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 Journal of Mathematical Modelling and Algorithms   [SJR: 0.358]   [H-I: 19]   [2 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1570-1166 - ISSN (Online) 1572-9214    Published by Springer-Verlag  [2302 journals]
• Planning a Capacitated Road Network with Flexible Travel Times: A Genetic
Algorithm
• Abstract: We are concerned with a capacitated location-multi allocation-routing problem in a road network with flexible travel times. It is assumed that all links are two-way and capacities of the server nodes and arcs for accepting of population are limited. The aim of our work is to find numbers and locations of server nodes, allocation of the existing population in existing demand nodes on the network to the servers and the allocation of existing population in each node to different routes to determine the decided server for each member so that total transportation time is minimized. Here, two basic concepts are considered: multi allocation and flexible travel times. The concept of multi allocation arises from the possibility of allocating the existing population in a demand node to more than one server node. Also, flexible travel times concentrate on impact of traveling population on the times of links simultaneously, that is, depending on how the population is distributed on the network, the travel times on links may be increased. So, to have the least increase in the time of each link, it is necessary to decide upon the distribution of population in the network. We formulate the proposed problem as a mixed-integer nonlinear programming model and then present a genetic algorithm (GA) for solving large problems Finally, we make two sets of numerical experiments and analyze the obtained results by LINGO solver and GA. Numerical results show the proposed GA to be highly efficient.
PubDate: 2015-05-19

• L (0,1)-labelling of Permutation Graphs
• Abstract: L(0,1)-labelling of a graph G=(V,E) is a function f from the vertex set V(G) to the set of non-negative integers such that adjacent vertices get number zero apart, and vertices at distance two get distinct numbers. The goal of L(0,1)-labelling problem is to produce a legal labelling that minimize the largest label used. In this article, it is shown that, for a permutation graph G with maximum vertex degree Δ, the upper bound of λ 0,1(G) is Δ−1. Finally, we prove that the result is exact for bipartite permutation graph.
PubDate: 2015-05-01

• Fuzzy Geometric Programming Approach in Multivariate Stratified Sample
Surveys Under Two Stage Randomized Response Model
• Abstract: This paper provide a profound study on optimum allocation of two stage multivariate stratified Warner’s randomized response (RR) model with linear and non linear cost function. The multi-objective problem is formulated as a Geometric Programming Problem (GPP). The fuzzy programming approach is adopted to solve the formulated problem. A numerical example is given to illustrate the computational details of the suggested method.
PubDate: 2015-04-22

• GPU implementation of Jacobi Method and Gauss-Seidel Method for Data
Arrays that Exceed GPU-dedicated Memory Size
• Abstract: The paper proposes a method to extend the dimension of grids that GPU-aided implicit finite difference method is capable to work with. The approach is based on the pyramid method. A predictive mathematical model for computation duration is proposed. This model allows to find optimal algorithm parameters. The paper provides computation experiment results that has shown the model to be accurate enough to predict optimal algorithm parameters.
PubDate: 2015-04-21

• Partial Trade Credit Policy of Retailer in Economic Order Quantity Models
for Deteriorating Items with Expiration Dates and Price Sensitive Demand
• Abstract: In a supplier-retailer-customer supply chain, a credit-worthy retailer frequently receives a permissible delay on the entire purchase amount without collateral deposits from his/her supplier (i.e., an up-stream full trade credit). By contrast, a retailer usually requests his/her credit-risk customers to pay a fraction of the purchase amount at the time of placing an order, and then grants a permissible delay on the remaining balance (i.e., a down-stream partial trade credit). Also, in selecting an item for use, the selling price of that item is one of the decisive factors to the customers. It is well known that the higher selling price of item decreases the demand rate of that item where the lesser price has the reverse effect. Hence, the demand rate of an item is dependent on the selling price of that item. In addition, many products such as fruits, vegetables, high-tech products, pharmaceuticals, and volatile liquids not only deteriorate continuously due to evaporation, obsolescence and spoilage but also have their expiration dates. However, only a few researchers take the expiration date of a deteriorating item into consideration. This paper proposes an economic order quantity model to allow for: (a) the strategy that supplier offers retailer a full trade credit policy whereas the retailer offers their customers a partial trade credit policy, (b) selling price dependent demand rate, (c) a profit maximization objective and (d) deteriorating items not only deteriorate continuously but also have their expiration dates. For the objective function sufficient conditions for the existence and uniqueness of the optimal solution are provided. An efficient algorithm is designed to determine the optimal pricing and inventory policies for the retailer. Finally, numerical examples are presented to illustrate the proposed model and the effect of key parameters on optimal solution is examined.
PubDate: 2015-04-19

• An Adaptive Trust Region Method Based on Simple Conic Models
• Abstract: A new adaptive trust region algorithm with simple conic models is proposed. By use of the simple conic model, the new method needs less memory capacitance and computational complexity. The nonmonotone and adaptive techniques are introduced to improve the efficiency of the proposed algorithm. The convergence results of the method are proved under certain conditions. Numerical tests show that the new algorithm is efficient and robust.
PubDate: 2015-03-26

