Traditional decomposition based branch-and-bound algorithms, like branch-and-price, can be very efficient if the duality gap is not too large. However, if this is not the case, the branch-and-bound tree may grow rapidly, preventing the method to find a good solution. In this paper, we present a new decompositon algorithm, called ADGO (Alternating Direction Global Optimization … Read more
We present a version of GMI (Gomory mixed-integer) cuts in a way so that they are derived with respect to a “dual form” mixed-integer optimization problem and applied on the standard-form primal side as columns, using the primal simplex algorithm. This follows the general scheme of He and Lee, who did the case of Gomory … Read more
In this paper we consider the Asymmetric Quadratic Traveling Salesman Problem. Given a directed graph and a function that maps every pair of consecutive arcs to a cost, the problem consists in finding a cycle that visits every vertex exactly once and such that the sum of the costs is minimum. We propose an extended … Read more
We consider the application of mixed-integer linear programming (MILP) solvers to the minimization of submodular functions. We evaluate common large-scale linear-programming (LP) techniques (e.g., column generation, row generation, dual stabilization) for solving a LP reformulation of the submodular minimization (SM) problem. We present heuristics based on the LP framework and a MILP solver. We evaluated … Read more
In Pareto bi-objective integer optimization the optimal result corresponds to a set of non- dominated solutions. We propose a generic bi-objective branch-and-bound algorithm that uses a problem-independent branching rule exploiting available integer solutions, and cutting plane generation taking advantage of integer objective values. The developed algorithm is applied to the bi-objective team orienteering problem with … Read more
A recurrent task in mathematical programming requires optimizing polytopes with prohibitively-many constraints, e.g., the primal polytope in cutting-plane methods or the dual polytope in Column Generation (CG). This paper is devoted to the ray projection technique for optimizing such polytopes: start from a feasible solution and advance on a given ray direction until intersecting a … Read more
The primal-dual column generation method (PDCGM) is a general-purpose column generation technique that relies on the primal-dual interior point method to solve the restricted master problems. The use of this interior point method variant allows to obtain suboptimal and well-centered dual solutions which naturally stabilizes the column generation. A reduction in the number of calls … Read more
Schedule disruptions require airlines to intervene through the process of recovery; this involves modifications to the planned schedule, aircraft routings, crew pairings and passenger itineraries. Passenger recovery is generally considered as the final stage in this process, and hence passengers experience unnecessarily large impacts resulting from flight delays and cancellations. Most recovery approaches considering passengers … Read more
We first present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop an algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. The cutting surface algorithm is also applicable to problems with non-differentiable semi-infinite … Read more
This research presents a very efficient method of solving a broad class of large-scale capacitated resource management problems by introducing a new formulation and decomposition. A heuristic called Likelihood of Assignment is utilized not only to find high quality initial integer feasible solutions, but also to guide the Branch-and-Price (B&P) Algorithm towards stabilization. Although Column … Read more