Search results for: linear combinatorial optimization

Authors: Liudmyla Koliechkina, Olena Dvirna

Abstract:

The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: discrete set, linear combinatorial optimization, multi-objective optimization, Pareto solutions, partial permutation set, structural graph

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Authors: Takahiro Hino, Michiharu Maeda

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Particle swarm optimization (PSO) is an optimization approach that achieves the social model of bird flocking and fish schooling. PSO works in continuous space and can solve continuous optimization problem with high quality. Set-based particle swarm optimization (SPSO) functions in discrete space by using a set. SPSO can solve combinatorial optimization problem with high quality and is successful to apply to the large-scale problem. In this paper, we present an algorithm of SPSO with status memory to decide the position based on the previous position for solving traveling salesman problem (TSP). In order to show the effectiveness of our approach. We examine SPSOSM for TSP compared to the existing algorithms.

Keywords: combinatorial optimization problems, particle swarm optimization, set-based particle swarm optimization, traveling salesman problem

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Authors: Li Dan, Zhao Junsuo, Zhang Wenjun

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Aiming at the shortcomings of the Quantum Genetic Algorithm such as the multimodal function optimization problems easily falling into the local optimum, and vulnerable to premature convergence due to no closely relationship between individuals, the paper presents an Improved Many Worlds Quantum Genetic Algorithm (IMWQGA). The paper using the concept of Many Worlds; using the derivative way of parallel worlds’ parallel evolution; putting forward the thought which updating the population according to the main body; adopting the transition methods such as parallel transition, backtracking, travel forth. In addition, the algorithm in the paper also proposes the quantum training operator and the combinatorial optimization operator as new operators of quantum genetic algorithm.

Keywords: quantum genetic algorithm, many worlds, quantum training operator, combinatorial optimization operator

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Authors: Sourabh Joshi, Tarun Sharma, Anurag Sharma

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Ant Colony Optimization is heuristic Algorithm which has been proven a successful technique applied on number of combinatorial optimization problems. Two variants of Ant Colony Optimization algorithm named Ant System and Max-Min Ant System are implemented in MATLAB to solve travelling Salesman Problem and the results are compared. In, this paper both systems are analyzed by solving the some Travelling Salesman Problem and depict which system solve the problem better in term of cost and time.

Keywords: Ant Colony Optimization, Travelling Salesman Problem, Ant System, Max-Min Ant System

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Authors: Saeed Ur Rahman, Naveed Ullah, Muhammad Irshad Khan, Quensheng Cao, Niaz Muhammad Khan

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In this paper the optimization performance of non-uniform linear antenna array is presented. The Particle Swarm Optimization (PSO) algorithm is presented to minimize Side Lobe Level (SLL) and Half Power Beamwidth (HPBW). The purpose of using the PSO algorithm is to get the optimum values for inter-element spacing and excitation amplitude of linear antenna array that provides a radiation pattern with minimum SLL and HPBW. Various design examples are considered and the obtain results using PSO are confirmed by comparing with results achieved using other nature inspired metaheuristic algorithms such as real coded genetic algorithm (RGA) and biogeography (BBO) algorithm. The comparative results show that optimization of linear antenna array using the PSO provides considerable enhancement in the SLL and HPBW.

Keywords: linear antenna array, minimum side lobe level, narrow half power beamwidth, particle swarm optimization

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Authors: Elham Kazemi

Abstract:

Quadratic Assignment Problem (QAP) is one the combinatorial optimization problems about which research has been done in many companies for allocating some facilities to some locations. The issue of particular importance in this process is the costs of this allocation and the attempt in this problem is to minimize this group of costs. Since the QAP’s are from NP-hard problem, they cannot be solved by exact solution methods. Cuckoo Optimization Algorithm is a Meta-heuristicmethod which has higher capability to find the global optimal points. It is an algorithm which is basically raised to search a continuous space. The Quadratic Assignment Problem is the issue which can be solved in the discrete space, thus the standard arithmetic operators of Cuckoo Optimization Algorithm need to be redefined on the discrete space in order to apply the Cuckoo Optimization Algorithm on the discrete searching space. This paper represents the way of discretizing the Cuckoo optimization algorithm for solving the quadratic assignment problem.