• A New Search Procedure for the Two-dimensional Orthogonal Packing Problem
• Abstract: In this paper we propose a new exact procedure for the two-dimensional orthogonal packing problem, based on F. Clautiaux et al. approach (Clautiaux et al. Eur. J. Oper. Res. 183(3), 1196–1211, 2007). The principle consists in searching first the positions of the items on the horizontal axis, so as that, at each position, the sum of the heights of the items does not exceed the height of the bin. Each time a valid placement of all the items is encountered, another procedure determines if it can be extended to a solution of the packing problem, searching the positions of the items on the vertical axis. Novel aspects of our approach include a simple and efficient search procedure, which only generates restricted placements, at least in a first stage, in order to reduce the search space, and the memorization of unsuccessful configurations, which are then used to detect dead-ends. We tested our implementation on a selection of orthogonal packing problems and strip packing problems, and we compared our results with those of recent successful approaches.
PubDate: 2015-03-14

• Solving the Nonlinear Power Flow Problem Through General Solutions of
Under-determined Linearised Systems
• Abstract: This work focuses on the solution of a set of algebraic nonlinear equations representing the steady state operation of electrical power systems. The classical modelling of the so-called power flow problem requires the statement of the power balance equations and the specification of some network variables. Usually Newton method is applied to solve these equations, which requires the solution of a linear system at each iteration. Here, the formulation of the power flow problem is modified by increasing the number of variables to be computed, such that an under-determined linear system is solved at each iteration. This strategy imparts flexibility to obtain solutions with respect to selected performance indexes. Numerical results obtained with test-systems ranging from 26 to 1916 equations and 30 to 2013 variables illustrate the main features of the proposed application.
PubDate: 2015-03-08

• An Adaptive Infeasible Interior-Point Algorithm with Full Nesterov-Todd
Step for Semidefinite Optimization
• Abstract: We present an adaptive full Nesterov-Todd step infeasible interior-point method for semidefinite optimization. The proposed algorithm requires two types of full Nesterov-Todd steps are called, feasibility steps and centering steps, respectively. At each iteration both feasibility and optimality are reduced exactly at the same rate. In each iteration of the algorithm we use the largest possible barrier parameter value θ. The value θ varies from iteration to iteration and it lies between the two values $$\frac {1}{4n}$$ and $$\frac {1}{5n}$$ , which results a faster algorithm.
PubDate: 2015-03-01

• Higher Order Fractional Symmetric Duality Over Cone Constraints
• Abstract: In this paper, a pair of Mond-Weir type higher order fractional symmetric dual program over cone constraints is formulated. Under higher order invexity assumptions, we prove weak, strong and strict duality theorems. Moreover, a self dual program is formulated and self duality theorem is discussed.
PubDate: 2015-03-01

• Derivative-Free Augmented Lagrangian for Global Optimization: Cost
Minimization in a Simplified Activated Sludge System Model
• Abstract: A methodology for finding the optimal values of the decision variables from an efficient simplified mathematical model of an activated sludge system is addressed in this paper. The work herein presented arises in a wastewater treatment plant design context, where investment and operational costs are to be minimized and computational effort is to be reduced. To achieve the best design, a non-linear optimization solution method based on an augmented Lagrangian approach is proposed. At each iteration, a subproblem is globally solved by a derivative-free recursive branching technique, known as the multilevel coordinate search algorithm of Huyer and Neumaier [20]. The presented technique has been shown to work quite well when solving the herein proposed non-convex and non-smooth constrained optimization model. The numerical results show the reliability of the obtained solutions at a reduced computational cost.
PubDate: 2015-03-01

• Mathematical Modeling and Computational Algorithm to Solve Multi-Echelon
Multi-Constraint Inventory Problem with Errors in Quality Inspection
• Abstract: In this research an integrated production-distribution inventory model is developed for a single-vendor single-buyer supply chain system with the consideration of quality inspection errors at the buyer’s end, the buyer’s warehouse has limited capacity and there is an upper bound on the purchase of products. Mathematical modeling is employed in this study for optimizing the replenishment lot-size and total number of deliveries from the vendor to the buyer in one production run with the objective of minimizing integrated expected total cost of the system while satisfying the constraints. We show that the model of this problem is a constrained non-linear programme and propose a simple Lagrangian multiplier algorithmic technique to solve it. The computational effort and time are small for the proposed algorithm and it is simple to implement. A numerical example is given to demonstrate the application and the performance of the proposed methodology. In addition, sensitivity analysis has been carried out to illustrate the behaviors of the proposed model and some managerial insights are also included.
PubDate: 2015-03-01

