Search

• Multi-objective non-linear fixed charge transportation problem. • Multiple modes of transportation with fixed capacities. • Solution using three metaheuristic algorithms NSGA-II, SPEA2 and GrEA. • Developed new crossover and mutation operators suitable for multiple modes of transportation. • Comparison of results using four standard performance measures namely, RNI value, HV, Spacing and GS. The main focus of this work is to formulate and solve a Fixed Charge Transportation Problem (FCTP) considering multiple modes of transport with different capacities. The condition for the feasibility is that the total capacity of all the modes of transport at each origin must be at least the total quantity of commodity available at the origin. The problem is modeled as a multi-objective minimization problem with two conflicting objectives: the total transportation cost and the total transportation time. For this purpose, crossover and mutation operators have been designed to make them suitable for the problem. The problem is solved by a modified NSGA-II, obtained by adapting the newly developed genetic operators in the metaheuristic structure of NSGA-II. Five numerical example problems of various sizes are solved using the modified NSGA-II. For a fair comparison of the performance of the modified NSGA-II, the same example problems are solved using two other algorithms: modified SPEA-2 and a modified GrEA, obtained by incorporating the same newly developed crossover and mutation respectively into SPEA-2 and GrEA. The results obtained by the modified NSGA-II, modified SPEA-2 and modified GrEA are compared using four performance metrics: RNI value, HV, Spacing and GS. The modified NSGA-II performs best for all example problems according to the metrics RNI value and GS, and for all the example problems except the example Problem 3 according to the metrics HV and spacing. For the example Problem 3, the modified GrEA yields the best performance with respect to the metrics HV and spacing. The modified SPEA2 performs worst in terms of all the metric values for all the example problems. Finally, some potential future research directions are discussed in the conclusion. [ABSTRACT FROM AUTHOR]

• A modified bat algorithm based on new position selection strategies is proposed. • The modified bat algorithm is hybrized with differantial evolution algorithm. • Exploration and exploitation abilities of the bat algorithm are balanced. • The algorithms are tested on classical benchmark functions and CEC test suites. • Hybrid method improved significantly the performance of the bat algorithm. The bat algorithm (BA) is one of the metaheuristic algorithms that are used to solve optimization problems. The differential evolution (DE) algorithm is also applied to optimization problems and has successful exploitation ability. In this study, an advanced modified BA (MBA) algorithm was initially proposed by making some modifications to improve the exploration and exploitation abilities of the BA. A hybrid system (MBADE), involving the use of the MBA in conjunction with the DE, was then suggested in order to further improve the exploitation potential and provide superior performance in various test problem clusters. The proposed hybrid system uses a common population, and the algorithm to be applied to the individual is selected on the basis of a probability value, which is calculated in accordance with the performance of the algorithms; thus, the probability of applying a successful algorithm is increased. The performance of the proposed method was tested on functions that have frequently been studied, such as classical benchmark functions, small-scale CEC 2005 benchmark functions, large-scale CEC 2010 benchmark functions, and CEC 2011 real-world problems. The obtained results were compared with the results obtained from the standard BA and other findings in the literature and interpreted by means of statistical tests. The developed hybrid system showed superior performance to the standard BA in all test problem sets and produced more acceptable results when compared to the published data for the existing algorithms. In addition, the contribution of the MBA and DE algorithms to the hybrid system was examined. [ABSTRACT FROM AUTHOR]