In this paper, we introduce a unified mathematical formulation for the Capacitated Vehicle Routing Problem (CVRP) and for the Capacitated Location Routing Problem (CLRP), adopting radiality constraints in order to guarantee valid routes and eliminate subtours. This idea is inspired by formulations already employed in electric power distribution networks, which requires a radial topology in its operation. The results show that the proposed formulation greatly improves the convergence of the solver.
This paper presents the implementation of an efficient modified genetic algorithm for solving the multi-traveling salesman problem (mTSP). The main characteristics of the method are the construction of an initial population of high quality and the implementation of several local search operators which are important in the efficient and effective exploration of promising regions of the solution space. Due to the combinatorial complexity of mTSP, the proposed methodology is especially applicable for real-world problems. The proposed algorithm was tested on a set of six benchmark instances, which have from 76 and 1002 cities to be visited. In all cases, the best known solution was improved. The results are also compared with other existing solutions procedure in the literature.
During the past two decades, there have been increasing interests on permutation flow shop with different types of objective functions such as minimizing the makespan, the weighted mean flow-time etc. The permutation flow shop is formulated as a mixed integer programming and it is classified as NP-Hard problem. Therefore, a direct solution is not available and meta-heuristic approaches need to be used to find the near-optimal solutions. In this paper, we present a new discrete firefly meta-heuristic to minimize the makespan for the permutation flow shop scheduling problem. The results of implementation of the proposed method are compared with other existing ant colony optimization technique. The preliminary results indicate that the new proposed method performs better than the ant colony for some well known benchmark problems.