Keywords: Quadratic Assignment Problem (QAP), Discrete Cuckoo Optimization Algorithm (DCOA), meta-heuristic algorithms, optimization algorithms

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Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor

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In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.

Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions

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Authors: Rimmy Yadav, Avtar Singh

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—Ant Colony Optimization (ACO) is a promising modern approach to the unused combinatorial optimization. Here ACO is applied to finding the shortest during communication link failure. In this paper, the performances of the prim’s and ACO algorithm are made. By comparing the time complexity and program execution time as set of parameters, we demonstrate the pleasant performance of ACO in finding excellent solution to finding shortest path during communication link failure.

Keywords: ant colony optimization, link failure, prim’s algorithm, shortest path

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Authors: Yassir AbdelRazig

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Evolutionary optimization methods such as genetic algorithms have been used extensively for the construction site layout problem. More recently, ant colony optimization algorithms, which are evolutionary methods based on the foraging behavior of ants, have been successfully applied to benchmark combinatorial optimization problems. This paper proposes a formulation of the site layout problem in terms of a sequencing problem that is suitable for solution using an ant colony optimization algorithm. In the construction industry, site layout is a very important planning problem. The objective of site layout is to position temporary facilities both geographically and at the correct time such that the construction work can be performed satisfactorily with minimal costs and improved safety and working environment. During the last decade, evolutionary methods such as genetic algorithms have been used extensively for the construction site layout problem. This paper proposes an ant colony optimization model for construction site layout. A simple case study for a highway project is utilized to illustrate the application of the model.

Keywords: ant colony, construction site layout, optimization, genetic algorithms

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Authors: M. Tiachachat, M. Mihoubi

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The Bell polynomials are special polynomials in combinatorial analysis that have a wide range of applications in mathematics. They have interested many authors. The exponential partial Bell polynomials have been well reduced to some special combinatorial sequences. Numerous researchers had already been interested in the above polynomials, as evidenced by many articles in the literature. Inspired by this work, in this work, we propose a family of special polynomials named after the 2-successive partial Bell polynomials. Using the combinatorial approach, we prove the properties of these numbers, derive several identities, and discuss some special cases. This family includes well-known numbers and polynomials such as Stirling numbers, Bell numbers and polynomials, and so on. We investigate their properties by employing generating functions

Keywords: 2-associated r-Stirling numbers, the exponential partial Bell polynomials, generating function, combinatorial interpretation

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Authors: Kenza Aida Amara, Bachir Djebbar

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We treat the two-dimensional bin packing problem which involves packing a given set of rectangles into a minimum number of larger identical rectangles called bins. This combinatorial problem is NP-hard. We propose a pretreatment for the oriented version of the problem that allows the valorization of the lost areas in the bins and the reduction of the size problem. A heuristic method based on the strategy first-fit adapted to this problem is presented. We present an approach of resolution by bee colony optimization. Computational results express a comparison of the number of bins used with and without pretreatment.

Keywords: bee colony optimization, bin packing, heuristic algorithm, pretreatment

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Authors: Kazuyoshi Mori, Keisuke Hashimoto

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In this paper, we consider the two-stage compensator designs of SISO plants. As an investigation of the characteristics of the two-stage compensator designs, which is not well investigated yet, of SISO plants, we implement three dimensional visualization systems of output signals and optimization system for SISO plants by the parametrization of stabilizing controllers based on the two-stage compensator design. The system runs on Mathematica by using “Three Dimensional Surface Plots,” so that the visualization can be interactively manipulated by users. In this paper, we use the discrete-time LTI system model. Even so, our approach is the factorization approach, so that the result can be applied to many linear models.

Keywords: linear systems, visualization, optimization, Mathematica

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Authors: Xinhuang Wu, Yousef Sardahi

