Network design problems involve constructing edges in a transportation or supply chain network to minimize construction and daily operational costs. We study a stochastic version where operational costs are uncertain due to fluctuating demand and estimated as a sample average from historical data. This problem is computationally challenging, and instances with as few as 100 … Read more
We propose an algorithm which appears to be the first bridge between the fields of conditional gradient methods and abs-smooth optimization. Our problem setting is motivated by various applications that lead to nonsmoothness, such as $\ell_1$ regularization, phase retrieval problems, or ReLU activation in machine learning. To handle the nonsmoothness in our problem, we propose … Read more
In this paper, we introduce a new effective matrix adaptation evolution strategy (MADFO) for noisy derivative-free optimization problems. Like every MAES solver, MADFO consists of three phases: mutation, selection and recombination. MADFO improves the mutation phase by generating good step sizes, neither too small nor too large, that increase the probability of selecting mutation points … Read more
More and more people order products online and have parcels delivered to their homes. This leads to more congestion, negatively impacting the environment, public health, and safety. Carriers can use parcel lockers to consolidate and serve their customers to reduce these negative impacts. The implementation of a locker network can, however, be financially challenging. To … Read more
In this article we introduce an algorithm that approximates Pareto fronts of multiobjective mixed-integer convex optimization problems. The algorithm constructs an inner and outer approximation of the front exploiting the convexity of the patches and is applicable to problems with an arbitrary number of criteria. In the algorithm, the problem is decomposed into patches, which … Read more
We study the lift-and-project rank of the stable set polytopes of graphs with respect to the Lovász-Schrijver SDP operator \( \text{LS}_+\), with a particular focus on a search for relatively small graphs with high \( \text{LS}_+\)-rank (the least number of iterations of the \( \text{LS}_+\) operator on the fractional stable set polytope to compute the … Read more
We introduce a column elimination procedure for the capacitated vehicle routing problem. Our procedure maintains a decision diagram to represent a relaxation of the set of feasible routes, over which we define a constrained network flow. The optimal solution corresponds to a collection of paths in the decision diagram and yields a dual bound. The … Read more
The political/electoral districting problem for the single-seat constituency system is a problem of decomposing a graph into connected components of a given number of seats under several conditions and objectives. We evaluate and analyze the current division of single-seat constituencies for the House of Representatives using optimization and enumeration. The objective function is to minimize … Read more
In the known Interval Scheduling problem with Machine Availabilities (ISMA), each machine has a contiguous availability interval and each job has a specic time interval which has to be scheduled. The objective is to schedule all jobs such that the machines’ availability intervals are respected or to decide that there exists no such schedule. We … Read more
In this paper we deal with non-monotone line-search methods to minimize a smooth cost function on a Riemannian manifold. In particular, we study the number of iterations necessary for this class of algorithms to obtain e-approximated stationary points. Specifically, we prove that under a regularity Lipschitz-type condition on the pullbacks of the cost function to … Read more