Andrea Tramontani

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In this paper we review the relevant literature on mathematical optimization with logical implications, i.e., where constraints can be either active or disabled depending on logical conditions to hold. In the case of convex functions, the theory of disjunctive programming allows one to formulate these logical implications as convex nonlinear programming(More)
Following the flurry of recent theoretical work on cutting planes from two-row mixed integer group relaxations of an LP tableau, we report on computational tests to evaluate the strength of two-row cuts based on lattice-free triangles having more than one integer point on one side. A heuristic procedure to generate such triangles (referred to in the(More)
We address the Open Vehicle Routing Problem (OVRP), a variant of the ‘‘classical’’ (capacitated and distance constrained) Vehicle Routing Problem (VRP) in which the vehicles are not required to return to the depot after completing their service. We present a heuristic improvement procedure for OVRP based on Integer Linear Programming (ILP) techniques. Given(More)
where x ∈ R is the vector of decision variables, c ∈ R is a linear objective function and S ⊂ R is the set of feasible solutions of (1). Because S is generally hard to deal with, a possible approach for tackling (1) is to optimize the objective function over a suitable relaxation (i.e., easy to solve) P ⊇ S. Let x be the optimal solution over P . If x ∈ S(More)
We discuss the variability in the performance of multiple runs of branchand-cut mixed integer linear programming solvers, and we concentrate on the one deriving from the use of different optimal bases of the linear programming relaxations. We propose a new algorithm exploiting more than one of those bases and we show that different versions of the(More)
The Traveling Salesman Problem with Time Windows (TSPTW) is the problem of finding a minimum-cost path visiting a set of cities exactly once, where each city must be visited within a given time window. We present an extended formulation for the problem based on partitioning the time windows into sub-windows, which we call buckets. We present cutting planes(More)