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In this work a strong framework is presented for solving the constrained nonlinear optimization problem that is a relatively complicated problem. These problems arise in a diverse range of sciences. There are a number of different approaches have been proposed. In this work, we employ the imperialist compet-itive algorithm (ICA) for solving constrained nonlinear optimization problems. Some well-known problems are presented to demonstrate the efficiency of this new robust optimization method in comparison to other known methods.

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... Huan-Tong et al. who proposed a modified evolution strategy based on probability ranking method to solve complicated nonlinear systems of equations [5]. Abdollahi et al. applied imperialist competitive algorithm (ICA) for solving nonlinear systems equations [6]. Ouyang et al. employed a hybrid particle swarm optimization algorithm. ...

... The obtained answers of mathematical methods are sensitive to the initial guess of the solution [9,11]. The population size of the evolutionary algorithms (GA [1], EGA [3], EA [10], PEA [2], MES [5], MSEOA [8], PSO [7], PPSO [12], ASA [13], ICA [6] and IWO [15]) is large and the convergence of the mentioned methods to the global minimum is slow. For this reason, it is necessary to find an efficient algorithm for solving the systems of nonlinear equations. ...

... The comparison of convergence history of ICA, COA and iCOA methods are presented in Figs. 3,4,5,6,7,8,9,10. The quality of the obtained solutions by iCOA in all of the tests and case studies is better. ...

Systems of nonlinear equations come into different range of sciences such as chemistry, economics, medicine, robotics, engineering, and mechanics. There are different methods for solving systems of nonlinear equations such as Newton type methods, imperialist competitive algorithm, particle swarm algorithm, conjugate direction method that each has their own advantages and weaknesses such as low convergence speed and poor quality of solutions. This paper improves cuckoo optimization algorithm for solving systems of nonlinear equations by changing the policy of egg laying radius, and some well-known problems are presented to demonstrate the efficiency and better performance of this new robust optimization algorithm. From obtained results, our approach found more accurate solutions with the lowest number of function evaluations.

... In recent years, with the developments of the stochastic algorithms, more and more scholars have realized the superiority of the stochastic algorithms and tried to solve the systems of nonlinear equations with them. Abdollahi et al. [3] employed imperialist competitive algorithm (ICA) to solve nonlinear equations systems and demonstrated the efficiency of this method with some well-known test problems; Raja et al. [4] developed a novel and efficient intelligent computing approach for solving nonlinear equations using evolutionary computational technique based on twelve variants of genetic algorithm (GA); Subsequently, in 2016, Raja et al. [5] introduced another memetic approach GA-SQP, which used variants of GA as a tool for global search method and sequential quadratic programming (SQP) for efficient local search and obtained satisfactory results; Meanwhile, Raja et al. [6] proposed a hybrid particle swarm optimization algorithm PSO-NMM by combining the strength of particle swarm optimization with Nelder-Mead method and solved some nonlinear benchmark models successfully. Grosan and Abraham [7] applied an evolutionary computation technique to solve the problem obtained by transforming the system into a multiobjective optimization problem; Mo et al. [8] introduced conjugate direction method into particle swarm optimization (PSO) in order to improve PSO and enable PSO to effectively optimize high-dimensional optimization problem and proposed the conjugate direction particle swarm optimization (CDPSO); Jaberipour et al. [9] used an improved particle swarm algorithm(PPSO) to solve the systems of nonlinear equations; Oliveira and Petraglia [10] proposed the fuzzy adaptive simulated annealing (ASA) for finding solutions of arbitrarily nonlinear systems of functional equations; Pourjafari et al. [11] introduced a novel optimization method based on invasive weed optimization (IWO), respectively, for finding all roots of systems of nonlinear equations; Pourrajabian et al. [12] and Muhammad et al. [13] used the genetic algorithm to study the solving systems of nonlinear equations, respectively. ...

... x 3 1.00000000e?00 3.86215466e-06 -9.66722245e-09 -6.77638053e-09 6.75869742e-01 -8.4068221e-01 -9.97038023e-01 1.95314704e-01 9.4576852e-01 6.9280787e-01 7.7919009e-01-7.1268794e-01 ...

