The SCIP Optimization Suite is a powerful collection of optimization software that consists of the branch-cut-and-price framework and mixed-integer programming solver SCIP, the linear programming solver SoPlex, the modeling language Zimpl, the parallelization framework UG, and the generic branch-cut-and-price solver GCG. Additionally, it features the extensions SCIP-Jack for solving Steiner tree problems, PolySCIP for solving … Read more
An important problem in the breeding of livestock, crops, and forest trees is the optimum of selection of genotypes that maximizes genetic gain. The key constraint in the optimal selection is a convex quadratic constraint that ensures genetic diversity, therefore, the optimal selection can be cast as a second-order cone programming (SOCP) problem. Yamashita et … Read more
Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of rings in rectangles and the recursive packing of rings into other rings. This problem is known as the Recursive Circle Packing Problem (RCPP). … Read more
We study the simultaneous convexification of graphs of bilinear functions that contain bilinear products between variables x and y, where x belongs to a general polytope and y belongs to a simplex. We propose a constructive procedure to obtain a linear description of the convex hull of the resulting set. This procedure can be applied … Read more
This paper presents a mixed-integer quadratically constrained programming (MIQCP) formulation for B-spline constraints. The formulation can be used to obtain an exact MIQCP reformulation of any spline-constrained optimization problem, provided that the polynomial spline functions are continuous. This reformulation allows practitioners to use a general-purpose MIQCP solver, instead of a special-purpose spline solver, when solving … Read more
We present a mixed-integer nonlinear programming (MINLP) formulation of a UAV path optimization problem in an attempt to find the globally optimum solution. As objective functions in UAV path optimization problems typically tend to be non-convex, traditional optimization solvers (typically local solvers) are prone to local optima, which lead to severely sub-optimal controls. For the … Read more
This paper considers the problem of cyclic ow shop robotic cell scheduling deploying several single and dual gripper robots. In this problem, dierent part types are successively processed on multiple machines with dierent pickup criteria including free pickup, pickup within time-windows and no-waiting times. The parts are transported between the machines by the robots. We … Read more
The design of hub-and-spoke transport networks is a strategic planning problem, as the choice of hub locations has to remain unchanged for long time periods. However, strikes, disasters or traffic breakdown can lead to the unavailability of a hub for a short period of time. Therefore it is important to consider such events already in … Read more
We consider a lender (bank) who determines the optimal loan price (interest rates) to offer to prospective borrowers under uncertain risk and borrowers’ response. A borrower may or may not accept the loan at the price offered, and in the presence of default risk, both the principal loaned and the interest income become uncertain. We … Read more
Mathematical modeling of market design issues in liberalized electricity markets often leads to mixed-integer nonlinear multilevel optimization problems for which no general-purpose solvers exist and which are intractable in general. In this work, we consider the problem of splitting a market area into a given number of price zones such that the resulting market design … Read more