Why is maximum clique often easy in practice?

To this day, the maximum clique problem remains a computationally challenging problem. Indeed, despite researchers’ best efforts, there exist unsolved benchmark instances with one thousand vertices. However, relatively simple algorithms solve real-life instances with millions of vertices in a few seconds. Why is this the case? Why is the problem apparently so easy in many … Read more

Strictly and Γ-Robust Counterparts of Electricity Market Models: Perfect Competition and Nash-Cournot Equilibria

This paper mainly studies two topics: linear complementarity problems for modeling electricity market equilibria and optimization under uncertainty. We consider both perfectly competitive and Nash–Cournot models of electricity markets and study their robustifications using strict robustness and the Γ-approach. For three out of the four combinations of economic competition and robustification, we derive algorithmically tractable … Read more

The sharpest column: stabilizing column generation for the bin packing problem via a lexicographic pricer

In spite of being an extremely successful method to tackle mathematical programs involving a very large number of variables, Column Generation (CG) is known to suffer from stabilization issues which can slow down its convergence significantly. In this article, we propose a new parameter-free stabilization technique for CG based on solving a lexicographic pricing problem. … Read more

Efficient Solution of Maximum-Entropy Sampling Problems

We consider a new approach for the maximum-entropy sampling problem (MESP) that is based on bounds obtained by maximizing a function of the form ldet M(x) over linear constraints, where M(x)is linear in the n-vector x. These bounds can be computed very efficiently and are superior to all previously known bounds for MESP on most … Read more

Multistage Stochastic Demand-side Management for Price-Making Major Consumers of Electricity in a Co-optimized Energy and Reserve Market

In this paper we take an optimization-driven heuristic approach, motivated by dynamic programming, to solve a multistage stochastic optimization of energy consumption for a large manufacturer who is a price-making major consumer of electricity. We introduce a mixed-integer program that co-optimizes consumption bids and interruptible load reserve offers, for such a major consumer over a … Read more

Decentralized Algorithms for Distributed Integer Programming Problems with a Coupling Cardinality Constraint

We consider a multi-player optimization where each player has her own optimization problem and the individual problems are connected by a cardinality constraint on their shared resources. We give distributed algorithms that allow each player to solve their own optimization problem and still achieve a global optimization solution for problems that possess a concavity property. … Read more

Dynamic Scheduling of Home Health Care Patients to Medical Providers

Home care provides personalized medical care and social support to patients within their own home. Our work proposes a dynamic scheduling framework to assist in the assignment of patients to health practitioners (HPs) at a single home care agency. We model the decision of which patients to assign to HPs as a discrete-time Markov decision … Read more

Finite convergence and weak sharpness for solutions of nonsmooth variational inequalities in Hilbert spaces

This paper deals with the study of weak sharp solutions for nonsmooth variational inequalities and finite convergence property of the proximal point method. We present several characterizations for weak sharpness of the solutions set of nonsmooth variational inequalities without using the gap functions. We show that under weak sharpness of the solutions set, the sequence … Read more

Coordination of a two-level supply chain with contracts

We consider the coordination of planning decisions of a single product in a supply chain composed of one supplier and one retailer, by using contracts. We assume that the retailer has the market power: he can impose his optimal replenishment plan to the supplier. Our aim is to minimize the supplier’s cost without increasing the … Read more

Efficient Algorithms for Flow over Time Evacuation Planning Problems with Lane Reversal Strategy

The contraflow techniques have widely been effective in evacuation planning research. We present effcient algorithms to solve the evacuation network flow problems, namely, the maximum, earliest arrival, quickest and lex-maximum dynamic contraflow problems having constant attributes and their generalizations with partial contraflow recon guration. Moreover, the contraflow models with inflow dependent and load dependent transit times … Read more