Computing an enclosure for multiobjective mixed-integer nonconvex optimization problems using piecewise linear relaxations

In this paper, a new method for computing an enclosure of the nondominated set of multiobjective mixed-integer problems without any convexity requirements is presented. In fact, our criterion space method makes use of piecewise linear relaxations in order to bypass the nonconvexity of the original problem. The method chooses adaptively which level of relaxation is … Read more

Optimal Reconfiguration with Variant Transmission Times on Network

Contraflow means lane reversals on networks. In lane reversal reconfiguration, the capacity of arc increases by reorienting arcs towards demand nodes, which maximizes the flow value and reduces the travel time. In this work, we survey the existing pieces of literature on single and multi-commodity contraflow problems with symmetric and asymmetric travel times on parallel … Read more

Continuous Covering on Networks: Strong Mixed Integer Programming Formulations

Covering problems are well-studied in the domain of Operations Research, and, more specifically, in Location Science. When the location space is a network, the most frequent assumption is to consider the candidate facility locations, the points to be covered, or both, to be discrete sets. In this work, we study the set-covering location problem when … Read more

Decision Diagrams for Discrete Optimization: A Survey of Recent Advances

In the last decade, decision diagrams (DDs) have been the basis for a large array of novel approaches for modeling and solving optimization problems. Many techniques now use DDs as a key tool to achieve state-of-the-art performance within other optimization paradigms, such as integer programming and constraint programming. This paper provides a survey of the … Read more

Targeted Multiobjective Dijkstra Algorithm

In this paper, we introduce the Targeted Multiobjective Dijkstra Algorithm (T-MDA), a label setting algorithm for the One-to-One Multiobjective Shortest Path (MOSP) Problem. The T-MDA is based on the recently published Multiobjective Dijkstra Algorithm (MDA) and equips it with A*-like techniques. The resulting speedup is comparable to the speedup that the original A* algorithm achieves … Read more

Incorporating Holding Costs in Continuous-TimeService Network Design: New Model, Relaxation, and Exact Algorithm

The continuous-time service network design problem (CTSNDP) occurs widely in practice. It aims to minimize the total operational cost by optimizing the schedules of transportation services and the routes of shipments for dispatching, which can occur at any time point along a continuous planning horizon. In order to be cost effective, shipments often wait to … Read more

A New Bilevel Optimization Approach for Computing Ramsey Numbers

In this article we address the problem of finding lower bounds for small Ramsey numbers $R(m,n)$ using circulant graphs. Our constructive approach is based on finding feasible colorings of circulant graphs using Integer Programming (IP) techniques. First we show how to model the problem as a Stackelberg game and, using the tools of bilevel optimization, … Read more

A Trilevel Model for Segmentation of the Power Transmission Grid Cyber Network

Network segmentation of a power grid’s communication system is one way to make the grid more resilient to cyber attacks. We develop a novel trilevel programming model to optimally segment a grid communication system, taking into account the actions of an information technolology (IT) administrator, attacker, and grid operator. The IT administrator is given an … Read more

On fault-tolerant low-diameter clusters in graphs

Cliques and their generalizations are frequently used to model “tightly knit” clusters in graphs and identifying such clusters is a popular technique used in graph-based data mining. One such model is the $s$-club, which is a vertex subset that induces a subgraph of diameter at most $s$. This model has found use in a variety … Read more

Interdicting Low-Diameter Cohesive Subgroups in Large-Scale Social Networks

The s-clubs model cohesive social subgroups as vertex subsets that induce subgraphs of diameter at most s. In defender-attacker settings, for low values of s, they can represent tightly-knit communities whose operation is undesirable for the defender. For instance, in online social networks, large communities of malicious accounts can effectively propagate undesirable rumors. In this … Read more