By Pierre Bonami, Mustafa Kilinç, Jeff Linderoth (auth.), Jon Lee, Sven Leyffer (eds.)
Many engineering, operations, and medical functions contain a mix of discrete and non-stop determination variables and nonlinear relationships regarding the choice variables that experience a said impression at the set of possible and optimum strategies. Mixed-integer nonlinear programming (MINLP) difficulties mix the numerical problems of dealing with nonlinear services with the problem of optimizing within the context of nonconvex services and discrete variables. MINLP is among the such a lot versatile modeling paradigms to be had for optimization; yet simply because its scope is so large, within the so much normal situations it's hopelessly intractable. still, an increasing physique of researchers and practitioners — together with chemical engineers, operations researchers, business engineers, mechanical engineers, economists, statisticians, desktop scientists, operations managers, and mathematical programmers — have an interest in fixing large-scale MINLP instances.
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Additional resources for Mixed Integer Nonlinear Programming
For branching strategies, MINLP BB contains implementations of most fractional branching, strong-branching, approximate strong-branching using secondorder information, pseudo-costs branching and reliability branching. MINLP BB is written in FORTRAN. 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.
MINLP BB is written in FORTRAN. 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).
1. Strong-branching. Strong-branching consists in computing i i and Dj+ by performing the branching on variable xj and the values Dj− solving the two associated sub-problems. For each variable xj currently ALGORITHMS AND SOFTWARE FOR CONVEX MINLP 17 i i and Nj+ obtained by fractional in x ˆij , we solve the two subproblems Nj− i branching down and up, respectively, on variable j. Because Nj− and/or i Nj+ may be proven infeasible, depending on their status, diﬀerent decision may be taken. • If both sub-problems are infeasible: the node N i is infeasible and is fathomed.
Mixed Integer Nonlinear Programming by Pierre Bonami, Mustafa Kilinç, Jeff Linderoth (auth.), Jon Lee, Sven Leyffer (eds.)