The multiple traveling salesperson problem (MTSP) is an extension of the well known traveling salesperson problem (TSP). Given m > 1 salespersons and n > m cities to visit, the MTSP seeks a partition of cities into m groups as well as an ordering among cities in each group so that each group of cities is visited by exactly one salesperson in their specified order in such a way that each city is visited exactly once and sum of total distance traveled by all the salespersons is minimized. Apart from the objective of minimizing the total distance traveled by all the salespersons, we have also considered an alternate objective of minimizing the maximum distance traveled by any one salesperson, which is related with balancing the workload among salespersons. In this paper, we have proposed a new grouping genetic algorithm based approach for the MTSP and compared our results with other approaches available in the literature. Our approach outperformed the other approaches on both the objectives.

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Given an undirected, connected, weighted graph, the leaf-constrained minimum spanning tree (LCMST) problem seeks a spanning tree of the graph with smallest weight among all spanning trees of the graph, which contains at least l leaves. In this paper we have proposed two new metaheuristic approaches for the LCMST problem. One is an ant-colony optimization (ACO) algorithm, whereas the other is a tabu search based algorithm. Similar to a previously proposed genetic algorithm, these metaheuristic approaches also use the subset coding that represents a leaf-constrained spanning tree by the set of its interior vertices. Our new approaches perform well in comparison with two best heuristics reported in the literature for the problem — the subset-coded genetic algorithm and a greedy heuristic.

Dimensionality reduction or the optimal selection of features is a challenging task due to large search space. Currently, many research has been performed in this domain to improve the accuracy as well as to minimize the computational complexity. Particle Swarm Optimization (PSO) based feature selection approach seems very promising and has been extensively used for this work. In this paper, a Threshold Controlled Binary Particle Swarm Optimization (TC-BPSO) along with Multi-Class Support Vector Machine (MC-SVM) is proposed and compared with Conventional Binary Particle Swarm Optimization (C-BPSO). TC-BPSO is used for the selection of features while MC-SVM is used to calculate the classification accuracy. 70% of the data is used to train the MC-SVM model while the test has been performed on rest 30% data to calculate the accuracy. Proposed approach is tested on ten different datasets having varying difficulties such as some datasets having large number of features while some have small, some have just two classes while some have many classes, some datasets having small number of instances while some have large number of instances and the results obtained on these datasets are compared with some of the existing methods. Experiments show that the obtained results are very promising and achieved the best accuracy in minimum possible features. Proposed approach outperforms C-BPSO in all contexts on most of the datasets and 3-4 times computationally faster. It also outperforms in all context when compared with the existing work and 5-8 times computationally faster.