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Changdar C.,Raja Nl Khan Womens College | Mahapatra G.S.,National Institute of Technology Tiruchirappalli | Kumar Pal R.,University of Calcutta
Swarm and Evolutionary Computation | Year: 2014

In this paper, we have presented a multi-objective solid travelling salesman problem (TSP) in a fuzzy environment. The attraction of the solid TSP is that a traveller visits all the cities in his tour using multiple conveyance facilities. Here we consider cost and time as two objectives of the solid TSP. The objective of the study is to find a complete tour such that both the total cost and the time are minimized. We consider travelling costs and times for one city to another using different conveyances are different and fuzzy in nature. Since cost and time are considered as fuzzy in nature, so the total cost and the time for a particular tour are also fuzzy in nature. To find out Pareto-optimal solution of fuzzy objectives we use fuzzy possibility and necessity measure approach. A multi-objective genetic algorithm with cyclic crossover, two-point mutation, and refining operation is used to solve the TSP problem. In this paper a multi-objective genetic algorithm has been modified by introducing the refining operator. Finally, experimental results are given to illustrate the proposed approach; experimental results obtained are also highly encouraging. © 2013 Elsevier B.V. © 2014 Elsevier Inc. © 2013ElsevierB.V. Allrightsreserved. Source

Changdar C.,Raja Nl Khan Womens College | Mahapatra G.S.,National Institute of Technology Tiruchirappalli | Pal R.K.,University of Calcutta
Expert Systems with Applications | Year: 2015

In this paper, we have proposed an improved genetic algorithm (GA) to solve constrained knapsack problem in fuzzy environment. Some of the objects among all the objects are associated with a discount. If at least a predetermined quantity of the object(s) (those are associated with a discount) is selected, then an amount (in $) is considered as discount. The aim of the model is to maximize the total profit of the loaded/selected objects with obtaining minimum discount price (predetermined). For the imprecise model, profit and weight (for each of the objects) have been considered as fuzzy number. This problem has been solved using two types of fuzzy systems, one is credibility measure and another is graded mean integration approach. We have presented an improved GA to solve the problem. The genetic algorithm has been improved by introducing 'refining' and 'repairing' operations. Computational experiments with different randomly generated data sets are given in experiment section. Some sensitivity analysis have also been made and presented in experiment section. © 2014 Elsevier Ltd. All rights reserved. Source

Changdar C.,Raja Nl Khan Womens College | Pal R.K.,University of Calcutta | Mahapatra G.S.,National Institute of Technology Tiruchirappalli
Soft Computing | Year: 2016

In this paper, a genetic-ant colony optimization algorithm has been presented to solve a solid multiple Travelling Salesmen Problem (mTSP) in fuzzy rough environment. In solid mTSP, a set of nodes (locations/cities) are given, and each of the cities must be visited exactly once by the salesmen such that all of them start and finish at a depot using different conveyance facility. A solid mTSP is an extension of mTSP where the travellers use different conveyance facilities for travelling from one city to another. To solve an mTSP, a hybrid algorithm has been developed based on the concept of two algorithms, namely genetic algorithm (GA) and ant colony optimization (ACO) based algorithm. Each salesman selects his/her route using ACO and the routes of different salesmen (to construct a complete solution) are controlled by the GA. Here, a set of simple ACO characteristics have further been modified by incorporating a special feature namely ‘refinement’. In this paper, we have utilized cyclic crossover and two-point’s mutation in the proposed algorithm to solve the problem. The travelling cost is considered as imprecise in nature (fuzzy-rough) and is reduced to its approximate crisp using fuzzy-rough expectation. Computational results with different data sets are presented and some sensitivity analysis has also been made. © 2016 Springer-Verlag Berlin Heidelberg Source

Changdar C.,Raja Nl Khan Womens College | Maiti M.K.,Mahishadal Raj College | Maiti M.,Vidyasagar University
Iranian Journal of Fuzzy Systems | Year: 2013

A solid travelling salesman problem (STSP) is a travelling salesman problem (TSP) where the salesman visits all the cities only once in his tour using different conveyances to travel from one city to another. Costs and environmental effect factors for travelling between the cities using different conveyances are different. Goal of the problem is to find a complete tour with minimum cost that damages the environment least. An ant colony optimization (ACO) algorithm is developed to solve the problem. Performance of the algorithm for the problem is compared with another soft computing algorithm, Genetic Algorithm(GA). Problems are solved with crisp as well as fuzzy costs. For fuzzy cost and environmental effect factors, cost function as well as environment constraints become fuzzy. As optimization of a fuzzy objective function is not well defined, fuzzy possibility approach is used to get optimal decision. To test the efficiency of the algorithm, the problem is solved considering only one conveyance facility ignoring the environmental effect constraint, i.e., a classical two dimensional TSP (taking standard data sets from TSPLIB for solving the problem). Different numerical examples are used for illustration. Source

Das Gupta R.,Raja Nl Khan Womens College | Chakravorty P.P.,Raja Nl Khan Womens College | Kaviraj A.,Kalyani University
Bulletin of Environmental Contamination and Toxicology | Year: 2010

The 96 h LC 50 values of six insecticides were determined on a non-target epigeic earthworm Perionyx excavatus under laboratory conditions. Cypermethrin was found most toxic to P. excavatus (LC 50-0.008 mg/kg), followed by endosulfan (LC 50-0.03 mg/kg), carbaryl (LC 50-6.07 mg/kg), chlorpyrifos (LC 50-7.3 mg/kg), aldicarb (LC 50-10.63 mg/kg) and monocrotophos (LC 50-13.04 mg/kg). When these LC 50 values were compared with their respective recommended agricultural doses, aldicarb and carbaryl appeared more dangerous than other pesticides because of their lower LC 50 values than their respective recommended agricultural dose. Mean lethal time to cause 50% mortality at recommended agricultural dose (LT 50) also indicated that aldicarb achieved the fastest LT 50 (26 h) followed by endosulfan (38 h) and carbaryl (44 h) indicating the danger of these pesticides to P. excavatus. © 2010 Springer Science+Business Media, LLC. Source

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