Different transformations for solving non-convex trim-loss problems by MINLP

Harjunkoski, Iiro; Westerlund, Tapio; Pörn, Ray; Skrifvars, Hans

doi:10.1016/s0377-2217(97)00066-0

Cited by 76 publications

(38 citation statements)

References 14 publications

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“…We next present a nontrivial set for which it can be proved from first principles that the convex extension property holds for orthogonal disjunctive sets. This set appears in a nonconvex formulation of the trim-loss problem proposed by Harjunkoski et al [12]. The model is designed to determine the best way to cut a finite number of large rolls of a raw-material into smaller products using a certain number of cutting patterns.…”

Section: N} We Say That S Has the Convex Extension Property For Orthmentioning

confidence: 99%

Strong valid inequalities for orthogonal disjunctions and bilinear covering sets

2010

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In this paper, we develop a convexification tool that enables the construction of convex hulls for orthogonal disjunctive sets using convex extensions and disjunctive programming techniques. A distinguishing feature of our technique is that, unlike most applications of disjunctive programming, it does not require the introduction of new variables in the relaxation. We develop and apply a toolbox of results that help in checking the technical assumptions under which the convexification tool can be employed. We demonstrate its applicability in integer programming by deriving the intersection cut for mixed-integer polyhedral sets and the convex hull of certain mixed/pure-integer bilinear sets. We then develop a key result that extends the applicability of the convexification tool to relaxing nonconvex inequalities, which are not naturally disjunctive, by providing sufficient conditions for establishing the convex extension property over the non-negative orthant. We illustrate the utility of this result by deriving the convex hull of a continuous bilinear covering set over the non-negative orthant.

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Section: N} We Say That S Has the Convex Extension Property For Orthmentioning

confidence: 99%

Strong valid inequalities for orthogonal disjunctions and bilinear covering sets

2010

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“…The binary variables often appear linearly in the formulation and may have different origins: (a) accounting for system operation in multiple consecutive time periods, as in the power systems scheduling problems for the day-ahead electricity markets or in multiperiod blending operations [15]; (b) allowing for connections between units only if the flowrate exceeds a certain minimum value, as in generalized pooling [21][22] or water network design problems [23][24]; (c) choosing between alternative technologies for treatment units [8,25]. In the trim loss problem [36][37], the bilinear terms involve integer variables related to the number of times a certain paper roll (product) is produced by each cutting pattern and the number of times that each cutting pattern is repeated during the process, appearing in the product demand satisfaction constraint.…”

Section: Introductionmentioning

confidence: 99%

Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems

Castro

Grossmann

2014

J Glob Optim

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We address nonconvex mixed-integer bilinear problems where the main challenge is the computation of a tight upper bound for the objective function to be maximized. This can be obtained by using the recently developed concept of multiparametric disaggregation following the solution of a mixed-integer linear relaxation of the bilinear problem. Besides showing that it can provide better bounds than a commercial global optimization solver within a given computational time, we propose to also take advantage of the relaxed formulation for contracting the variables domain and further reduce the optimality gap. Through the solution of a real-life case study from a hydroelectric power system, we show that this can be an efficient approach depending on the problem size. The relaxed formulation from multiparametric formulation is provided for a generic numeric representation system featuring a base between 2 (binary) and 10 (decimal).

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“…We assume the functions f and g are convex and continuously differentiable. MINLP problems are important in a number of applications, such as chemical process synthesis [16], product marketing [18], capital budgeting [27], portfolio optimization [9] and trim-loss optimization [21,22].…”

Section: Introductionmentioning

confidence: 99%

Solving Convex MINLP Optimization Problems Using a Sequential Cutting Plane Algorithm

Still

Westerlund

2005

Comput Optim Applic

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In this article we look at a new algorithm for solving convex mixed integer nonlinear programming problems. The algorithm uses an integrated approach, where a branch and bound strategy is mixed with solving nonlinear programming problems at each node of the tree. The nonlinear programming problems, at each node, are not solved to optimality, rather one iteration step is taken at each node and then branching is applied. A Sequential Cutting Plane (SCP) algorithm is used for solving the nonlinear programming problems by solving a sequence of linear programming problems. The proposed algorithm generates explicit lower bounds for the nodes in the branch and bound tree, which is a significant improvement over previous algorithms based on QP techniques. Initial numerical results indicate that the described algorithm is a competitive alternative to other existing algorithms for these types of problems.

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Different transformations for solving non-convex trim-loss problems by MINLP

Cited by 76 publications

References 14 publications

Strong valid inequalities for orthogonal disjunctions and bilinear covering sets

Strong valid inequalities for orthogonal disjunctions and bilinear covering sets

Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems

Solving Convex MINLP Optimization Problems Using a Sequential Cutting Plane Algorithm

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