In this article, we provide an overview of the current state of the art with respect to solution of mixed integer linear optimization problems (MILPS) in parallel. Sequential algorithms for solving MILPs have improved substantially in the last two decades and commercial MILP solvers are now considered effective off-the-shelf tools for optimization. Although concerted development of parallel MIL...

This thesis presents methods for finding optimal trajectories for vehicles subjected to avoidance and assignment requirements. The former include avoidance of collisions with obstacles or other vehicles and avoidance of thruster plumes from spacecraft. Assignment refers to the inclusion of decisions about terminal constraints in the optimization, such as assignment of waypoints to UAVs and the ...

SelfSplit is a simple mechanism to convert a sequential tree-search code into a parallel one. In this paradigm, tree-search is distributed among a set of workers, each of which is able to autonomously determine—without any communication with the other workers—the job parts it has to process. SelfSplit already proved quite effective in parallelizing Constraint Programming solvers. In the present...

This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as lift-and-project cuts, Gomory mixed integer cuts, mixed integer rounding cuts, split cuts and intersection cuts, and it reveals the relationships between these...

This paper presents an approach to solving discretely constrained, mixed linear complementarity problems (DC-MLCPs). Such formulations include a variety of interesting and realistic models of which two are highlighted: a market-clearing auction typical in electric power markets but suitable in other more general contexts, and a network equilibrium suitable to energy markets as well as other gri...

ÐIn this paper, we propose an enumeration method to check link conflicts in the mapping of n-dimensional uniform dependence algorithms with arbitrary convex index sets into k-dimensional processor arrays. Previous methods on checking the link conflicts had to examine either the whole index set or the I/O spaces whose size are O…N2n† or O…Nnÿ1†, respectively, where N is the problem size of the n...

A central result in the theory of integer optimization states that a system of linear diophantine equations Ax = b has no integral solution if and only if there exists a vector in the dual lattice, yT A integral such that yT b is fractional. We extend this result to systems that both have equations and inequalities {Ax = b, Cx ≤ d}. We show that a certificate of integral infeasibility is a line...

The theory of duality for linear programs is well-developed and has been successful in advancing both the theory and practice of linear programming. In principle, much of this broad framework can be extended to mixed integer linear programs, but this has proven difficult, in part because duality theory does not integrate well with current computational practice. This paper surveys what is known...

We consider the integer L-shaped method for two-stage stochastic integer programs. To improve the performance of the algorithm, we present and combine two strategies. First, to avoid timeconsuming exact evaluations of the second-stage cost function, we propose a simple modification that alternates between linear and mixed-integer subproblems. Then, to better approximate the shape of the second-...