Mixed Integer Nonlinear Programming by Sven Leyffer, Jon Lee

By Sven Leyffer, Jon Lee

Many engineering, operations, and clinical purposes contain a mix of discrete and non-stop determination variables and nonlinear relationships concerning the choice variables that experience a suggested impact at the set of possible and optimum options. Mixed-integer nonlinear programming (MINLP) difficulties mix the numerical problems of dealing with nonlinear capabilities with the problem of optimizing within the context of nonconvex capabilities and discrete variables. MINLP is without doubt one of the so much versatile modeling paradigms on hand for optimization; yet simply because its scope is so huge, within the so much normal circumstances it really is hopelessly intractable.

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FLay: The FLay problems [98] are farmland layout problems where the objective is to determine the optimal length and width of a number of rectangular patches of land with fixed area, such that the perimeter of the set of patches is minimized. fo-m-o: These are block layout design problems [33], where an orthogonal arrangement of rectangular departments within a given rectangular facility is required. A distance-based objective function is to be minimized, and the length and width of each department should satisfy given size and area requirements.

To avoid cycling, the removed cuts are usually stored in a pool. Whenever a cut of the pool is found to be violated by the current solution it is put back into the formulation. Linearization Point Selection. A fundamental question in any linearization-based algorithm (like OA, ECP, or LP/NLP-BB) is at which points should the linearizations be taken. Each algorithm specifies a minimal set of points at which linearizations must be taken in order to ensure convergence to the optimal solution. However, the algorithm performance may be improved by additional linearizations.

Thus, there is no dynamic memory allocation, and the user must specify a maximum memory (stack) size at the beginning of algorithm to store the list of open nodes. For the computational experiments with MINLP BB, different levels of stack size were tried in an attempt to use the entire available memory for each instance. The default search strategies of depth-first-search with backtrack to best-bound and pseudo-costs branching were employed in MINLP BB (v20090811). 6. SBB. SBB [30] is a NLP-based branch-and-bound solver that is available through the GAMS modeling language.

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