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  • Articles  (149)
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  • Articles  (149)
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  • 1
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    Optimizing Wiener and Randić Indices of Graphs (2020)
    Hindawi
    Details
    Publication Date: 2020-09-26
    Description: Wiener and Randić indices have long been studied in chemical graph theory as connection strength measures of graphs. Later, these indices were used in different fields such as network analysis. We consider two optimization problems related to these indices, with potential applications to network theory, in particular to epidemiological networks. Given a connected graph and a fixed total edge weight, we investigate how individual weights must be assigned to edges, minimizing the connection strength of the graph. In order to measure the connection strength, we use the weighted Wiener index and a modified version of the ordinary Randić index. Wiener index optimization is linear, while Randić index optimization turns out to be both nonlinear and nonconvex. Hence, we adopt the technique of separable programming to generate solutions. We present our experimental results by applying relevant algorithms to several graphs.
    Print ISSN: 1687-9147
    Electronic ISSN: 1687-9155
    Topics: Mathematics , Economics
    Published by Hindawi
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  • 2
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    Route Optimization of Electric Vehicle considering Soft Time Windows and Two Ways of Power Replenishment (2020)
    Hindawi
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    Publication Date: 2020-05-20
    Description: Under the background of severe air pollution and energy shortage, electric vehicles (EVs) are promising vehicles to support green supply chain and clean production. In the world, the renewal of EVs has become a general trend. Therefore, the concern about EVs is a hot issue at present, but EVs have the characteristics of limited driving distance and long charging time. When the EVs are used in logistics transportation, these characteristics have a significant impact on the vehicle routing problems. Therefore, based on the research experience of traditional vehicle routing optimization, combining with the characteristics of EVs, this paper presents an optimal problem of electric vehicle routes with time windows based on two charging methods and it also designs a mathematical model which was caused by early and late arrival as the objective function to minimize the transportation cost, vehicle use cost, power supply cost, and penalty cost. The model is solved using an ant colony algorithm. Finally, the ant colony algorithm is tested and analysed with an example.
    Print ISSN: 1687-9147
    Electronic ISSN: 1687-9155
    Topics: Mathematics , Economics
    Published by Hindawi
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  • 3
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    A Particle Swarm Optimization Algorithm for Solving Pricing and Lead Time Quotation in a Dual-Channel Supply Chain with Multiple Customer Classes (2020)
    Hindawi
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    Publication Date: 2020-04-22
    Description: The combination of traditional retail channel with direct channel adds a new dimension of competition to manufacturers’ distribution system. In this paper, we consider a make-to-order manufacturer with two channels of sale, sale through retailers and online direct sale. The customers are classified into different classes, based on their sensitivity to price and due date. The orders of traditional retail channel customers are fulfilled in the same period of ordering. However, price and due date are quoted to the online customers based on the available capacity as well as the other orders in the pipeline. We develop two different structures of the supply chain: centralized and decentralized dual-channel supply chain which are formulated as bilevel binary nonlinear models. The Particle Swarm Optimization algorithm is also developed to obtain a satisfactory near-optimal solution and compared to a genetic algorithm. Through various numerical analyses, we investigate the effects of the customers’ preference of a direct channel on the model’s variables.
    Print ISSN: 1687-9147
    Electronic ISSN: 1687-9155
    Topics: Mathematics , Economics
    Published by Hindawi
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  • 4
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    Green Scheduling of Jobs and Flexible Periods of Maintenance in a Two-Machine Flowshop to Minimize Makespan, a Measure of Service Level and Total Energy Consumption (2020)
    Hindawi
    Details
    Publication Date: 2020-04-14
    Description: The success of an industry today depends on its ability to innovate. In terms of energy performance, this innovation is reflected in the ability of manufacturers to implement new solutions or technologies that enable better energy management. In this regard, this paper aims to address this gap by incorporating energy consumption as an explicit criterion in flowshop scheduling of jobs and flexible preventive maintenance. Leveraging the variable speed of machining operations leading to different energy consumption levels, we explore the potential for energy saving in manufacturing. We develop a mixed integer linear multiobjective optimization model for minimizing the makespan and the total energy consumption. In the literature, no papers considering both production scheduling and flexible periods of maintenance with minimizing both objective the total of energy consumption in flowshop and makespan. The performance of the proposed mixed binary integer programming model is evaluated based on the exact method of branch and bound algorithm. A study of the results proved the performance of the model developed.
    Print ISSN: 1687-9147
    Electronic ISSN: 1687-9155
    Topics: Mathematics , Economics
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  • 5
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    Inverting the Multiple-Assisting Tool Network Problem to Solve for Optimality (2020)
    Hindawi
    Details
    Publication Date: 2020-03-20
    Description: Many network problems deal with the routing of a main tool comprised of several parallel assisting tools. These problems can be found with multi-tool-head routing of CNC machines, waterjets, plasma sprayers, and cutting machines. Other applications involve logistics, distribution, and material handling that require a main tool with assisting tools. Currently no studies exist that optimally route a main tool comprised of and fitted with multiple tools, nor do any studies evaluate the impact of adding additional capabilities to the tool set. Herein we define the network routing problem for a main tool comprised of multiple secondary tools. We introduce first principles to properly configure the main tool with the appropriate number of supporting tools such that that system is not overstatured. We invert the network geometry to extract the “best case” configuration for toolset configuration to include speed, range, and number of such that the system is lean. Our computational studies reveal that the theorems introduced herein greatly improve the overall system performance without oversaturating it with unused resources. In order to validate experiments, we define a mixed integer program and compare it to our metaheuristics developed for experimentation. Both the MIP and the metaheuristics herein optimally route a main tool with multiple assisting tools as well as the routing of a parcel delivery truck comprised of many drones.
