The clustering problem under the criterion of minimum sum of squares is a non-convex and non-linear program, which possesses many locally optimal values, resulting that its solution often falls into these trap and therefore cannot converge to global optima solution. In this paper, an efficient hybrid optimization Algorithm is developed for solving this problem, called Tabu-KM. It gathers the optimization property of Tabu Search and the local Search capability of k-means Algorithm together. The contribution of proposed Algorithm is to produce Tabu space for escaping from the trap of local optima and finding better solutions effectively. The Tabu-KM Algorithm is tested on several simulated and standard datasets and its performance is compared with k-means, simulated annealing, Tabu Search, genetic Algorithm, and ant colony optimization Algorithms. The experimental results on simulated and standard test problems denote the robustness and efficiency of the Algorithm and confirm that the proposed method is a suitable choice for solving data clustering problems.

The development of transportation has a significant impact on economic systems, both production and service, which makes the vehicle routing problem a special issue, one of the most important decisions in executive departments is to pay special attention to finding optimal routes, eliminating unnecessary routes, improving the distance traveled and reducing the number of fleets. In this regard, it is one of the complex and very important problem in the transportation network, this problem has a high potential in determining the optimal set of vehicle fleets with the aim of serving a set of customers, which many efforts have been made to solve it. Various meta-heuristic Algorithms have been developed in recent years, one of them is the Tabu Search Algorithm because it has good performance and ability to solve NP-Hard problems, and now in this article, the Tabu Search Algorithm is used to solve the vehicle routing problem with simultaneous pick-up and delivery of goods which by applying some changes in its coding in MATLAB software. Determining the parameters of the repetition value of the Algorithm, specifying the number of neighborhoods and the amount of the Tabu list improved the results obtained in the distances traveled by vehicles and optimized the number of fleets. Finally, the new proposed Algorithm was implemented on 14 standard sample problems from the Salhi and Nagi series of problems, and the obtained values were compared with the best available results from other Algorithms, which had satisfactory results in small-scale problems..

The most important operational decision related to transportation in the supply chain planning is the routing and scheduling of deliveries. Vehicle Routing and Scheduling Problem (VRSP) is a significant task in both supply chain planning and distribution optimization. A very large body of reSearch and modeling literature has been devoted to address VRSP. But most of them concentrated on hypothetical or simplified problems and disregarded many practical aspects of such problems. On the other hand, many practical problems have been tackled by different commercial systems for this class of problems, but little has been published about them. The primary objective of this paper is to develop a flexible Algorithm for solving complex real VRSP arises in practice.VRSP can be simply defined as: planning efficient flow of goods between facilities by a fleet of carriers through the transportation networks. This statement reveals the main components or objects of VRSP problems, namely, goods, facilities, carriers and transportation networks. Each object may have its owners, who impose their objectives and restrictions to the problem. For example, drivers may be considered as the owners of vehicles who may impose working time or region constraints.In developing the Algorithm, the most important criteria have been flexibility and speed. Most of new Algorithms developed by reSearchers are problem specific. They might improve the quality of results at the expense of reducing the flexibility of Algorithm to handle new constraints or increasing its computation time.Among various families of heuristics for optimization problems, Tabu Search (TS), Genetic Algorithms (GA) and Simulated Annealing (SA) have shown promising performance to solve various combinatorial problems. TS have several features which make it suitable candidate for real life complex cases. Robustness, simplicity and flexibility are the most important features of TS. In our experiences, the flexibility of GA is questionable and SA needs complicated parameter adjustment to gain high quality results. Therefore, we selected TS as framework for developing optimization Algorithm.In TS Algorithm, during the Search process, current solution may deteriorate from one iteration to the next. To avoid cycling, recent explored solutions are temporarily declared forbidden by putting their selected attributes in the Tabu list. The TS Algorithm has been evolved over time and several innovative features are included in this Algorithm by reSearchers to enhance its performance.In the proposed Algorithm, a cheapest insertion routine has been used for building initial solution. Neighborhood structure is another component which heavily influences the behavior of the Algorithm. In order to improve the quality of solution or speed up the Algorithm, numerous enhanced neighborhood structures have been proposed by reSearchers. Practical experiments show that a combination of relocation, exchange and 2opt* can provide high quality results within low computational time. We have examined more complex routines like CROSS and 3-opt, which resulted in no meaningful value and higher computation time. Since the problem contains contradicting objectives, using specific to artificially help the Algorithm in finding better solutions is harmful and reduces the effectiveness of the Algorithm.In order to evaluate the performance of proposed Algorithm optimization engine, a comprehensive experiment is conducted on a set of standard problem available in the literature. In this experiment we have used the (CMT) 14 standard VRP benchmark instances. These problems contain 50 to 199 cities in addition to depot. Our intention was to demonstrate the capability of proposed Algorithm on classical VRP for which enormous reSearch and experiments has been done. The performance of proposed Algorithm is compared with several best known advanced heuristic Algorithms.The average deviation of proposed Algorithm results from the best known solutions is 0.55 percent. In three instances, it provides the best known solutions. This experiment shows that the proposed Algorithm can provide comparable results with sophisticated TS Algorithm for classical VRP.  Since the proposed Algorithm is designed for real complex problems, we believe that it can easily attain higher quality solutions than Algorithms which are designed and tested for standard problems.  Most of available Algorithms are quite specific and need special modification for more complex cases.The computation time of Algorithms can not be compared directly, since they have run on different machines. Its average run time for the proposed Algorithm on CMT set is 0.5 minutes, which is also an outstanding performance. This experiments shows that the proposed Algorithm can provide high quality results comparing to the leading edge heuristic Algorithms.

