Authors:Gizem Temelcan, Mustafa Sivri, Inci Albayrak Pages: 47 - 54 Abstract: Nonlinear equations arise frequently while modeling chemistry, physics, economy and engineering problems. In this paper, a new iterative approach for finding a solution of a nonlinear equations system (NLES) is presented by applying a linearization technique. The proposed approach is based on computational method that converts NLES into a linear equations system by using Taylor series expansion at the chosen arbitrary nonnegative initial point. Using the obtained solution of the linear equations system, a linear programming (LP) problem is constructed by considering the equations as constraints and minimizing the objective function constructed as the summation of balancing variables. At the end of the presented algorithm, the exact solution of the NLES is obtained. The performance of the proposed approach has been demonstrated by considering different numerical examples from literature. PubDate: 2020-01-14 DOI: 10.11121/ijocta.01.2020.00684 Issue No:Vol. 10, No. 1 (2020)

Authors:Raheleh Khanduzi, Asyieh Ebrahimzadeh, Samaneh Panjeh Ali Beik Pages: 55 - 65 Abstract: This paper elaborated an effective and robust metaheuristic algorithm with acceptable performance based on solution accuracy. The algorithm applied in solution of the optimal control of fractional Volterra integro-differential (FVID) equation which be substituted by nonlinear programming (NLP). Subsequently the FIVD convert the problem to a NLP by using spectral collocation techniques and thereafter we execute the grey wolf optimizer (GWO) to improve the speed and accuracy and find the solutions of the optimal control and state as well as the optimal value of the cost function. It is mentioned that the utilization of the GWO is simple, due to the fact that the GWO is global search algorithm, the method can be applied to find optimal solution of the NLP. The efficiency of the proposed scheme is shown by the results obtained in comparison with the local methods. Further, some illustrative examples introduced with their approximate solutions and the results of the present approach compared with those achieved using other methods. PubDate: 2020-01-14 DOI: 10.11121/ijocta.01.2020.00753 Issue No:Vol. 10, No. 1 (2020)

Authors:Nihal Ozgur, Nihal Taş, James Francis Peters Pages: 66 - 72 Abstract: We present a new type of activation functions for a complex-valued neural network (CVNN). A proposed activation function is constructed such that it fixes a given ellipse. We obtain an application to a complex-valued Hopfield neural network (CVHNN) using a special form of the introduced complex functions as an activation function. Considering the interesting geometric properties of the plane curve ellipse such as focusing property, we emphasize that these properties may have possible applications in various neural networks. PubDate: 2020-01-14 DOI: 10.11121/ijocta.01.2020.00756 Issue No:Vol. 10, No. 1 (2020)

Authors:Hatıra Günerhan Pages: 73 - 77 Abstract: In this work, we have used reduced differential transform method (RDTM) to compute an approximate solution of the Two-Dimensional Convection-Diffusion equations (TDCDE). This method provides the solution quickly in the form of a convergent series. Also, by using RDTM the approximate solution of two-dimensional convection-diffusion equation is obtained. Further, we have computed exact solution of non-homogeneous CDE by using the same method. To the best of my knowledge, the research work carried out in the present paper has not been done, and is new. Examples are provided to support our work. PubDate: 2020-01-14 DOI: 10.11121/ijocta.01.2020.00781 Issue No:Vol. 10, No. 1 (2020)

Authors:Mahir Kadakal Pages: 78 - 84 Abstract: In this paper, we introduce a new class of functions called as (P;m)-function and quasi-m-convex function. Some inequalities of Hadamard's type for these functions are given. Some special cases are discussed. Results represent signicant renement and improvement of the previous results. We should especially mention that the denition of (P;m)-function and quasi-m-convexity are given for the first time in the literature and moreover, the results obtained in special cases coincide with the well-known results in the literature. PubDate: 2020-01-16 DOI: 10.11121/ijocta.01.2020.00787 Issue No:Vol. 10, No. 1 (2020)

Authors:Ozlem Defterli Pages: 85 - 93 Abstract: A dengue epidemic model with fractional order derivative is formulated to investigate the effect of temperature on the spread of the vector-host transmitted dengue disease. The model consists of system of fractional order differential equations formulated within Caputo fractional operator. The stability of the equilibrium points of the considered dengue model is studied. The corresponding basic reproduction number R_0 is derived and it is proved that if R_0 < 1, the disease-free equilibrium (DFE) is locally asymptotically stable. L1 method is applied to solve the dengue model numerically. Finally, numerical simulations are also presented to illustrate the analytical results showing the influence of the temperature on the dynamics of the vector-host interaction in dengue epidemics. PubDate: 2020-01-28 DOI: 10.11121/ijocta.01.2020.00862 Issue No:Vol. 10, No. 1 (2020)

