The purpose of this paper is to introduce a new pivot rule of the simplex algorithm. The simplex algorithm first presented by George B. Dantzig, is a widely used method for solving a linear programming problem (LP). O...The purpose of this paper is to introduce a new pivot rule of the simplex algorithm. The simplex algorithm first presented by George B. Dantzig, is a widely used method for solving a linear programming problem (LP). One of the important steps of the simplex algorithm is applying an appropriate pivot rule to select the basis-entering variable corresponding to the maximum reduced cost. Unfortunately, this pivot rule not only can lead to a critical cycling (solved by Bland’s rules), but does not improve efficiently the objective function. Our new pivot rule 1) solves the cycling problem in the original Dantzig’s simplex pivot rule, and 2) leads to an optimal improvement of the objective function at each iteration. The new pivot rule can lead to the optimal solution of LP with a lower number of iterations. In a maximization problem, Dantzig’s pivot rule selects a basis-entering variable corresponding to the most positive reduced cost;in some problems, it is well-known that Dantzig’s pivot rule, before reaching the optimal solution, may visit a large number of extreme points. Our goal is to improve the simplex algorithm so that the number of extreme points to visit is reduced;we propose an optimal improvement in the objective value per unit step of the basis-entering variable. In this paper, we propose a pivot rule that can reduce the number of such iterations over the Dantzig’s pivot rule and prevent cycling in the simplex algorithm. The idea is to have the maximum improvement in the objective value function: from the set of basis-entering variables with positive reduced cost, the efficient basis-entering variable corresponds to an optimal improvement of the objective function. Using computational complexity arguments and some examples, we prove that our optimal pivot rule is very effective and solves the cycling problem in LP. We test and compare the efficiency of this new pivot rule with Dantzig’s original pivot rule and the simplex algorithm in MATLAB environment.展开更多
Evolutionary computation based on the idea of biologic evolution is one type of global optimization algorithm that uses self-adaptation, self-organization and random searching to solve optimization problems. The evolu...Evolutionary computation based on the idea of biologic evolution is one type of global optimization algorithm that uses self-adaptation, self-organization and random searching to solve optimization problems. The evolutionary-simplex algorithm is introduced in this paper. It contains floating encoding which combines the evolutionary computation and the simplex algorithm to ovcrcomc the problems encountered in the genetic algorithm and evolutionary strategy methods.Numerical cxpcrimcnts arc performed using seven typical functions to verify the algorithm. An inverse analysis method to identify structural physical parameters based on incomplete dynamic responses obtained from the analysis in the time domain is prcscntcd by using the evolutionary-simplex algorithm. The modal evolutionary-simplex algorithm converted from the time domain to the modal domain is proposed to improve the inverse efficiency. Numerical calculations for a 50-DOF system show that whcn compared with other methods, the evolutionary-simplex algorithm offers advantages of high precision,cfficient searching ability, strong ability to resist noise, independence of initial value, and good adaptation to incomplete information conditions.展开更多
Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simpl...Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic feasible solution is not easily at hand and the later method needs to an initial dual basic feasible solution. In this paper, we develop a novel approach namely the primal-dual simplex algorithm to overcome mentioned shortcomings. A numerical example is given to illustrate the proposed approach.展开更多
The computation of the basis inverse is the most time-consuming step in simplex type algorithms. This inverse does not have to be computed from scratch at any iteration, but updating schemes can be applied to accelera...The computation of the basis inverse is the most time-consuming step in simplex type algorithms. This inverse does not have to be computed from scratch at any iteration, but updating schemes can be applied to accelerate this calculation. In this paper, we perform a computational comparison in which the basis inverse is computed with five different updating schemes. Then, we propose a parallel implementation of two updating schemes on a CPU-GPU System using MATLAB and CUDA environment. Finally, a computational study on randomly generated full dense linear programs is preented to establish the practical value of GPU-based implementation.展开更多