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A hybrid and optimal multi-loop control structure combining linear and nonlinear control algorithms are introduced in this paper to regulate the position of a quadcopter unmanned aerial vehicle (UAV) driven by four brushless DC motors. To this end, a nonlinear mathematical model of the UAV is derived and then linearized around one of its operating points. Using the nonlinear version of the model, a sliding mode control is used to derive the control laws of the motor thrust forces required to drive the UAV to a certain position. The linear model is used to design two controllers, XG-controller and YG-controller, responsible for calculating the required roll and pitch to maneuver the vehicle to the desired X and Y position. Three attitude controllers are designed to calculate the desired angular rates of rotors, assuming that the Euler angles are minimal. After that, a many-objective optimization problem involving 20 design parameters and ten objective functions is formulated and solved by HypE (Hypervolume estimation algorithm), one of the widely used many-objective optimization algorithms approaches. Both stability and performance constraints are imposed on the optimization problem. The optimization results in terms of Pareto sets and fronts are obtained and show that some of the design objectives are competing. That is, when one objective goes down, the other goes up. Also, Numerical simulations conducted on the nonlinear UAV model show that the proposed optimization method is quite effective.

Keywords: optimal control, many-objective optimization, sliding mode control, linear control, cascade controllers, UAV, drones

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Authors: Yiwei Huang, Chunyu Zhao, Jingjing Ding

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Electrical Resistivity Tomography has been widely used in the medicine and the geology, such as the imaging of the lung impedance and the analysis of the soil impedance, etc. Linear Back Projection is the core algorithm of Electrical Resistivity Tomography, but the traditional Linear Back Projection can not make full use of the information of the electric field. In this paper, an imaging method of Parallel Electrode Linear Back Projection for Electrical Resistivity Tomography is proposed, which generates the electric field distribution that is not linearly related to the traditional Linear Back Projection, captures the new information and improves the imaging accuracy without increasing the number of electrodes by changing the connection mode of the electrodes. The simulation results show that the accuracy of the image obtained by the inverse operation obtained by the Parallel Electrode Linear Back Projection can be improved by about 20%.

Keywords: electrical resistivity tomography, finite element simulation, image optimization, parallel electrode linear back projection

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Authors: H. Nikzad, S. Yoshitomi

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In this paper, an optimization procedure is applied for 3D Reinforced concrete building structure with shear wall.  In the optimization problem, cross sections of beams, columns and shear wall dimensions are considered as design variables and the optimal cross sections can be derived to minimize the total cost of the structure. As for final design application, the most suitable sections are selected to satisfy ACI 318-14 code provision based on static linear analysis. The validity of the method is examined through numerical example of 15 storied 3D RC building with shear wall.  This optimization method is expected to assist in providing a useful reference in design early stage, and to be an effective and powerful tool for structural design of RC shear wall structures.

Keywords: structural optimization, linear static analysis, ETABS, MATLAB, RC moment frame, RC shear wall structures

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Authors: Boumesbah Asma, Chergui Mohamed El-amine

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Since it has been shown that the multi-objective minimum spanning tree problem (MOST) is NP-hard even with two criteria, we propose in this study a hybrid NSGA-II algorithm with an exact mutation operator, which is only used with low probability, to find an approximation to the Pareto front of the problem. In a connected graph G, a spanning tree T of G being a connected and cycle-free graph, if k edges of G\T are added to T, we obtain a partial graph H of G inducing a reduced size multi-objective spanning tree problem compared to the initial one. With a weak probability for the mutation operator, an exact method for solving the reduced MOST problem considering the graph H is then used to give birth to several mutated solutions from a spanning tree T. Then, the selection operator of NSGA-II is activated to obtain the Pareto front approximation. Finally, an adaptation of the VNS metaheuristic is called for further improvements on this front. It allows finding good individuals to counterbalance the diversification and the intensification during the optimization search process. Experimental comparison studies with an exact method show promising results and indicate that the proposed algorithm is efficient.

Keywords: minimum spanning tree, multiple objective linear optimization, combinatorial optimization, non-sorting genetic algorithm, variable neighborhood search

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Authors: Abiodun Ladanu Ajala, Wuyi Oke

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Mathematical simulation and optimization models packaged within interactive computer programs provide a common way for planners and managers to predict the behaviour of any proposed water resources system design or management policy before it is implemented. Modeling presents a principal technique of predicting the behaviour of the proposed infrastructural designs or management policies. Models can be developed and used to help identify specific alternative plans that best meet those objectives. This study discusses various types of models, their development, architecture, data requirements, and applications in the field of engineering. It also outlines the advantages and limitations of each the optimization and simulation models presented. The techniques explored in this review include; dynamic programming, linear programming, fuzzy optimization, evolutionary algorithms and finally artificial intelligence techniques. Previous studies carried out using some of the techniques mentioned above were reviewed, and most of the results from different researches showed that indeed optimization and simulation provides viable alternatives and predictions which form a basis for decision making in building engineering structures and also in engineering planning and management.

