Classical Benders decomposition fails when the subproblem is a mixed-integer program, due to the absence of strong duality. We propose a novel class of dual-free indicator cuts that are applicable to all Benders-decomposable problems with a pure-integer master problem and mixed-integer linear programming (MILP) subproblems. These cuts are derived from the monotonicity property of the … Read more
We consider a broad class of bilevel linear programs in which the follower’s decisions are all continuous, while the leader’s decisions may include integrality restrictions. Solving such problems to optimality is known to be NP-hard. A classical approach in bilevel optimization for constructing lower and upper bounds is based on a single-level relaxation, in which … Read more
We present an algorithm that finds an epsilon-approximate solution to a mixed integer quadratic programming (MIQP) problem, and that runs on a Turing machine in time polynomial in the size of the instance and in 1/epsilon, provided that the number of integer variables and the number of negative eigenvalues of the Hessian of the objective … Read more
We consider mixed-integer convex optimization problems in which binary indicators control continuous variables. We introduce the Coordinate Optimality Reformulation (CORe) framework, which augments standard indicator formulations by incorporating coordinate-wise optimality information. The resulting reformulations preserve global optimality while substantially improving branch-and-bound performance, particularly in sparse and structured settings where the coordinate-wise optimality conditions expose exploitable … Read more
We address the problem of optimal route planning for competitive orien- teering on real terrain. A Geographic Information System (GIS) pipeline transforms orienteering map data and digital terrain models into a fully asymmetric cost matrix that captures directional slope costs (via the Minetti metabolic model) and cumulative athlete fatigue. The resulting problem, the Asymmetric Orienteering … Read more
Live reoptimization of operating room schedules is required to cope with disruptions such as emergency arrivals and deviations in surgery durations under strict time limits. The resulting problem can be formulated as a large-scale Resource Constrained Project Scheduling Problem (RCPSP). While exact optimization methods are attractive in this context due to their ability to provide … Read more
We study cutting-plane generation for binary polynomial optimization (BPO), whose feasible region is the multilinear set of a hypergraph. Strong inequalities for this set—such as two-links, flowers, and odd $\beta$-cycles—are classically hand-derived for fixed support patterns. Instead, we propose a decision-diagram (DD) approach: for any chosen support, it separates a facet-defining cut in the local … Read more
Classical optimization methods determine a single optimal or near-optimal solution for a decision problem. In many applications, however, the decision maker is interested in evaluating a pool of high-quality solutions, to encode fairness-oriented criteria or to obtain a portfolio of alternatives to use in case of unexpected scenarios. In this paper, we consider the problem … Read more
The length-constrained cycle partition problem (LCCP) is a graph optimization problem in which a set of nodes must be partitioned into a minimum number of cycles. Every node is associated with a critical time and the length of every cycle must not exceed the critical time of any node in the cycle. We formulate LCCP … Read more