Abstract: The Quadratic Assignment Problem (QAP) is one of the classical combinatorial optimization problems and is known for its diverse applications. The QAP is an NP-hard optimization problem which attracts the use of heuristic or metaheuristic algorithms that can find quality solutions in an acceptable computation time. On the other hand, there is quite a broad spectrum of mathematical programming techniques that were developed for finding the lower bounds for the QAP. This paper presents a fusion of the two approaches whereby the solutions from the computations of the lower bounds are used as the starting points for a metaheuristic, called HC12, which is implemented on a GPU CUDA platform. We perform extensive computational experiments that demonstrate that the use of these lower bounding techniques for the construction of the starting points has a significant impact on the quality of the resulting solutions.

	© 2010 by the authors; licensee Growing Science, Canada. This is an open access article distributed under the terms and conditions of the license. Creative Commons Attribution (CC-BY)

Abstract: This article presents a novel algorithm based on the cluster first-route second method, which executes a solution through K-means and Optics clustering techniques and Nearest Neighbor and Local Search 2-opt heuristics, for the solution of a vehicle routing problem with time windows (VRPTW). The objective of the problem focuses on reducing distances, supported by the variables of demand, delivery points, capacities, time windows and type of fleet in synergy with the model's taxonomy, based on data referring to deliveries made by a logistics operator in Colombia. As a result, good solutions are generated in minimum time periods after fulfilling the agreed constraints, providing high performance in route generation and solutions for large customer instances. Similarly, the algorithm demonstrates efficiency and competitiveness compared to other methods detailed in the literature, after being benchmarked with the Solomon instance data set, exporting even better results.

	© 2010 by the authors; licensee Growing Science, Canada. This is an open access article distributed under the terms and conditions of the license. Creative Commons Attribution (CC-BY)

Abstract: Hybrid flowshop scheduling problem (HFSP) is a mixture of two classical scheduling problems as parallel machine scheduling (PMS) and flowshop scheduling (FS). In the HFSP, a series of jobs are processed respectively in a set of stages that at least one of these stages has more than one parallel machine (identical, uniform or unrelated). HFSP is a widespreadly studied subject in the literature and there are various application areas such as transportation, healthcare management, agricultural activities, cloud computing, and the most common manufacturing. Therefore, it will be useful to present a review study including recent papers and developments related to this problem for researchers. For this aim, in this paper, a systematic literature survey has been conducted with respect to HFSPs by means of Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodology which enables to realize systematic review and meta-analyses in a specified subject. 172 articles which are published in the 2010-2020 year interval, related to production scheduling and including a mathematical programming model to express scheduling problems have been determined as a result of this methodological review process. These articles have been statistically analyzed according to many features such as year, country, journal, number of stages, type of parallel machines, constraints, objective functions, solution methods, test instances and type of parameters. The results of statistical analyses have been presented through charts so as to provide a visual demonstration to researchers. Furthermore, it has been aimed to answer 14 predetermined research questions by means of analyses realized in the scope of this review study. Consequently, it has revealed the existing literature, recent developments and future research suggestions related to HFSP and therefore it is possible to say that this review paper provides a beneficial road map for researchers studying in this field.

	© 2010 by the authors; licensee Growing Science, Canada. This is an open access article distributed under the terms and conditions of the license. Creative Commons Attribution (CC-BY)

Abstract: This paper aims at presenting a customer order scheduling environment in which the setup times are explicit and depend on the production sequence. The considered objective function is the total tardiness minimization. Since the variant under study is NP-hard, we propose a mixed-integer linear programming (MILP) model, an adaptation of the Order-Scheduling Modified Due-Date heuristic (OMDD) (referred to as Order-Scheduling Modified Due-Date Setup (OMMD-S)), an adaptation of the Framinan and Perez-Gonzalez heuristic (FP) (hereinafter referred to as Framinan and Perez-Gonzalez Setup (FP-S)), a matheuristic with Same Permutation in All Machines (SPAM), and the hybrid matheuristic SPAM-SJPO based on Job-Position Oscillation (JPO). The algorithms under comparison have been compared on an extensive benchmark of randomly generated test instances, considering two performance measures: Relative Deviation Index (RDI) and Success Rate (SR). For the small-size evaluated instances, the SPAM is the most efficient algorithm, presenting the better values of RDI and SR. For the large-size evaluated instances, the hybrid matheuristic SPAM-JPO and MILP model are the most efficient methods.