Keywords: linear programming, mutation, optimization, simulation

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Authors: Seyedehsomayeh Hosseini

Abstract:

Much attention has been paid over centuries to understanding and solving the problem of minimization of functions. Compared to linear programming and nonlinear unconstrained optimization problems, nonlinear constrained optimization problems are much more difficult. Since the procedure of finding an optimizer is a search based on the local information of the constraints and the objective function, it is very important to develop techniques using geometric properties of the constraints and the objective function. In fact, differential geometry provides a powerful tool to characterize and analyze these geometric properties. Thus, there is clearly a link between the techniques of optimization on manifolds and standard constrained optimization approaches. Furthermore, there are manifolds that are not defined as constrained sets in R^n an important example is the Grassmann manifolds. Hence, to solve optimization problems on these spaces, intrinsic methods are used. In a nondifferentiable problem, the gradient information of the objective function generally cannot be used to determine the direction in which the function is decreasing. Therefore, techniques of nonsmooth analysis are needed to deal with such a problem. As a manifold, in general, does not have a linear structure, the usual techniques, which are often used in nonsmooth analysis on linear spaces, cannot be applied and new techniques need to be developed. This paper presents necessary and sufficient conditions for a strict local minimum of extended real-valued, nonsmooth functions defined on Riemannian manifolds.

Keywords: Riemannian manifolds, nonsmooth optimization, lower semicontinuous functions, subdifferential

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Authors: Elham Kiyani, S. Mansour Vaezpour, Javad Tavakoli

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In this paper, we first introduce a new distance function in a linear space not necessarily endowed with a topology. The algebraic concepts of interior and closure are useful to study optimization problems without topology. So, we define Q-weak efficient solutions generated by the algebraic interior of a set Q, where Q is not necessarily convex. Studying nonconvex vector optimization is valuable since, for a convex cone K in topological spaces, we have int(K)=cor(K), which means that topological interior of a convex cone K is equal to the algebraic interior of K. Moreover, we used the scalarization technique including the distance function generated by the vectorial closure of a set to characterize these Q-weak efficient solutions. Scalarization is a useful approach for solving vector optimization problems. This technique reduces the optimization problem to a scalar problem which tends to be an optimization problem with a real-valued objective function. For instance, Q-weak efficient solutions of vector optimization problems can be characterized and computed as solutions of appropriate scalar optimization problems. In the convex case, linear functionals can be used as objective functionals of the scalar problems. But in the nonconvex case, we should present a suitable objective function. It is the aim of this paper to present a new distance function that be useful to obtain sufficient and necessary conditions for Q-weak efficient solutions of general optimization problems via scalarization.

Keywords: weak efficient, algebraic interior, vector closure, linear space

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Authors: P. Parthiban, Sonu Rajak, N. Kannan, R. Dhanalakshmi

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This paper deals with the Vehicle Routing Problem (VRP) with environmental considerations which is called Pollution Routing Problem (PRP). The objective is to minimize the operational and environmental costs. It consists of routing a number of vehicles to serve a set of customers, and determining fuel consumption, driver wages and their speed on each route segment, while respecting the capacity constraints and time windows. In this context, we presented an Ant Colony Optimization (ACO) approach, combined with a Speed Optimization Algorithm (SOA) to solve the PRP. The proposed solution method consists of two stages. Stage one is to solve a Vehicle Routing Problem with Time Window (VRPTW) using ACO and in the second stage a SOA is run on the resulting VRPTW solutions. Given a vehicle route, the SOA consists of finding the optimal speed on each arc of the route in order to minimize an objective function comprising fuel consumption costs and driver wages. The proposed algorithm tested on benchmark problem, the preliminary results show that the proposed algorithm is able to provide good solutions.

