The Multiple Traveling Salesman Problem (MTSP) was able to model and solve various theoretical and real-life applications. This problem is one of the many difficult issues that have no perfect solution yet. In this paper, on the one hand genetic algorithms with different combinations of operators and simulated annealing were used to solve the MTSP. On the other hand, the genetic algorithm with the combination of operators that gave the best solutions of the MTSP was hybridized with a Simulated Annealing algorithm. The simulation results showed that the hybrid algorithm significantly outperforms most of the comparable methods in obtaining the best-fitness solutions compared to the other methods in most of the test cases. In addition, by scaling the fitness function according to the amplitude of tours, it was obvious that the non-dominated front obtained by the hybrid algorithm was better than the non-dominated front obtained by the other algorithms.

Stochastic optimization algorithm provides a robust and efficient approach for solving complex real world problems. Backtracking Search Optimization Algorithm (BSA) is a new stochastic evolutionary algorithm and the aim of this paper is to introduce a hybrid approach combining the BSA and Quadratic approximation (QA), called HBSAfor solving unconstrained non-linear, non-differentiable optimization problems. For the validity of the proposed method the results are compared with five state-of-the-art particle swarm optimization (PSO) variant approaches in terms of the numerical result of the solutions. The sensitivity analysis of the BSA control parameter (F) is also performed.

Facility location models are observed in many diverse areas such as communication networks, transportation, and distribution systems planning. They play significant role in supply chain and operations management and are one of the main well-known topics in strategic agenda of contemporary manufacturing and service companies accompanied by long-lasting effects. We define a new approach for solving stochastic single source capacitated facility location problem (SSSCFLP). Customers with stochastic demand are assigned to set of capacitated facilities that are selected to serve them. It is demonstrated that problem can be transformed to deterministic Single Source Capacitated Facility Location Problem (SSCFLP) for Poisson demand distribution. A hybrid algorithm which combines Lagrangian heuristic with adjusted mixture of Ant colony and Genetic optimization is proposed to find lower and upper bounds for this problem. Computational results of various instances with distinct properties indicate that proposed solving approach is efficient.

In this paper a hybrid algorithm for solving bound constrained optimization problems having continuously differentiable objective functions using Fletcher Reeves method and advanced Genetic Algorithm (GA) have been proposed. In this approach, GA with advanced operators has been applied for computing the step length in the feasible direction in each iteration of Fletcher Reeves method. Then this idea has been extended to a set of multi-point approximations instead of single point approximation to avoid the convergence of the existing method at local optimum and a new method, called population based Fletcher Reeves method, has been proposed to find the global or nearer to global optimum. Finally to study the performance of the proposed method, several multi-dimensional standard test functions having continuous partial derivatives have been solved. The results have been compared with the same of recently developed hybrid algorithm with respect to different comparative factors.

One of the primary concerns on many traditional capacitated facility location/network problems is to consider transportation and setup facilities in one single objective function. This simple assumption may lead to misleading solutions since the cost of transportation is normally considered for a short period time and, obviously, the higher cost of setting up the facilities may reduce the importance of the transportation cost/network. In this paper, we introduce capacitated facility location/network design problem (CFLNDP) with two separate objective functions in forms of multi-objective with limited capacity. The proposed model is solved using a new hybrid algorithm where there are two stages. In the first stage, locations of facilities and design of fundamental network are determined and in the second stage demands are allocated to the facilities. The resulted multi-objective problem is solved using Lexicography method for a well-known example from the literature with 21 node instances. We study the behaviour of the resulted problem under different scenarios in order to gain insight into the behaviour of the model in response to changes in key problem parameters.