	© 2010 by the authors; licensee Growing Science, Canada. This is an open access article distributed under the terms and conditions of the license. Creative Commons Attribution (CC-BY)

Abstract: Hybrid algorithms are widely used today to increase the performance of existing algorithms. In this paper, a new hybrid algorithm called IMVOSA that is based on multi-verse optimizer (MVO) and simulated annealing (SA) is used. In this model, a new method called the black hole selection (BHS) is proposed, in which exploration and exploitation can be increased. In the BHS method, the acceptance probability feature of the SA algorithm is used to increase exploitation by searching for the best regions found by the MVO algorithm. The proposed IMVOSA algorithm has been tested on 50 benchmark functions. The performance of IMVOSA has been compared with other latest and well-known metaheuristic algorithms. The consequences show that IMVOSA produces highly successful and competitive results.

	© 2010 by the authors; licensee Growing Science, Canada. This is an open access article distributed under the terms and conditions of the license. Creative Commons Attribution (CC-BY)

Abstract: In this paper it is presented an improvement of the branch and bound algorithm for the permutation flow shop problem with blocking-in-process and setup times with the objective of minimizing the total flow time and tardiness, which is known to be NP-Hard when there are two or more machines involved. With that objective in mind, a new machine-based lower bound that exploits some structural properties of the problem. A database with 27 classes of problems, varying in number of jobs (n) and number of machines (m) was used to perform the computational experiments. Results show that the algorithm can deal with most of the problems with less than 20 jobs in less than one hour. Thus, the method proposed in this work can solve the scheduling of many applications in manufacturing environments with limited buffers and separated setup times.

	© 2010 by the authors; licensee Growing Science, Canada. This is an open access article distributed under the terms and conditions of the license. Creative Commons Attribution (CC-BY)

Abstract: An assignment problem (AP) usually deals with how a set of persons/tasks can be assigned to a set of tasks/persons on a one-to-one basis in an optimal manner. It has been observed that balancing among the persons and jobs in several real-world situations is very hard, thus such scenarios can be seen as unbalanced assignment models (UAP) being a lack of workforce. The solution techniques presented in the literature for solving UAP’s depend on the assumption to allocate some of the tasks to fictitious persons; those tasks assigned to dummy persons are ignored at the end. However, some situations in which it is inevitable to assign more tasks to a single person. This paper addresses a practical variant of UAP called k-cardinality unbalanced assignment problem (k-UAP), in which only of persons are asked to perform jobs and all the persons should perform at least one and at most jobs. The k-UAP aims to determine the optimal assignment between persons and jobs. To tackle this problem optimally, an enumerative Lexi-search algorithm (LSA) is proposed. A comparative study is carried out to measure the efficiency of the proposed algorithm. The computational results indicate that the suggested LSA is having the great capability of solving the smaller and moderate instances optimally.

	© 2010 by the authors; licensee Growing Science, Canada. This is an open access article distributed under the terms and conditions of the license. Creative Commons Attribution (CC-BY)

Abstract: This document addresses the problem of scheduling and routing a specific number of vehicles to visit a set of customers in specific time windows during a planning horizon. The vehicles have a homogeneous limited capacity and have their starting point and return in a warehouse or initial node, in addition, multiple variants of the classic VRP vehicle routing problem are considered, where computational complexity increases with the increase in the number of customers to visit, as a characteris-tic of an NP-hard problem. The solution method used consists of two connected phases, the first phase makes the allocation through a mixed-integer linear programming model, from which the visit program and its frequency in a determined plan-ning horizon are obtained. In the second phase, the customers are grouped through an unsupervised learning algorithm, the routing is carried out through an Ant Colony Optimization metaheuristic that includes local heu-ristics to make sure com-pliance with the restrictive factors. Finally, we test our algorithm by performance measures using instances of the literature and a comparative model, and we prove the effectiveness of the proposed algorithm.

	© 2010 by the authors; licensee Growing Science, Canada. This is an open access article distributed under the terms and conditions of the license. Creative Commons Attribution (CC-BY)