• Optimal Preservation Technology Investment, Retail Price and Ordering
Policies for Deteriorating Items under Trended Demand and Two Level Trade
Credit Financing
• Abstract: This research analyzes the impact of deploying suitable preservation technology for an inventory system in which units are subject to constant rate of deterioration. The demand is considered to be function of time and retail price. It is assumed that the supplier offers a fixed credit period to the retailer and retailer also offers credit period to the customers. The goal is to maximize the total profit per unit time with respect to optimal investment to be made in preservation technology, retail price of an item and purchase quantity. The concavity of the total profit is validated using numerical example. The managerial issues are discussed.
PubDate: 2015-03-01

• ILIGRA: An Efficient Inverse Line Graph Algorithm
• Abstract: This paper presents a new and efficient algorithm, IligraLIGRA, for inverse line graph construction. Given a line graph H, ILIGRA constructs its root graph G with the time complexity being linear in the number of nodes in H. If ILIGRA does not know whether the given graph H is a line graph, it firstly assumes that H is a line graph and starts its root graph construction. During the root graph construction, ILIGRA checks whether the given graph H is a line graph and ILIGRA stops once it finds H is not a line graph. The time complexity of ILIGRA with line graph checking is linear in the number of links in the given graph H. For sparse line graphs of any size and for dense line graphs of small size, numerical results of the running time show that ILIGRA outperforms all currently available algorithms.
PubDate: 2015-03-01

• Second-Order Nondifferentiable Multiobjective Mixed Symmetric Dual
Programs Over Cones
• Abstract: In this paper, a pair of second-order mixed symmetric nondifferentiable multiobjective dual programs over arbitrary cones where each of the objective functions contains a pair of support functions is considered. Further, weak, strong and converse duality theorems are established under the assumptions of second-order K- (F,ρ)-convexity. Moreover, we have illustrated a numerical example which is second-order K- (F,ρ)-convex but not second-order F-convex. Several special cases are also obtained.
PubDate: 2015-03-01

• Solving Large 0–1 Multidimensional Knapsack Problems by a New
Simplified Binary Artificial Fish Swarm Algorithm
• Abstract: The artificial fish swarm algorithm has recently been emerged in continuous global optimization. It uses points of a population in space to identify the position of fish in the school. Many real-world optimization problems are described by 0–1 multidimensional knapsack problems that are NP-hard. In the last decades, several exact as well as heuristic methods have been proposed for solving these problems. In this paper, a new simplified binary version of the artificial fish swarm algorithm is presented, where a point/fish is represented by a binary string of 0/1 bits. Trial points are created by using crossover and mutation in the different fish behavior that are randomly selected by using two user defined probability values. In order to make the points feasible, the presented algorithm uses a random heuristic drop-item procedure followed by an add-item procedure aiming to increase the profit throughout the adding of more items in the knapsack. A cyclic reinitialization of 50 % of the population, and a simple local search that allows the progress of a small percentage of points towards optimality and after that refines the best point in the population greatly improve the quality of the solutions. The presented method is tested on a set of benchmark instances and a comparison with other methods available in literature is shown. The comparison shows that the proposed method can be an alternative method for solving these problems.
PubDate: 2015-02-28

• A New Bi-objective Location-routing Problem for Distribution of Perishable
Products: Evolutionary Computation Approach
• Abstract: Supply, manufacture, and distribution of perishable products are challenging jobs in supply chains. Location of warehouses and routing of vehicles are essential issues to distribute perishable products properly. In this paper, a new bi-objective mixed integer mathematical programming is proposed to reduce the total cost of the supply chain and to balance the workload of distribution centers while the due dates of delivery of perishable product are met, concurrently. The considered properties and constraints of proposed model made it well-posed to illustrate the real life situation. As the proposed model is NP-Hard, an evolutionary algorithm called Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) is customized to solve the problem. The structure of chromosome and genetic operators are customized for the problem. The performance of proposed NSGA-II and an efficient exact Multi-objective method, called ε-constraint, is compared using accuracy and diversity metrics on several benchmark instances.
PubDate: 2015-02-24

• Balking and Reneging Multiple Working Vacations Queue with Heterogeneous
Servers
• Abstract: This paper presents the analysis of a renewal input multiple working vacations queue with balking, reneging and heterogeneous servers. Whenever the system becomes empty the second server leaves for a working vacation whereas the first server remains idle in the system. During a working vacation the second server provides service at a slower rate rather than completely stopping service. The steady-state probabilities of the model are obtained using supplementary variable and recursive techniques. Various performance measures of the model such as expected system length, expected balking rate, etc., have been discussed. Finally, some numerical results have been presented to show the effect of model parameters on the system performance measures.
PubDate: 2015-01-23

• Multi-objective Compromise Allocation in Multivariate Stratified Sampling
Using Extended Lexicographic Goal Programming with Gamma Cost Function
• Abstract: In the present paper, a new Gamma cost function is proposed for an optimum allocation in multivariate stratified random sampling with linear regression estimator. Extended lexicographic goal programming is used for solution of multi-objective non-linear integer allocation problem. A real data set is used to illustrate the application.
PubDate: 2014-12-18

• Preface
• PubDate: 2014-12-01

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