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Meta-heuristics have already received considerable attention in various engineering optimization fields. As one of the most rewarding tasks, eigenvalue optimization of truss structures is concerned in this study. In the proposed problem formulation the fundamental eigenvalue is to be maximized for a constant structural weight. The optimum is searched using Particle Swarm Optimization, PSO and its variant PSOPC with Passive Congregation as a recent meta-heuristic. In order to make further improvement an additional hybrid PSO with genetic algorithm is also proposed as PSOGA with the idea of taking benefit of various movement types in the search space. A number of benchmark examples are then treated by the algorithms. Consequently, PSOGA stood superior to the others in effectiveness giving the best results while PSOPC had more efficiency and the least fit ones belonged to the Standard PSO.

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The open vehicle routing problem (OVRP) is a variance of the vehicle routing problem (VRP) that has a unique character which is its open path form. This means that the vehicles are not required to return to the depot after completing service. Because this problem belongs to the NP-hard problems, many metaheuristic approaches like the ant colony optimization (ACO) have been used to solve OVRP in recent years. The versions of ACO have some shortcomings like its slow computing speed and local-convergence. Therefore, in this paper, we present an efficient hybrid elite ant system called EHEAS in which a new state transition rule, tabu search as an effective local search algorithm and a new pheromone updating rule are used for more improving solutions. These modifications avoid the premature convergence and make better solutions. Computational results on sixteen standard benchmark problem instances show that the proposed algorithm finds closely the best known solutions for most of the instances in which ten best known solutions are also found. In addition, EHEAS is comparable in terms of solution quality to the best performing published metaheuristics.

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The capacity vehicle routing problem (CVRP) is one of the most famous issues in combinatorial optimization that has been considered so far, and has attracted the attention of many scientists and researchers today. Therefore, many exact, heuristic and meta-heuristic methods have been presented in recent decades to solve it. In this paper, due to the weaknesses in the particle swarm optimization (PSO), a hybrid-modified version of this algorithm called PPSO is presented to solve the CVRP problem. In order to evaluate the efficiency of the algorithm, 14 standard examples from 50 to 199 customers of the existing literature were considered and the results were compared with other meta-heuristic algorithms. The results show that the proposed algorithm is competitive with other meta-heuristic algorithms. Besides, this algorithm obtained very close answers to the best known solutions (BKSs) for most of the examples, so that the seven BKSs were produced by PPSO.

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The balanced vehicle routing problem (BVRP) is one of the most famous research problems in operations, which has a very important position in combination optimization problems. In this problem, a fleet of vehicles with capacity Q starts moving from a node called the warehouse and returns to it after serving customers, provided that they visit each customer only once and never exceed the capacity Q. The goal is to minimize the paths traveled by vehicles provided that the distances traveled by the vehicles are the same as possible, for more justice in working time and income. This article presents the application of a hybrid imperialist competitive algorithm (HICA) to solve the problem. Unlike other optimization methods, this method is inspired by the socio-political process of societies and uses the competition between colonizing and colonized countries to reach the solution. To test the effectiveness of the algorithm, a set of standard examples are considered and the algorithm is implemented on it. The calculation results on these examples, which have a size of 50 to 200, show that the proposed algorithm has been able to compete well with well-known meta-heuristic algorithms in terms of the quality of the answers. In addition, the solutions close to the best answers obtained so far are generated for most of the examples.