Implementing Automatic Benders Decomposition in a Modern MIP Solver

We describe the automatic Benders decomposition implemented in the commercial solver IBM CPLEX. We propose several improvements to the state-of-the-art along two lines: making a numerically robust method able to deal with the general case and improving the efficiency of the method on models amenable to decomposition. For the former, we deal with: unboundedness, failures … Read more

Exploiting Partial Convexity of Pump Characteristics in Water Network Design

The design of water networks consists of selecting pipe connections and pumps to ensure a given water demand to minimize investment and operating costs. Of particular importance is the modeling of variable speed pumps, which are usually represented by degree two and three polynomials approximating the characteristic diagrams. In total, this yields complex mixed-integer (non-convex) … Read more

Conflict-Free Learning for Mixed Integer Programming

Conflict learning plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. A major step for MIP conflict learning is to aggregate the LP relaxation of an infeasible subproblem to a single globally valid constraint, the dual proof, that proves infeasibility within the local bounds. Among others, … Read more

Computational Aspects of Infeasibility Analysis in Mixed Integer Programming

The analysis of infeasible subproblems plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from infeasible subproblems. The first is to analyze the sequence of implications, obtained by domain propagation, that led to infeasibility. The … Read more

Compact Formulations for Split Delivery Routing Problems

Split delivery routing problems are concerned with serving the demand of a set of customers with a fleet of capacitated vehicles at minimum cost, where a customer can be served by more than one vehicle if beneficial. They generalize traditional variants of routing problems and have applications in commercial as well as humanitarian logistics. Previously, … Read more