In this lecture, we will talk about the technique of using Linear Programming (LP) to solve combinatorial optimization problems. The lecture is divided into two parts. In the first part, we discuss the theoretical aspects of LP and illustrate by exmaples how combinatoric problems can be reforumated as LP problems. In the second part, we introduce two popular algorithms in solving LP problems: t...

The Berth Allocation Problem (BAP) consists on programming and allocating ships to berthing areas along a quay. The BAP is modeled as a vehicle routing problem and a recently proposed evolutionary hybrid method denominated PTA/LP is used to solve it. The PTA/LP combines the Population Training Algorithm with Linear Programming to generate improving incoming columns in a column generation proces...

We estimate the number of violator spaces of given dimension d and number of constraints n. We show that the number of nondegenerate regular violator spaces is at most n d , and that the number of all violator spaces is at least of order exp(n). This is related to the question whether the class of optimization problems described by violator spaces (or LP-type problems) is more general than line...

The formulation of complex planning models, such as linear programming (LP) systems, is a difficult task that enjqs little support by current decision support systems tools. It is aypothesized that current artificial intelligence technology is insufficient to build generalized formulation tools that would be usable by OR-naive end users. As an alternative, this paper presents a domain-specific ...

We formally derive the standard deterministic linear program (LP) for bid-price control by making an affine functional approximation to the optimal dynamic programming value function. This affine functional approximation gives rise to a new LP that yields tighter bounds than the standard LP. Whereas the standard LP computes static bid prices, our LP computes a time trajectory of bid prices. We ...

In this paper, two-person matrix games is considered whose elements of pay-off matrix are triangular fuzzy numbers (TFNs). To solve such game a new method based on α-cut of TFN is developed for each of the players. In this method, two auxiliary bi-objective linear programming (BOLP) models are derived. Then using average weighted approach these two BOLP models are decomposed into two auxiliary ...

The problem of linear programming (LP) is one of the earliest formulated problems in mathematical programming where a linear function has to be maximized (minimized) over a convex constraint polyhedron X. The simplex algorithm was early suggested for solving this problem by moving toward a solution on the exterior of the constraint polyhedron X. In 1984, the area of linear programming underwent...

The covariance matrix in the Mahalanobis distance can be trained by semi-definite programming, but training for a large size data set is inefficient. In this paper, we constrain the covariance matrix to be diagonal and train Mahalanobis kernels by linear programming (LP). Training can be formulated by ν-LP SVMs (support vector machines) or regular LP SVMs. We clarify the dependence of the solut...

MAP inference for general energy functions remains a challenging problem. While most efforts are channeled towards improving the linear programming (LP) based relaxation, this work is motivated by the quadratic programming (QP) relaxation. We propose a novel MAP relaxation that penalizes the Kullback-Leibler divergence between the LP pairwise auxiliary variables, and QP equivalent terms given b...