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Showing 39 results for Algorithm
Emilio Spedicato, Marco Bonomi, Antonino Del Popolo, Volume 1, Issue 1 (52008)
Abstract
Abstract We consider an application of the ABS procedure to the linear systems arising from the primaldual interior point methods where Newton method is used to compute path to the solution. When approaching the solution the linear system, which has the form of normal equations of the second kind, becomes more and more ill conditioned. We show how the use of the Huang algorithm in the ABS class can reduce the ill conditioning. Preliminary numerical experiments show that the proposed approach can provide a residual in the computed solution up to sixteen orders lower.
Nezam MahdaviAmiri, Seyed Hadi Nasseri, Alahbakhsh Yazdani, Volume 1, Issue 2 (62009)
Abstract
Jain, Lachhwani, Volume 2, Issue 1 (42010)
Abstract
We develop an algorithm for the solution of multiobjective linear plus fractional programming problem (MOL+FPP) when some of the constraints are homogeneous in nature. Using homogeneous constraints, first we construct a transformation matrix T which transforms the given problem into another MOL+FPP with fewer constraints. Then, a relationship between these two problems, ensuring that the solution of the original problem can be recovered from the solution of the transformed problem, is established. We repeat this process of transformation until all the homogeneous constraints are removed. Then, we discuss the multi objective programming part, for which fuzzy programming methodology is proposed which works for the minimization of perpendicular distances between two hyper planes (curves) at the optimal points of the objective functions. A suitable membership function is defined with the help of the supremum perpendicular distance. A compromised optimal solution is obtained as a result of the minimization of the The supremum perpendicular distance. The corresponding optimal solution to the original problem is obtained using the transformation matrix. Finally, an example is given to illustrate the proposed model.
Moeen Moghadas, Taghizadeh Kakhki, Volume 2, Issue 2 (62011)
Abstract
We consider the maximal covering locationallocation problem with multiple servers. The objective is to maximize the population covered, subject to constraints on the number of service centers, total number of servers in all centers, and the average waiting time at each center. Each center operates as an M/M/k queuing system with variable number of servers. The total costs of establishing centers and locating servers should not exceed a predetermined amount. We present a mathematical model for the problem, and propose a heuristic solution procedure with two local search algorithms for improving the solutions. Finally, some computational results are presented.
Sheibani, Volume 2, Issue 2 (62011)
Abstract
We describe a hybrid metaheuristic algorithm for combinatorial optimization problems with a specific reference to the travelling salesman problem (TSP). The method is a combination of a genetic algorithm (GA) and greedy randomized adaptive search procedure (GRASP). A new adaptive fuzzy a greedy search operator is developed for this hybrid method. Computational experiments using a wide range of standard benchmark problems indicate that the proposed hybrid metaheuristic approach is very efficient.
Etebari, Aaghaie, Khoshalhan, Volume 3, Issue 1 (42012)
Abstract
In recent years, enriching traditional revenue management models by considering the customer choice behavior has been a main challenge for researchers. The terminology for the airline application is used as representative of the problem. A popular and an efficient model considering these behaviors is choicebased deterministic linear programming (CDLP). This model assumes that each customer belongs to a segment, which is characterized by a consideration set, which is a subset of the products provided by the firm that a customer views as options. Initial models consider a market segmentation, in which each customer belongs to one specific segment. In this case, the segments are defined by disjoint consideration sets of products. Recent models consider the extension of the CDLP to the general case of overlapping segments. The main difficulty, from a computational standpoint, in this approach is solving the CDLP efficiently by column generation. Indeed, it turns out that the column generation subproblem is difficult on its own. It has been shown that for the case of nonoverlapping segments, this can be done in polynomial time. For the more general case of overlapping segments, the column generation subproblem is NPhard for which greedy heuristics are proposed for computing approximate solutions. Here, we present a new approach to solve this problem by using a genetic algorithm and compare it with the column generation method. We comparatively investigate the effect of using the new approach for firm’s revenue
Noori Darvish, TavakkoliMoghaddam, Javadian, Volume 3, Issue 1 (42012)
Abstract
We consider an open shop scheduling problem. At first, a biobjective possibilistic mixedinteger programming formulation is developed. The inherent uncertainty in processing times and due dates as fuzzy parameters, machinedependent setup times and removal times are the special features of this model. The considered biobjectives are to minimize the weighted mean tardiness and weighted mean completion times. After converting the original formulation into a singleobjective crisp one by using an interactive approach and obtaining the Paretooptimal solutions for smallsized instances, an efficient multiobjective particle swarm optimization (MOPSO) is proposed in order to achieve a good approximate Paretooptimal set for medium and largesized examples. This algorithm exploits new selection regimes of the literature for the global best and personal best. Furthermore, a modified decoding scheme is designed to reduce the search area in the solution space, and a local search algorithm is proposed to generate initial particle positions. Finally, the efficiency of the proposed MOPSO (PMOPSO) is shown by comparing with the common MOPSO (CMOPSO) by the use of the design of experiments (DOE) based on three comparison metrics.