Keywords: ant colony optimization, CO2 emissions, combinatorial optimization, speed optimization, vehicle routing

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Authors: Xiaobao Han, Huacong Li, Jia Li

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For dynamic decoupling of linear parameter varying system, a robust dominance pre-compensator design method is given. The parameterized pre-compensator design problem is converted into optimal problem constrained with parameterized linear matrix inequalities (PLMI); To solve this problem, firstly, this optimization problem is equivalently transformed into a new form with elimination of coupling relationship between parameterized Lyapunov function (PLF) and pre-compensator. Then the problem was reduced to a normal convex optimization problem with normal linear matrix inequalities (LMI) constraints on a newly constructed convex polyhedron. Moreover, a parameter scheduling pre-compensator was achieved, which satisfies robust performance and decoupling performances. Finally, the feasibility and validity of the robust diagonal dominance pre-compensator design method are verified by the numerical simulation of a turbofan engine PLPV model.

Keywords: linear parameter varying (LPV), parameterized Lyapunov function (PLF), linear matrix inequalities (LMI), diagonal dominance pre-compensator

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Authors: Yang Yi-Fei, Luo Min-Zhou, Zhang Fu-Chun, He Nai-Bao, Xing Shao-Bang

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This paper presents an electromagnetic finite element model of permanent magnet synchronous linear motor and distortion rate of the air gap flux density waveform is analyzed in detail. By designing the sample space of the parameters, nonlinear regression modeling of the orthogonal experimental design is introduced. We put forward for possible air gap flux density waveform sine electromagnetic scheme. Parameters optimization of the permanent magnet synchronous linear motor is also introduced which is based on chaotic search and adaptation function. Simulation results prove that the pole shifting does not affect the motor back electromotive symmetry based on the structural parameters, it provides a novel way for the optimum design of permanent magnet synchronous linear motor and other engineering.

Keywords: permanent magnet synchronous linear motor, finite element analysis, chaotic search, optimization design

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Authors: Aouaouche Elmaouhab, Hassina Beggar

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Solving multi-objective discrete optimization applications has always been limited by the resources of one machine: By computing power or by memory, most often both. To speed up the calculations, the grid computing represents a primary solution for the treatment of these applications through the parallelization of these resolution methods. In this work, we are interested in the study of some methods for solving multiple objective integer linear programming problem based on Branch-and-Bound and the study of grid computing technology. This study allowed us to propose an implementation of the method of Abbas and Al on the grid by reducing the execution time. To enhance our contribution, the main results are presented.

Keywords: multi-objective optimization, integer linear programming, grid computing, parallel computing

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Authors: Ernesto Linan, Linda Cruz, Lucero Becerra

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In this paper, a new hybridized algorithm based on Chemical Reaction Optimization and Simulated Annealing is proposed to solve the alignment sequence Problem. The Chemical Reaction Optimization is a population-based meta-heuristic algorithm based on the principles of a chemical reaction. Simulated Annealing is applied to solve a large number of combinatorial optimization problems of general-purpose. In this paper, we propose hybridization between Chemical Reaction Optimization algorithm and Simulated Annealing in order to solve the Sequence Alignment Problem. An initial population of molecules is defined at beginning of the proposed algorithm, where each molecule represents a sequence alignment problem. In order to simulate inter-molecule collisions, the process of Chemical Reaction is placed inside the Metropolis Cycle at certain values of temperature. Inside this cycle, change of molecules is done due to collisions; some molecules are accepted by applying Boltzmann probability. The results with the hybrid scheme are better than the results obtained separately.

Keywords: chemical reaction optimization, sequence alignment problem, simulated annealing algorithm, metaheuristics

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Authors: A. A. Behroozpoor, M. M. Mazarei

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In this paper, a fuzzy recurrent neural network is proposed for solving the classical quadratic control problem subject to linear equality and bound constraints. The convergence of the state variables of the proposed neural network to achieve solution optimality is guaranteed.

Keywords: REFERENCES [1] Xia, Y, A new neural network for solving linear and quadratic programming problems. IEEE Transactions on Neural Networks, 7(6), 1996, pp.1544–1548. [2] Xia, Y., & Wang, J, A recurrent neural network for solving nonlinear convex programs subject to linear constraints. IEEE Transactions on Neural Networks, 16(2), 2005, pp. 379–386. [3] Xia, Y., H, Leung, & J, Wang, A projection neural network and its application to constrained optimization problems. IEEE Transactions Circuits and Systems-I, 49(4), 2002, pp.447–458.B. [4] Q. Liu, Z. Guo, J. Wang, A one-layer recurrent neural network for constrained seudoconvex optimization and its application for dynamic portfolio optimization. Neural Networks, 26, 2012, pp. 99-109.

