We introduce EETTlib, an instance library for the Energy-Efficient Train Timetabling problem. The task in this problem is to adjust a given timetable draft such that several key indicators relating to the energy consumption of the resulting railway traffic are minimized. These include peak power consumption, total energy consumption, loss in recuperation energy, fluctuation in … Read more
In this paper, a new randomized solver (called VRDFON) for noisy unconstrained derivative-free optimization (DFO) problems is discussed. Complexity result in the presence of noise for nonconvex functions is studied. Two effective ingredients of VRDFON are an improved derivative-free line search algorithm with many heuristic enhancements and quadratic models in adaptively determined subspaces. Numerical results … Read more
It is a challenging task to fairly compare local solvers and heuristics against each other and against global solvers. How does one weigh a faster termination time against a better quality of the found solution? In this paper, we introduce the confined primal integral, a new performance measure that rewards a balance of speed and … Read more
We revisit and strengthen splitting methods for solving doubly nonnegative, DNN, relaxations of the quadratic assignment problem, QAP. We use a modified restricted contractive splitting method, rPRSM, approach. Our strengthened bounds and new dual multiplier estimates improve on the bounds and convergence results in the literature. Citation Department of Combinatorics & Optimization, University of Waterloo, … Read more
Two-stage stochastic models give rise to very large optimization problems. Several approaches have been devised for efficiently solving them, including interior-point methods (IPMs). However, using IPMs, the linking columns associated to first-stage decisions cause excessive fill-in for the solution of the normal equations. This downside is usually alleviated if variable splitting is applied to first-stage … Read more
Different versions of polyhedral outer approximation is used by many algorithms for mixed-integer nonlinear programming (MINLP). While it has been demonstrated that such methods work well for convex MINLP, extending them to solve also nonconvex problems has been challenging. One solver based on outer linearization of the nonlinear feasible set of MINLP problems is the … Read more
We present new theory, heuristics and algorithms for preprocessing instances of the Stable Marriage with Ties and Incomplete lists (SMTI), the Hospitals/Residents with Ties (HRT), and the Worker-Firms with Ties (WFT) problems. We show that instances of these problems can be preprocessed by removing from the preference lists of some agents entries that correspond to … Read more
The minimum cut problem, MC, and the special case of the vertex separator problem, consists in partitioning the set of nodes of a graph G into k subsets of given sizes in order to minimize the number of edges cut after removing the k-th set. Previous work on this topic uses eigenvalue, semidefinite programming, SDP, … Read more
In state-of-the-art mixed-integer programming solvers, a large array of reduction techniques are applied to simplify the problem and strengthen the model formulation before starting the actual branch-and-cut phase. Despite their mathematical simplicity, these methods can have significant impact on the solvability of a given problem. However, a crucial property for employing presolving techniques successfully is … Read more
We report on the selection process leading to the sixth version of the Mixed Integer Programming Library. Selected from an initial pool of 5,721 instances, the new MIPLIB 2017 collection consists of 1,065 instances. A subset of 240 instances was specially selected for benchmarking solver performance. For the first time, these sets were compiled using … Read more