On the truck dispatching problem

This article considers the minmax version of the m-Traveling Salesman Problem in which the objective is to minimize the length of the longest route. Tabu search heuristics and exact search schemes are developed. Problems involving up to 50 vertices are solved to optimality. (A)

The m-traveling salesman problem with minmax objective

A practical distribution system that arises in the context of delivering liquefied petroleum gas (LPG) through cylinders is considered in this study. To meet all the challenging constraints, the model is explicitly considered as a simultaneous pickup and delivery single commodity truncated vehicle routing problem with the homogeneous fleet of vehicles. The aim of this problem is to find the optimal routes for the set of vehicles locating at the distributing agency (DA), which offers simultaneous pickup and delivery operations over single commodity (i.e. LPG cylinders) to a fixed subset (need not serve all delivery centers) of delivery centers at rural level. The model is designed using zero-one integer linear programming. For proper treatment of the present model, an exact Lexi-search algorithm (LSA) has been developed. A comparative study is performed between the LSA and existing results for the relaxed version of the present model. Further, the efficiency of the LSA is tested through numerical experiments over small and medium CVRP benchmark test instances. The extensive computational results have shown that the LSA is productive and revealed that the real solutions have more consistent than the integral solutions in the presence of truncation constraint.

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Designing optimal route for the distribution chain of a rural LPG delivery system

The routing problems pertain to the search for a shortest route (minimum cost or minimum distance or maximum flow, etc) connecting two specified stations or nodes described as ‘source’ and ‘sink’ The paper aims at obtaining an optimal route of a more realistic situation as to scheduling maximum flows at a minimum cost from a source to a destination The distance (cost) and arc capacity between any two stations are given The objective is to find the maximum flow with the minimum cost from the source to the destination in a network The problem has many applications in the field of network flow theories Several special cases of the problem were intensively studied in the literature and proposed various techniques to solve Here we solved the present problem by the lexicographic search technique, which gives the exact solution to the problem The solution procedure is illustrated with a suitable example The algorithm is also tested in C-language and the computational details are also reported

The problem of maximum flow with minimum attainable cost in a network

Article history: Received January 16, 2017 Received in revised format: May 22, 2017 Accepted July 23, 2017 Available online July 25, 2017 This paper deals with the degree constrained k-cardinality minimum spanning tree (k-MSTPD) problem defined on a connected, edge weighted and undirected graph. The aim of this problem is to determine the least weighted spanning tree with exactly k vertices such that except the root vertex, no other vertex in the resultant spanning tree exceeds the specified degree limit. The k-MSTPD problem has many practical applications for the design of electric, communication, and transportation networks. The problem is then formulated as a zero-one programming. In this paper, an exact algorithm known as Lexi-search algorithm (LSA) is developed to tackle the k-MSTPD problem. Furthermore, the developed LSA is programmed in Matlab and tested on some benchmark instances as well as on random instances and the respective results are reported. The obtained experimental results showed that the developed LSA takes significantly less time to find the optimal solutions. Growing Science Ltd. All rights reserved. 8 © 201

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The degree constrained k-cardinality minimum spanning tree problem: a lexi-search algorithm

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An open close multiple travelling salesman problem with single depot

This study aims to optimize the number of nodes and arcs in a constructed network employing a given criteria. For this, we subject the constructed network using the methods like Shortest Path (SP), Critical Path (CP) and Max-Flow (MF) between any pair of nodes. A set of iterative algorithms have been generated using matrix operations to meet the above requirement, which is named as Pandit’s algorithm. The equivalent algorithms for SP, CP and MF are hereby represented as Pandit’s Mini-additive, Maxi-additive and Max-min algorithms respectively. The generated algorithms take less number of iterations when compared to the established methods. The proposed new algorithms are shown with suitable numerical examples and discuss their merits over the established methods. These new algorithms take less computational time and hence suggested for solving the bulk networks such as transportation GIS, telecommunication networks, information systems, project scheduling etc.

A new approach for solving the network problems

This paper deals with the bi-criteria travelling salesman subtour problem with time threshold (BTSSP-T), which comes from the family of the travelling salesman problem (TSP) and is NP-hard in the strong sense. The problem arises in several application domains, mainly in routing and scheduling contexts. Here, the model focuses on two criteria: total travel distance and gains attained. The BTSSP-T aims to determine a subtour that starts and ends at the same city and visits a subset of cities at a minimum travel distance with maximum gains, such that the time spent on the tour does not exceed the predefined time threshold. A zero-one integer-programming problem is adopted to formulate this model with all practical constraints, and it includes a finite set of feasible solutions (one for each tour). Two algorithms, namely, the Lexi-Search Algorithm (LSA) and the Tabu Search (TS) algorithm have been developed to solve the BTSSP-T problem. The proposed LSA implicitly enumerates the feasible patterns and provides an efficient solution with backtracking, whereas the TS, which is metaheuristic, will give the better approximate solution. A numerical example is demonstrated in order to understand the search mechanism of the LSA. Numerical experiments are carried out in the MATLAB environment, on the different benchmark instances available in the TSPLIB domain as well as on randomly generated test instances. The experimental results show that the proposed LSA works better than the TS algorithm in terms of solution quality and, computationally, both LSA and TS are competitive.

Bi-criteria travelling salesman subtour problem with time threshold

This paper deals with a variant of minimum spanning tree problem with multiple constraints, which includes degree, weight and budgeting constraints simultaneously together. To model the problem, a zero-one programming is incorporated. An exact solution procedure called pattern recognition technique-based lexi-search algorithm is developed. A suitable numerical illustration is given to check the applicability of the developed algorithm. Furthermore, the algorithm is programmed in C and tested with randomly generated hard instances, computational results are also reported. The overall results reveal that the proposed algorithm is fairly proficient in the sense of both acquiring the optimal solutions and computational time.

Purusotham Singamsetty

Papers

Designing optimal route for the distribution chain of a rural LPG delivery system

An open close multiple travelling salesman problem with single depot

A new approach for solving the network problems

Bi-criteria travelling salesman subtour problem with time threshold

An exact algorithm for multi-constrained minimum spanning tree problem