Authors:Münevver Mine Özyetkin, Dumitru Baleanu Pages: 94 - 103 Abstract: In this study, an algebraic stability test procedure is presented for fractional order time delay systems. This method is based on the principle of eliminating time delay. The stability test of fractional order systems cannot be examined directly using classical methods such as Routh-Hurwitz, because such systems do not have analytical solutions. When a system contains the square roots of s, it is seen that there is a double value function of s. In this study, a stability test procedure is applied to systems including sqrt(s) and/or different fractional degrees such as s^alpha where 0 < α < 1, and α include in R. For this purpose, the integer order equivalents of fractional order terms are first used and then the stability test is applied to the system by eliminating time delay. Thanks to the proposed method, it is not necessary to use approximations instead of time delay term such as Pade. Thus, the stability test procedure does not require the solution of higher order equations. PubDate: 2020-01-28 DOI: 10.11121/ijocta.01.2020.00803 Issue No:Vol. 10, No. 1 (2020)

Authors:Hakan Kutucu, Firdovsi Sharifov Pages: 104 - 112 Abstract: In the paper, we present the maximum cut problem as maximization of a non-smooth convex function over polytope which is the convex hull of bases of the polymatroid associated with a submodular function defined on the subsets of node set of a given graph. We also formulate other new models for this problem and give necessary and enough conditions on an optimal solution in terms of network flow. PubDate: 2020-01-31 DOI: 10.11121/ijocta.01.2020.00826 Issue No:Vol. 10, No. 1 (2020)

Authors:Esma Ates Pages: 113 - 117 Abstract: This paper study the complex Ginzburg-Landau equation with two different forms of nonlinearity. The Jacobi elliptic ansatz method is used to obtain the optical soliton solutions of this equation in the kerr and parabolic law media. Bright and dark optical soliton solutions are acquired as well as Jacobi elliptic function solutions. The existence criteria of these solutions are also indicated. PubDate: 2020-01-31 DOI: 10.11121/ijocta.01.2020.00813 Issue No:Vol. 10, No. 1 (2020)

Authors:Jeerayut Wetweerapong, Pikul Puphasuk Pages: 118 - 136 Abstract: In this research, an improved differential evolution algorithm with a restart technique (DE-R) is designed for solutions of systems of nonlinear equations which often occurs in solving complex computational problems involving variables of nonlinear models. DE-R adds a new strategy for mutation operation and a restart technique to prevent premature convergence and stagnation during the evolutionary search to the basic DE algorithm. The proposed method is evaluated on various real world and synthetic problems and compared with the recently developed methods in the literature. Experiment results show that DE-R can successfully solve all the test problems with fast convergence speed and give high quality solutions. It also outperforms the compared methods. PubDate: 2020-01-31 DOI: 10.11121/ijocta.01.2020.00797 Issue No:Vol. 10, No. 1 (2020)

Authors:Melih Burak Koca, Muhammet Burak Kilic, Yusuf Şahin Pages: 137 - 146 Abstract: Renewable energy has become a prominent subject for researchers since fossil fuel reserves have been decreasing and are not promising to meet the energy demand of the future. Wind takes an important place in renewable energy resources and there is extensive research on wind speed modeling. Herein, one of the most commonly used distributions for wind speed modeling is the Weibull distribution with its simplicity and flexibility. Maximum likelihood (ML) method is the most frequently used technique in Weibull parameter estimation. Iterative techniques such as Newton-Raphson (NR) use random initial values to obtain the ML estimators of the parameters of the Weibull distribution. Therefore, the success of the iterative techniques highly depends on the initial value selection. In order to deliver a solution to the initial value problem, genetic algorithm (GA) is considered to obtain the estimators of the model parameters. The ML estimators obtained using the GA and NR techniques are compared with the method of moments (MoM) estimators via Monte Carlo simulation and wind speed applications. The results show that the ML estimators obtained using GA present superiority over MoM and the ML estimators obtained using NR. PubDate: 2020-02-01 DOI: 10.11121/ijocta.01.2020.00741 Issue No:Vol. 10, No. 1 (2020)

