In wet-lab experiments, the slime mold Physarum polycephalum has demonstrated its ability to tackle a variety of computing tasks, among them computation shortest paths and design efficient networks. For path problem, mathematical model for evolution is available it been shown in computer experiments through analysis that dynamics solves problem. this paper, we generalize network We formulate as...

Inverse maximum flow (IMDF), is among the most important problems in the field ofdynamic network flow, which has been considered the Euclidean norms measure in previousresearches. However, recent studies have mainly focused on the inverse problems under theHamming distance measure due to their practical and important applications. In this paper,we studies a general approach for handling the inv...

We introduce a novel, node flow based mathematical model for the fixed-time version of a central problem in the liner shipping industry called the Liner Shipping Fleet Repositioning Problem (LSFRP). We call this version of the problem the Inflexible Visitation LSFRP (IVLSFRP). During repositioning, vessels are moved between routes in a liner shipping network. Shipping lines wish to reposition v...

We solve an important problem for the liner shipping industry called the Liner Shipping Fleet Repositioning Problem (LSFRP). The LSFRP poses a large financial burden on liner shipping firms. During repositioning, vessels are moved between services in a liner shipping network. Shippers wish to reposition vessels as cheaply as possible without disrupting the cargo flows of the network. The LSFRP ...

In this paper new and generalized lower bounds for the graph partitioning problem are presented. These bounds base on the well known lower bound of embedding a clique into the given graph with minimal congestion which is equivalent to a multicommodity flow problem where each vertex sends a commodity of size one to every other vertex. Our new bounds use arbitrary multicommodity flow instances fo...

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...

In this paper we present a computational comparison of four different flow formulations for the capacitated location-routing problem. We introduce three new flow formulations for the problem, namely a two-index two-commodity flow formulation, a three-index vehicle-flow formulation and a three-index two-commodity flow formulation. We also consider the known two-index vehicle-flow formulation and...

A variety of integer programming formulations have been proposed for Vehicle Routing Problems (VRPs), including the so-called twoand three-index formulations, the set partitioning formulation, and various formulations based on extra variables representing the flow of one or more commodities. Until now, there has not been a systematic study of how these formulations relate to each other. An exce...

As the Internet becomes more virtualized and software-defined, new functionality is introduced in the network core: the distributed resources available in ISP central offices, universal nodes, or datacenter middleboxes can be used to process (e.g., filter, aggregate or duplicate) data. Based on this new networking paradigm, we formulate the Constrained Virtual Steiner Arborescence Problem (CVSA...

This paper presents a network design problem with relays considering the twoedge network connectivity. The problem arises in telecommunication and logistic networks where a constraint is imposed on the distance that a commodity can travel on a route without being processed by a relay, and the survivability of the network is critical in case of a component failure. The network design problem inv...