

Improving Efficiency of a Multistart with Interrupted Hooke-and-Jeeves Filter Search for Solving MINLP Problems

“…New techniques for MINLP can be found in [1,2,3,4,5]. The recent work presented in [6] is a detailed literature review and contains theoretical contributions, algorithmic developments, software implementations and applications for MINLP. The area of nonconvex MINLP has deserved a lot of attention from researchers working with heuristics, like genetic algorithm [7], ant colony [8], evolutionary algorithms [9], pattern search algorithms [10], multistart Hooke-and-Jeeves algorithm [11,12] and differential evolution [13].…”