Flow shop scheduling problem with missing operations is studied in this paper. Missing operations assumption refers to the fact that at least one job does not visit one machine in the production process. A mixed-binary integer programming model has been presented for this problem to minimize the make span. The genetic Algorithm (GA) and Tabu Search (TS) are used to deal with the optimization problem. According to computational experiments on data sets, it is suggested that GA is a more appropriate method to solve this problem. GA can reach good-quality solutions in short computational time, and can be used to solve large scale problems effectively.

Job shop scheduling problem (JSP) is an attractive field for reSearchers and production managers since it is a famous problem in many industries and a complex problem for reSearchers. Due to NP-hardness property of this problem, many meta-heuristics are developed to solve it. Solution representation (solution seed) is an important element for any meta-heuristic Algorithm. Therefore, many reSearchers try to present different encodings to solve this problem. Fattahi et al., and Gen & Cheng suggested two solutions for this problem that both have advantages and weaknesses in Searching solution space to reach an acceptable solution. In the current paper, a cyclic Algorithm based on Tabu Search Algorithm was proposed to improve the exploration and exploitation powers of these encodings. Also, several problems of different sizes are solved by it and the obtained results were compared. Results showed the applicability and effectiveness of the proposed solution representation in comparison with the existing ones.

Supply chain network design includes key decisions that have a major impact on the supply chain operational structure. Efficient supply chain design improves performance in organizations. This has led to the emergence of new concepts in the supply chain issue in the past decade. In this study, the supply chain network design problem in agile organizations has been taken into account with multi-level and multi-period. This problem is considered under conditions of having multiple customers with a high demand volume. The decisions include the selection of companies at each level, the amount of production, storage and transportation of each company. The problem has been modeled to integrate all decision variables with the goal of minimizing overall operating costs across the entire supply chain and Satisfaction of customers' complete demand and Satisfaction with them. Since multi-period multi-level supply chain design problem solving is one of the NP-Hard issues in uncertainty conditions, it is better to use innovative and meta-Algorithms to reduce problem solving time. For this reason, the Algorithm for banning Search Algorithms, which is one of the meta-Algorithms, has been used to solve the model. The results of this reSearch show that as the number of problem-solving repetitions increases, answers with less than 3% of the difference between the optimal answer are achieved. The Search Algorithm is forbidden to get the optimal response compared to the Lagrange Algorithm.