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Abstract: Multi-objective (MO) optimization is a challenging research topic because it involves the simultaneous optimization of several complex and conflicting objectives that requires researchers to address many issues which are unique to MO problems. However multi-objectivity is only one aspect of real-world applications and there is a growing interest in the optimization of solutions that are insensitive to parametric variations as well. In order to evaluate the capability of MO evolutionary algorithms (MOEAs) to find robust solutions, it is important to employ suitable test functions. In this paper, empirical studies are conducted to examine the suitability of existing robust test functions. Results suggest that these test functions have a bias towards the region where the robust solutions lie, rendering it difficult to assess the true capability of MOEAs. Motivated by such a finding, we present a framework for the construction of robust continuous MO test functions characterized by different noise-induced features. These noise-induced features can pose different difficulties to the optimization algorithms. A fitness-inheritance scheme is also presented and incorporated into two well-known MOEAs. Empirical analysis of the proposed robust MO test functions reveals that some noise-induced features present greater challenges to robust MOEAs as compared to existing robust test functions. In addition, the vehicle routing problem with stochastic demand (VRPSD) is presented as a practical example of robust combinatorial MO optimization problems. The work presented in this paper should encourage further studies and the development of more effective algorithms for robust MO optimization. [Copyright &y& Elsevier]

Abstract: This paper presents a real-value version of particle swarm optimization (PSO) for solving the open vehicle routing problem (OVRP) that is a well-known combinatorial optimization problem. In OVRP a vehicle does not return to the depot after servicing the last customer on a route. A particular decoding method is proposed for implementing PSO for OVRP. In the decoding method, a vector of the customer’s position is constructed in descending order. Then each customer is assigned to a route with taking into account feasibility conditions. Finally one-point move has been applied on constructed routes that seem promising to result in a better solution. Experimental evaluations on benchmark data sets demonstrate the competitiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: Cross-docking is considered as an efficient method to control the inventory flow, which is essential in supply chain management. In this paper, we consider a model that integrates cross-docking into the vehicle routing problem. In the model, a set of identical vehicles are used to transport goods from supplies to retailers through a cross-dock and the whole process must be completed in the planning horizon. Each supplier and retailer can be visited only once and the total quantity of goods in a vehicle must be less than its capacity. The objective of the problem is to determine the number of vehicles and a set of vehicle schedules with a minimum sum of operational cost and transportation cost. A new tabu search (TS) algorithm is proposed to obtain a good feasible solution for the problem. Through extensive computational experiments, it is shown that the proposed TS algorithm can achieve better performance than an existing TS algorithm while using much less computation time. The average improvements are as high as 10–36% for different size of problems. [Copyright &y& Elsevier]

Abstract: Vehicle routing problems have been extensively analyzed within the last few decades, since they play a central role in optimization of distribution networks. This paper presents a new Hybrid Electromagnetism-like Algorithm for solving capacitated vehicle routing problems. Electromagnetism-like Algorithm is a population-based algorithm based on attraction–repulsion mechanisms between charged particles. A modified objective function value calculation approach, utilizing the Random-Key Procedure makes it possible for Electromagnetism-like Algorithm to solve known combinatorial optimization problems like capacitated vehicle routing problems. Here, the solutions obtained such are improved by a relatively new local search method, Iterated Swap Procedure, and tested on several benchmarking problems. The computational results show that the proposed Hybrid Electromagnetism-like Algorithm gives promising results within acceptable computational times when compared to other novel meta-heuristics. [Copyright &y& Elsevier]

Abstract: The capacitated vehicle routing problem (CVRP) is one of the most important problems in the optimization of distribution networks. The objective of CVRP, known demands on the cost of originating and terminating at a delivery depot, is to determine the optimal set of routes for a set of vehicles to deliver customers. CVRP is known to be NP-hard problem, and then it is difficult to solve this problem directly when the problem size is large. In this paper, a hybrid algorithm of simulated annealing and tabu search is applied to solve CVRP. It takes the advantages of simulated annealing and tabu search for solving CVRP. Simulation results are reported on classical fourteen instances and twenty large-scale benchmark instances. From simulation results, the proposed algorithm finds eight best solutions of classical fourteen instances. Additionally, the solutions of the proposed algorithm have also admirable performance for twenty large-scale benchmark instances. It shows that the proposed algorithm is competitive with other existing algorithms for solving CVRP. [Copyright &y& Elsevier]