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Authors: P. W. Tsai, W. L. Hong, C. W. Chen, C. Y. Chen

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In this paper, we present a neural network (NN) based approach represent a nonlinear Tagagi-Sugeno (T-S) system. A linear differential inclusion (LDI) state-space representation is utilized to deal with the NN models. Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear structural systems. Moreover, the concept of utilizing the Parallel Particle Swarm Optimization (PPSO) algorithm to solve the common P matrix under the stability criteria is given in this paper.

Keywords: Lyapunov stability, parallel particle swarm optimization, linear differential inclusion, artificial intelligence

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Authors: Aleksandar Jovanovic, Katarina Kukic, Ana Uzelac, Dusan Teodorovic

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Wisdom of the Crowd (WoC) is a decentralized method that uses the collective intelligence of humans. Individual guesses may be far from the target, but when considered as a group, they converge on optimal solutions for a given problem. We will utilize WoC to address the challenge of controlling traffic lights within intersections from the streets of Kragujevac, Serbia. The problem at hand falls within the category of NP-hard problems. We will employ an algorithm that leverages the swarm intelligence of bees: Bee Colony Optimization (BCO). Data regarding traffic signal timing at a single intersection will be gathered from citizens through a survey. Results obtained in that manner will be compared to the BCO results for different traffic scenarios. We will use Vissim traffic simulation software as a tool to compare the performance of bees’ and humans’ collective intelligence.

Keywords: wisdom of the crowd, traffic signal control, combinatorial optimization, bee colony optimization

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Authors: Angelina Anani, Ignacio Ortiz Flores, Haitao Li

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The use of underground mining methods have increased significantly over the past decades. This increase has also been spared on by several mines transitioning from surface to underground mining. However, determining the transition depth can be a challenging task, especially when coupled with production schedule optimization. Several researchers have simplified the problem by excluding operational features relevant to production schedule optimization. Our research objective is to investigate the extent to which operational features of transition mines accounted for affect the optimal production schedule. We also provide a framework for factors to consider in production schedule optimization for transition mines. An integrated mixed-integer linear programming (MILP) model is developed that maximizes the NPV as a function of production schedule and transition depth. A case study is performed to validate the model, with a comparative sensitivity analysis to obtain operational insights.

Keywords: underground mining, transition mines, mixed-integer linear programming, production schedule

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Authors: Aydin Teymourifar, Gurkan Ozturk

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In this paper, a new hybrid particle swarm optimization algorithm is proposed for the multi-objective flexible job shop scheduling problem that is very important and hard combinatorial problem. The Pareto approach is used for solving the multi-objective problem. Several new local search heuristics are integrated into an algorithm based on the critical block concept to enhance the performance of the algorithm. The algorithm is compared with the recently published multi-objective algorithms based on benchmarks selected from the literature. Several metrics are used for quantifying performance and comparison of the achieved solutions. The algorithms are also compared based on the Weighting summation of objectives approach. The proposed algorithm can find the Pareto solutions more efficiently than the compared algorithms in less computational time.

Keywords: swarm-based optimization, local search, Pareto optimality, flexible job shop scheduling, multi-objective optimization

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Authors: Mohammed Affanuddin H. Siddique, Jayesh S. Shukla, Chetan B. Meshram

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The neural networks are one of the power tools of machine learning. After the invention of perceptron in early 1980's, the neural networks and its application have grown rapidly. Neural networks are a technique originally developed for pattern investigation. The structure of a neural network consists of neurons connected through synapse. Here, we have investigated the different algorithms and cost function reduction techniques for optimization of vertical axis wind turbine (VAWT) rotor blades. The aerodynamic force coefficients corresponding to the airfoils are stored in a database along with the airfoil coordinates. A forward propagation neural network is created with the input as aerodynamic coefficients and output as the airfoil co-ordinates. In the proposed algorithm, the hidden layer is incorporated into cost function having linear and non-linear error terms. In this article, it is observed that the ANNs (Artificial Neural Network) can be used for the VAWT’s optimization.

Keywords: VAWT, ANN, optimization, inverse design

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