Mansouri, Siyavash, Zangiabadi, Volume 3, Issue 1 (42012)
Abstract
We present a new algorithm obtained by changing the search directions in the algorithm given in [8]. This algorithm is based on a new technique for finding the search direction and the strategy of the central path. At each iteration, we use only the full NesterovTodd (NT)step. Moreover, we obtain the currently best known iteration bound for the infeasible interiorpoint algorithms with full NT steps, namely O(nlogn/e) , which is as good as the linear analogue.
Lalwani, Kumar, Spedicato, Gupta, Volume 3, Issue 1 (42012)
Abstract
We present an application of ABS algorithms for multiple sequence alignment (MSA). The Markov decision process (MDP) based model leads to a linear programming problem (LPP), whose solution is linked to a suggested alignment. The important features of our work include the facility of alignment of multiple sequences simultaneously and no limit for the length of the sequences. Our goal here is to avoid the excessive computing time, needed by dynamic programming based algorithms for alignment of a large number of sequences. In an attempt to demonstrate the integration of the ABS approach with complex mathematical frameworks, we apply the ABS implicit LX algorithm to elucidate the LPP, constructed with the assistance of MDP. The MDP applied for MSA is a pragmatic approach and entails a scope for future work. Programming is done in the MATLAB environment
Khalili, TavakkoliMoghaddam, Volume 4, Issue 1 (52013)
Abstract
We relax some assumptions of the traditional scheduling problem and suggest an adapted metaheuristic algorithm to optimize efficient utilization of resources and quick response to demands simultaneously. We intend to bridge the existing gap between theory and real industrial scheduling assumptions (e.g., hot metal rolling industry, chemical and pharmaceutical industries). We adapt and evaluate a wellknown algorithm based on electromagnetic science. The motivation behind our proposed metaheuristic approach has arisen from the attractionrepulsion mechanism of electromagnetic theories in physics. In this basic idea, we desire to bring our search closer to a region with a superior objective function while going away from the region with the inferior objective function in order to move the solution gradually towards optimality. The algorithm is carefully evaluated for its performance against two existing algorithms using multiobjective performance measures and statistical tools. The results show that our proposed solution method outperforms the others.
Morovatdar, Aghaie, Roghanian, Asl Haddad, Volume 4, Issue 1 (52013)
Abstract
We consider criticality in project networks having imprecise activity duration times. It is well known that finding all possibly critical paths of an imprecise project network is an NPhard problem. Here, based on a method for finding critical paths of crisp networks by using only the forward recursion of critical path method, for the first time an algorithm is proposed which can find all possibly critical paths of intervalvalued project networks. The proposed algorithm considers interactivity among paths which has not been yet considered in the fuzzy project scheduling literature. The extension of the proposed algorithm to the fuzzy network calculates criticality degrees of activities and paths of projects without any need to enumerate all project paths. Although algorithms for calculating criticality degrees in fuzzy networks have been previously proposed, despite the fact that they mostly consider a specific type of fuzzy numbers as activity duration times, the exiting algorithms do not discriminate possibly critical paths before calculating the criticality degrees. The computational experience on a series of wellknown project samples confirms the algorithm to be remarkably more efficient than similar algorithms for fuzzy networks.
Dr. Behrouz Kheirfam, Volume 4, Issue 1 (52013)
Abstract
We present a new full Nesterov and Todd step infeasible interiorpoint algorithm for semidefinite optimization. The algorithm decreases the duality gap and the feasibility residuals at the same rate. In the algorithm, we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Every main iteration of the algorithm consists of a feasibility step and some centering steps. We show that the algorithm converges and finds an approximate solution in polynomial time. A numerical study is made for the numerical performance. Finally, a comparison of the obtained results with those by other existing algorithms is made.