Authors:Onur Alp İlhan, Hasan Bulut, Tukur Abdulkadir Sulaiman, Haci Mehmet Baskonus Pages: 1 - 8 Abstract: The analytical solution of the longitudinal wave equation in the MEE circular rod is analyzed by the powerful sine-Gordon expansion method. Sine - Gordon expansion is based on the well-known wave transformation and sine - Gordon equation. In the longitudinal wave equation in mathematical physics, the transverse Poisson MEE circular rod is caused by the dispersion. Some solutions with complex, hyperbolic and trigonometric functions have been successfully implemented. Numerical simulations of all solutions are given by selecting the appropriate parameter values. The physical meaning of the analytical solution explaining some practical physical problems is given. PubDate: 2019-09-04 DOI: 10.11121/ijocta.01.2020.00837 Issue No:Vol. 10, No. 1 (2019)

Authors:Banu Yetkin Ekren, Bartu Arslan Pages: 9 - 16 Abstract: Since it affects the performance of whole supply chain significantly, definition of correct inventory control policy in a supply chain is critical. Recent technological development enabled real time visibility of a supply network by horizontal integration of each node in a supply network. By this opportunity, inventory sharing among stocking locations is also possible in the effort of cost minimization in supply chain management. Hence, lateral transshipment gained popularity and studies seeking the best lateral-transshipment policy is still under research. In this study, we aim to compare different lateral-transshipment policies for an s, S inventory control problem for a single-echelon supply chain network system. In this work, we consider a supply network with three stocking locations which may perform lateral transshipment among them when backorder takes place. We develop the simulation models of the systems in ARENA 14.5 commercial software and compare the performance of the policies by minimizing the total cost under a pre-defined fill rate constraint by using an optimization tool, OptQuest, integrated in that software. The results show that lateral transshipment works well compared to the scenario when there is no lateral transshipment policy in the network. PubDate: 2019-09-16 DOI: 10.11121/ijocta.01.2020.00789 Issue No:Vol. 10, No. 1 (2019)

Authors:Elif G. Dayıoğlu, Kenan Karagül, Yusuf Şahin, Michael G. Kay Pages: 17 - 25 Abstract: In this study, procedures are presented that can be used to determine the routes of the packages transported within a modular storage system. The problem is a variant of robot motion planning problem. The structures of the procedures are developed in three steps for the simultaneous movement of multiple unit-sized packages in a modular warehouse. The proposed heuristic methods consist of route planning, tagging, and main control components. In order to demonstrate the solution performance of the methods, various experiments were conducted with different data sets and the solution times and qualities of the proposed methods were compared with previous studies. It was found that the proposed methods provide better solutions when taking the number of steps and solution time into consideration. PubDate: 2019-09-19 DOI: 10.11121/ijocta.01.2020.00752 Issue No:Vol. 10, No. 1 (2019)

Authors:Özgün Yücel, Önder Bulut Pages: 26 - 36 Abstract: This study considers a make-to-stock production system with multiple identical parallel servers, fixed production start-up costs and lost sales. Processing times are assumed to be two-phase Coxian random variables that allows us to model the systems having rework or remanufacturing operations. First, the dynamic programming formulation is developed and the structure of the optimal production policy is characterized. Due to the highly dynamic nature of the optimal policy, as a second contribution we propose an easy-to-apply production policy. The proposed policy makes use of the dynamic state information and controlled by only two parameters. We test the performance of the proposed policy at several instances and reveal that it is near optimal. We also assess the value of dynamic state information in general by comparing the proposed policy with the well-known static inventory position based policy. PubDate: 2019-09-24 DOI: 10.11121/ijocta.01.2020.00801 Issue No:Vol. 10, No. 1 (2019)

Authors:Gülçin Bektur Pages: 37 - 46 Abstract: In this study, a multi-resource agent bottleneck generalized assignment problem (MRBGAP) is addressed. In the bottleneck generalized assignment problem (BGAP), more than one job can be assigned to an agent, and the objective function is to minimize the maximum load over all agents. In this problem, multiple resources are considered and the capacity of the agents is dependent on these resources and it has minimum two indices. In addition, agent qualifications are taken into account. In other words, not every job can be assignable to every agent. The problem is defined by considering the problem of assigning jobs to employees in a firm. BGAP has been shown to be NP- hard. Consequently, a multi-start iterated tabu search (MITS) algorithm has been proposed for the solution of large-scale problems. The results of the proposed algorithm are compared by the results of the tabu search (TS) algorithm and mixed integer linear programming (MILP) model. PubDate: 2019-10-06 DOI: 10.11121/ijocta.01.2020.00796 Issue No:Vol. 10, No. 1 (2019)