In the present paper, a modified cuckoo search algorithm is proposed for solving nonlinear equations, that is, the niche cuckoo search algorithm (NCSA) based on fitness-sharing principle. Niche strategy is introduced to enhance the ability of the cuckoo search algorithm to solve nonlinear equations. So as to evaluate the efficiency of NCSA, NCSA has been first benchmarked by twenty standard test functions by comparing with standard genetic algorithm, chaos gray-coded genetic algorithm and standard cuckoo search algorithm. Then, solutions for several examples of nonlinear systems are presented and compared with results obtained by other approaches. Moreover, the sensitivity analysis of the method to initial interval, nests number, probability and niche number has been studied. Comparison results reveal that the proposed algorithm can cope with the highly nonlinear problems and outperforms many algorithms which exist in the literature.

... Thus, according to the existing infrastructures in Iran and the budget for the implementation of next generation networks, the permutation method seems more appropriate. As a future work, we are planning to optimize the quality of service (QOS) in NGN with evolutionary optimization algorithms such as genetic algorithm, particle swarm algorithm, imperialist competitive algorithm, and cuckoo optimization algorithm [16][17][18][19][20]. ...

In recent years, telecom operators have taken big steps towards Next Generation Network (NGN). Although the concept of NGN and the need to pass it, is known, but discussion on different strategies for migration still continues. The migration to NGN should be done with the best design, the lowest cost, the fastest time and the least error for operators who intend to migrate. Due to the complex nature of this topic, the main goal of this paper is to identify the common steps that telecom service providers consider to migrate to NGN, and previously published papers are intended as a basis for research. This paper covers the analysis of the capabilities of NGN, preparation steps, and migration scenarios to NGN.

... The simulation of human gradual evolution caused the creation of random optimization methods which were called evolutionary algorithms. We can name some different types of evolutionary algorithms such as genetic algorithm, particle swarm algorithm, imperialist competitive algorithm, and cuckoo optimization algorithm [4][5][6][7][8]. In the following, we discuss the structure of genetic algorithm, particle swarm algorithm, and hybrid algorithm. ...

Nowadays unstructured mobile networks (Mobile Ad Hoc Networks) are of utmost importance that various aspects of these networks are the subject of many investigations. In this type of networks, information is transferred in the form of data packets using wireless technology. To transfer information from the source node to the destination node, the optimal path must be chosen. In this study, a hybrid algorithm for routing in ad hoc networks is introduced. Evaluations conducted show that the proposed hybrid algorithm finds the optimal path with a relative decrease in all criteria compared to the previous methods. Index Terms— MANET (Mobile Ad-hoc Network), Quality of Service (QOS), Evolutionary Algorithm (EA), Routing.

... Later on there came RST dependent algorithms like Genetic Algorithms (GA) and their hybrids [5], [10], [13], [14] and [15] which are based on evolution and which were universally used by many researchers to solve many complex non-linear problems. There are also many more evolutionary and heuristic algorithms and their hybrids and extensions which have been used in the study of these complex non-linear problems like the tabu search algorithms [15], SQP [6], Particle Swarm Optimization (PSO) [1], [3], [5], [8], Ant Colony Optimization (ACO) [9], Imperialist Competitive Algorithms (ICA) [2], Lineup competition algorithms [11], Big bang-big crunch [7] and many more. There has also been a lot of work going on for non-linear problems that are unconstrained [4]. ...

Constrained non-linear optimization problems (CNLP) with bounds on the decision variables, where objective functions are minimized/maximized under given constraints frequently appear in real world. There are many traditional as well as heuristic algorithms to solve CNLP, most of which are based on numerical approximations. In the past two decades, the use and development of heuristic-based algorithms to solve CNLP have significantly grown. In fact, now a days Excel Solver and MATLAB® toolboxes are using GA as inbuilt function to solve these CNLP. The objective of this paper is to identify connections and contrasts between the Excel Solver, MATLAB® toolboxes and heuristics algorithms written by researchers to solve some of the constrained non-linear benchmark problems. The theoretical and graphical investigation of the computational results obtained using different techniques is discussed here. It is observed that Excel solver and MATLAB®toolboxes can effectively be used to solve CNLP up to 10 variables and 8 constraints with bounds on the decision variables.

