Submodular Flow Problem with a Nonseparable Cost Function

Submodular Flow Problem with a Nonseparable Cost Function

The submodular flow problem is extended by considering a nonseparable cost function, which is assumed to enjoy a variant of the exchange property of the base polyhedron of a submodular system. Two optimality criteria are established, one in terms of potentials associated with vertices and the other in terms of negative cycles in an auxiliary graph. These are natural extensions of the well-known...

A Novel Experimental Analysis of the Minimum Cost Flow Problem

In the GA approach the parameters that influence its performance include population size, crossover rate and mutation rate. Genetic algorithms are suitable for traversing large search spaces since they can do this relatively fast and because the mutation operator diverts the method away from local optima, which will tend to become more common as the search space increases in size. GA’s are base...

Submodular Cost Allocation Problem and Applications

We study the Minimum Submodular-Cost Allocation problem (MSCA). In this problem we are given a finite ground set V and k non-negative submodular set functions f1, . . . , fk on V . The objective is to partition V into k (possibly empty) sets A1, · · · , Ak such that the sum ∑k i=1 fi(Ai) is minimized. Several well-studied problems such as the non-metric facility location problem, multiway-cut i...

A Fuzzy Random Minimum Cost Network Flow Programming Problem

In this paper, a fuzzy random minimum cost flow problem is presented. In this problem, cost parameters and decision variables are fuzzy random variables and fuzzy numbers respectively. The object of the problem is to find optimal flows of a capacitated network. Then, two algorithms are developed to solve the problem based on Er-expected value of fuzzy random variables and chance-constrained pro...

A Faster Capacity Scaling Algorithm for Minimum Cost Submodular Flow