M. ForghaniElahabad, N. MahdaviAmiri, Volume 4, Issue 2 (102013)
Abstract
A number of problems in several areas such as power transmission and distribution, communication and transportation can be formulated as a stochasticflow network (SFN). The system reliability of an SFN can be computed in terms of all the upper boundary points, called dMinCuts (dMCs). Several algorithms have been proposed to find all the dMCs in an SFN. Here, some recent studies in the literature on search for all dMCs are investigated. We show that some existing results and the corresponding algorithms are incorrect. Then, correct versions of the results are established. By modifying an incorrect algorithm, we also propose an improved algorithm. In addition, complexity results on a number of studies are shown to be erroneous and correct counts are provided. Finally, we present comparative numerical results in the sense of performance profile of Dolan and Moré showing the proposed algorithm to be more efficient than some existing algorithms.
N. Hoseini Monjezi, Volume 5, Issue 1 (52014)
Abstract
Here, a quasiNewton algorithm for constrained multiobjective optimization is proposed. Under suitable assumptions, global convergence of the algorithm is established.
A.m. Bagirov, Volume 5, Issue 1 (52014)
Abstract
Here, an algorithm is presented for solving the minimum sumofsquares clustering problems using their difference of convex representations. The proposed algorithm is based on an incremental approach and applies the well known DC algorithm at each iteration. The proposed algorithm is tested and compared with other clustering algorithms using large real world data sets.
A. Eshraghniaye Jahromi, Ali A. Yahyatabar Arabi, Volume 5, Issue 2 (102014)
Abstract
An availability model is developed to optimize the availability of a series repairable system with multiple koutofn subsystems in this paper. There are two types of decision variables that determine the system designer’s decision to allocate the number of repairmen and to allocate the number of redundant components in each subsystem in the presence of weight, volume and cost constraints. As per the nonlinear structure of the objective in the model, the model is located into the nonlinear programming category. A classical Particle Swarm Optimization (PSO) algorithm is proposed to solve seven various instances of the model. The aim of this study is to illustrate the model and to propose an applicable algorithm for the problem. The efficiency of the proposed PSO is illustrated by comparison with Simulated Annealing (SA) method.
Godfrey Chagwiza, Brian Jones, Senelani Hove Musekwa, Sobona Mtisi, Volume 5, Issue 2 (102014)
Abstract
We introduce a new way of generating cutting planes of a mixed integer programme by way of taking binary variables. Four binary variables are introduced to form quartic inequalities, which results in a reduced firstlevel mixed integer programme. A new way of weakening the inequalities is presented. An algorithm to carryout the separation of the inequalities, which are exponential in number, is developed. The proposed method of cuts generation, separation and strengthening is compared to the Gomory, linear branching and coordinated cutting plane methods. The computational results show that the proposed method is promising but becomes complicated as number of variables increases.
M Aman, J Tayyebi, Volume 5, Issue 2 (102014)
Abstract
Given an instance of the minimum cost flow problem, a version of the corresponding inverse problem, called the capacity inverse problem, is to modify the upper and lower bounds on arc flows as little as possible so that a given feasible flow becomes optimal to the modified minimum cost flow problem. The modifications can be measured by different distances. In this article, we consider the capacity inverse problem under the bottlenecktype and the sumtype weighted Hamming distances. In the bottlenecktype case, the binary search technique is applied to present an algorithm for solving the problem in O(nm log n) time. In the sumtype case, it is shown that the inverse problem is strongly NPhard even on bipartite networks
Dr Alireza GhaffariHadigheh, Mehdi Djahangiri, Volume 6, Issue 1 (32015)
Abstract
It is a wellknown fact that finding a minimum dominating set and consequently the domination number of a general graph is an NPcomplete problem. In this paper, we first model it as a nonlinear binary optimization problem and then extract two closely related semidefinite relaxations. For each of these relaxations, different rounding algorithm is exploited to produce a nearoptimal dominating set. Feasibility of the generated solutions and efficiency of the algorithms are analyzed as well.
Dr Yahia Zare Mehrjerdi, Mitra Moubed, Volume 6, Issue 1 (32015)
Abstract
This paper proposes a robust model for optimizing collaborative reverse supply chains. The primary idea is to develop a collaborative framework that can achieve the best solutions in the uncertain environment. Firstly, we model the exact problem in the form of a mixed integer nonlinear programming. To regard uncertainty, the robust optimization is employed that searches for an optimum answer with nearly all possible deviations in mind. In order to allow the decision maker to vary the protection level, we used the "budget of uncertainty" approach. To solve the nphard problem, we suggest a hybrid heuristic algorithm combining dynamic programming, ant colony optimization and tabu search. To confirm the performance of the algorithm, two validity tests are done firstly by comparing with the previously solved problems and next by solving a sample problem with more than 900 combinations of parameters and comparing the results with the nominal case. In conclusion, the results of different combinations and prices of robustness are compared and some directions for future researches are suggested finally.