Because of the nonrenewable conventional sources of energy and rising of energy prices, these kinds of energy sources are not responsible to meet increasing of demand any more. So the use of on-grid hybrid systems for their unique characteristics has increased. These forms of organizations would result in reducing of transmission losses, pollution and the ability to exert energy management. This report introduces an economic model for the fuel cell, photovoltaic panels and wind turbine. Three sources of energy beside the local grid can respond to all variations of demand. Since sources of energy should change their productions according to the demand variations, we call it sources’ response. The model consists of the cost of supplying energy, cost of recovered thermal energy from the fuel cell, wind turbine power production cost, solar power generation cost, cost of exchange power with the local grid and the cost of maintenance. Finally, it is trying to minimize total cost by the help of three different evolutionary planning methods. Encouraging results promise the use of hybrid systems in supplying residential load in near future.

A new heuristic approach for minimizing possiblynonlinear and non-differentiable continuous spacefunctions is presented. By means of an extensivetestbed it is demonstrated that the new methodconverges faster and with more certainty than manyother acclaimed global optimization methods. The newmethod requires few control variables, is robust, easyto use, and lends itself very well to parallelcomputation.

In this paper, we develop a new filled function method to solve nonlinear integer programming problem. It is shown that any local minimizer of the new filled function constructed from a current local minimizer is either a better local minimizer of the original integer programming problem or a vertex of its constrained domain. Hence a better local minimizer can be obtained just by local search scheme for the new filled function. An algorithm based on the nice properties of the new filled function is proposed for locating the global minimizer of the original integer programming problem. Several numerical examples are presented to show the efficiency of the algorithm.

In this paper, we formulate an optimal design problem of system reliability as a nonlinear integer programming problem with interval coefficients, transform it into a bicriteria 0–1 nonlinear programming problem without interval coefficients, and solve it directly using GA with holding nonlinear objective functions. Also, we demonstrate the efficiency of this method with a numerical example.

Penalty function is popular method for constrained optimization problems. Generally, a penalty parameter controls the degree of penalty for a constrained violation and an optimal parameter exists, but the value is difficult to define and its optimal value is different for different questions. Here, we propose an improved multi-population genetic algorithm to solve this problem. Each population uses different penalty strategy, then each subpopulation evolve independently for a certain number of generations, after that exchange individuals between different subpopulations. This method can perform multi-directional searches by manipulating several subpopulations of potential solutions for different penalty degree for constraints violation and obtain mixed information from these different directional searches, so it can make the selection of the penalty degree much easier and has more chance to find an optimal solution

This paper proposes an algorithm for optimization inspired by the imperialistic competition. Like other evolutionary ones, the proposed algorithm starts with an initial population. Population individuals called country are in two types: colonies and imperialists that all together form some empires. Imperialistic competition among these empires forms the basis of the proposed evolutionary algorithm. During this competition, weak empires collapse and powerful ones take possession of their colonies. Imperialistic competition hopefully converges to a state in which there exist only one empire and its colonies are in the same position and have the same cost as the imperialist. Applying the proposed algorithm to some of benchmark cost functions, shows its ability in dealing with different types of optimization problems.

As an extension of the hybrid Genetic Algorithm-HGA proposed by Tang et al. (Comput. Math. Appl. 36 (1998) 11). this paper focuses on the critical techniques in the application of the GA to nonlinear programming (NLP) problems with equality and inequality constraints. Taking into account the equality constraints and embedding the information of infeasible points/chromosomes into the evaluation function, an extended fuzzy-based methodology and three new evaluation functions are proposed to formulate and evaluate the infeasible chromosomes. The extended version of concepts of dominated semi-feasible direction (DSFD), feasibility degree (FD,) of semi-feasible direction, feasibility degree (FD,) of infeasible points 'belonging to' feasible domain are introduced. Combining the new evaluation functions and weighted gradient direction search into the Genetic Algorithm, an extended hybrid Genetic Algorithm (EHGA) is developed to solve nonlinear programming (NLP) problems with equality and inequality constraints. Simulation shows that this new algorithm is efficient.