In this paper, we present a polynomial-sized linear programming formulation of the Traveling Salesman Problem (TSP). The proposed linear program is a network flow-based model. Numerical implementation issues and results are discussed. KeyWords: Linear Programming; Network Optimization; Integer Programming; Traveling Salesman Problem; Combinatorial Optimization; Scheduling; Sequencing.

In this paper, system planning network is formulated with mixed-integer programming. Two meta-heuristic procedures are considered for this problem. The cost function of this problem consists of the capital investment cost in discrete form, the cost of transmission losses and the power generation costs. The DC load flow equations for the network are embedded in the constraints of the mathematica...

Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivalent nonconvex quadratic programming problem, interior point methods for solving network flow probl...

The supply chain network design not only assists organizations production process (e.g.,plan, control and execute a product’s flow) but also ensure what is the growing need for companies in a longterm. This paper develops a three-echelon supply chain network problem including multiple plants, multiple distributors, and multiple retailers with amulti-mode demand satisfaction policy inside of pro...

A quadratic programming method with network flow constraints is proposed to improve crowd pedestrian counting in video surveillance. Most of the existing approaches estimate the number of pedestrians within one frame, which result in inconsistent predictions in temporal domain. In this paper, firstly, we segment the foreground of each frame into different groups, each of which contains several ...

in the maximum flow network interdiction problem, an attacker attempts to minimize the maximum flow by interdicting flow on the arcs of network. in this paper, our focus is on the nodal interdiction for network instead of the arc interdiction. two path inequalities for the node-only interdiction problem are represented. it has been proved that the integrality gap of relaxation of the maximum fl...

This paper shows that partial differential equations may be a possible area of application of mathematical programming. The solution of Laplace's equation with Neumann's condition is shown to be a minimum cost network flow problem with cost proportional to the arc flow. An algorithm of solving minimum quadratic cost network flow is given.