The additive algorithm was one of the early versions of the approach known as implicit enumeration or branch and bound. It solves a linear program in n 0-1 variables by systematically enumerating an (often small) subset of the 2” possible binary n-vectors, while using the logical implications of the 0-1 property to ensure that the whole set is implicitly examined. [The Science Citation Index® (...

This paper shows some useful properties of the adjacency structures of a class of combinatorial polyhedra including the equality constrained 0-1 polytopes. The class of polyhedra considered here includes 0-1 polytopes related to some combinatorial optimization problems; e.g., set partitioning polytopes, set packing polytopes, perfect matching polytopes, vertex packing polytopes and all the face...

The soft-clustered vehicle-routing problem (SoftCluVRP) is a variant of the classical capacitated problem. Customers are partitioned into clusters and all customers same cluster must be served by vehicle. In this paper, we present large multiple neighborhood search for SoftCluVRP. We design analyze destroy repair operators as well two post-optimization components, which both based on variable d...

We present a perfect formulation for a single generator in the unit commitment problem, inspired by the dynamic programming approach taken by Frangioni and Gentile. This generator can have characteristics such as ramp up/down constraints, time-dependent start-up costs, and start-up/shut-down limits. To develop this perfect formulation we extend the result of Balas on unions of polyhedra to pres...

A conditional lower bound on the minimand of an integer program is a number which would be a valid lower bound if the constraint set were amended by certain inequalities, also called conditional. If such a conditional lower bound exceeds some known upper bound, then every solution better than the one corresponding to the upper bound violates at least one of the conditional inequalities. This yi...