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    Electronic ISSN: 1687-9155
    Topics: Mathematics , Economics
    Published by Hindawi
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  • 6
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    Solving Capacitated Facility Location Problem Using Lagrangian Decomposition and Volume Algorithm (2020)
    Hindawi
    Details
    Publication Date: 2020-02-04
    Description: In this research, we will focus on one variant of the problem: the capacitated facility location problem (CFLP). In many formulations of the CFLP, it is assumed that each demand point can be supplied by only one open facility, which is the simplest case of the problem. We consider the case where each demand point can be supplied by more than one open facility. We first investigate a Lagrangian relaxation approach. Then, we illustrate in the problem decomposition how to introduce tighter constraints, which solve the CFLP faster while achieving a better quality solution as well. At the same time, we apply the volume algorithm to improve both the lower and the upper bound on the optimum solution of the original problem for the large problem size.
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    Electronic ISSN: 1687-9155
    Topics: Mathematics , Economics
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  • 7
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    Inverting the Truck-Drone Network Problem to Find Best Case Configuration (2020)
    Hindawi
    Details
    Publication Date: 2020-01-22
    Description: Many industries are looking for ways to economically use truck/rail/ship fitted with drone technologies to augment the “last mile” delivery effort. While drone technologies abound, few, if any studies look at the proper configuration of the drone based on significant features of the problem: delivery density, operating area, drone range, and speed. Here, we first present the truck-drone problem and then invert the network routing problem such that the best case drone speed and range are fitted to the truck for a given scenario based on the network delivery density. By inverting the problem, a business can quickly determine the drone configuration (proper drone range and speed) necessary to optimize the delivery system. Additionally, we provide a more usable version of the truck-drone routing problem as a mixed integer program that can be easily adopted with standardized software used to solve linear programming. Furthermore, our computational metaheuristics and experiments conducted in support of this work are available for download. The metaheuristics used herein surpass current best-in-class algorithms found in literature.
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    Electronic ISSN: 1687-9155
    Topics: Mathematics , Economics
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  • 8
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    A New Technique for Determining Approximate Center of a Polytope (2019)
    Hindawi
    Details
    Publication Date: 2019-11-15
    Description: In this article, we have presented a method for finding the approximate center of a linear programming polytope. This method provides a point near the center of a polytope in few simple and easy steps. Geometrical interpretation and some numerical examples have also been presented to demonstrate the proposed approach and comparison of quality of the center obtained by using the new method with existing methods of finding exact and approximate centers. At the end, we also presented computational results on the randomly generated polytopes to compare the quality of the center obtained by using the new method.
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    Electronic ISSN: 1687-9155
    Topics: Mathematics , Economics
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  • 9
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    A Goal Programming Approach to Multichoice Multiobjective Stochastic Transportation Problems with Extreme Value Distribution (2019)
    Hindawi
    Details
    Publication Date: 2019-09-11
    Description: This paper presents the study of a multichoice multiobjective transportation problem (MCMOTP) when at least one of the objectives has multiple aspiration levels to achieve, and the parameters of supply and demand are random variables which are not predetermined. The random variables shall be assumed to follow extreme value distribution, and the demand and supply constraints will be converted from a probabilistic case to a deterministic one using a stochastic approach. A transformation method using binary variables reduces the MCMOTP into a multiobjective transportation problem (MOTP), selecting one aspiration level for each objective from multiple levels. The reduced problem can then be solved with goal programming. The novel adapted approach is significant because it enables the decision maker to handle the many objectives and complexities of real-world transportation problem in one model and find an optimal solution. Ultimately, a mixed-integer mathematical model has been formulated by utilizing GAMS software, and the optimal solution of the proposed model is obtained. A numerical example is presented to demonstrate the solution in detail.
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    Topics: Mathematics , Economics
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  • 10
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    Multiobjective Simulated Annealing: Principles and Algorithm Variants (2019)
    Hindawi
    Details
    Publication Date: 2019-05-23
    Description: Simulated annealing is a stochastic local search method, initially introduced for global combinatorial mono-objective optimisation problems, allowing gradual convergence to a near-optimal solution. An extended version for multiobjective optimisation has been introduced to allow a construction of near-Pareto optimal solutions by means of an archive that catches nondominated solutions while exploring the feasible domain. Although simulated annealing provides a balance between the exploration and the exploitation, multiobjective optimisation problems require a special design to achieve this balance due to many factors including the number of objective functions. Accordingly, many variants of multiobjective simulated annealing have been introduced in the literature. This paper reviews the state of the art of simulated annealing algorithm with a focus upon multiobjective optimisation field.
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    Topics: Mathematics , Economics
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