The algorithm under this name, together with the variants, is a method that solves the problems of optimal flow and costs. Examples of such problems are planning and procurement, scheduling by contractors, distributio...The algorithm under this name, together with the variants, is a method that solves the problems of optimal flow and costs. Examples of such problems are planning and procurement, scheduling by contractors, distribution and supply systems, transport on the road or rail network, electricity transmission, computer and telecommunications networks, pipe transmission systems (water, oil, …), and the like. The main goal of any business organization is to increase profits and satisfy its customers. Because business is an integral part of our environment, their goals will be limited by certain environmental factors and economic conditions. The out-of-kilter algorithm is used to solve a complex allocation problem involving interactive and conflicting personal choices subject to interactive resource constraints. The paper presents an example of successful use of this algorithm and proposes an extension to the areas of corporate and social planning. Customer demand, warehousing, and factory capacity were used as input for the model. First, we propose a linear programming approach to determine the optimal distribution pattern to reduce overall distribution costs. The proposed model of linear programming is solved by the standard simplex algorithm and the Excel-solver program. It is noticed that the proposed model of linear programming is suitable for finding the optimal distribution pattern and total minimum costs.展开更多
In this papers we propose two new perturbation simplex variants. Solving linear programming problems without introducing artificial variables, each of the two uses the dual pivot rule to achieve primal feasibility, an...In this papers we propose two new perturbation simplex variants. Solving linear programming problems without introducing artificial variables, each of the two uses the dual pivot rule to achieve primal feasibility, and then the primal pivot rule to achieve optimality. The second algorithm, a modification of the first, is designed to handle highly degenerate problems more efficiently. Some interesting results concerning merit of the perturbation are established. Numerical results from preliminary tests are also reported.展开更多
In this paper, a hybrid simplex-improved genetic algorithm (HSIGA) which combines simplex method (SM) and genetic algorithm (GA) is proposed to solve global numerical optimization problems. In this hybrid algorithm so...In this paper, a hybrid simplex-improved genetic algorithm (HSIGA) which combines simplex method (SM) and genetic algorithm (GA) is proposed to solve global numerical optimization problems. In this hybrid algorithm some improved genetic mechanisms, for example, non-linear ranking selection, competition and selection among several crossover offspring, adaptive change of mutation scaling and stage evolution, are adopted; and new population is produced through three ap-proaches, i.e. elitist strategy, modified simplex strategy and improved genetic algorithm (IGA) strategy. Numerical experi-ments are included to demonstrate effectiveness of the proposed algorithm.展开更多
This paper works on a modified simplex algorithm for the local optimization of Continuous Piece Wise Linear(CPWL) programming with generalization of hinging hyperplane objective and linear constraints. CPWL programmin...This paper works on a modified simplex algorithm for the local optimization of Continuous Piece Wise Linear(CPWL) programming with generalization of hinging hyperplane objective and linear constraints. CPWL programming is popular since it can be equivalently transformed into difference of convex functions programming or concave optimization. Inspired by the concavity of the concave CPWL functions, we propose an Objective Variation Simplex Algorithm(OVSA), which is able to find a local optimum in a reasonable time. Computational results are presented for further insights into the performance of the OVSA compared with two other algorithms on random test problems.展开更多
The purpose of this research paper is to introduce Easy Simplex Algorithm which is developed by author. The simplex algorithm first presented by G. B. Dantzing, is generally used for solving a Linear programming probl...The purpose of this research paper is to introduce Easy Simplex Algorithm which is developed by author. The simplex algorithm first presented by G. B. Dantzing, is generally used for solving a Linear programming problem (LPP). One of the important steps of the simplex algorithm is to convert all unequal constraints into equal form by adding slack variables then proceeds to basic solution. Our new algorithm i) solves the LPP without equalize the constraints and ii) leads to optimal solution definitely in lesser time. The goal of suggested algorithm is to improve the simplex algorithm so that the time of solving an LPP will be definitely lesser than the simplex algorithm. According to this Easy Simplex (AHA Simplex) Algorithm the use of Big M method is not required.展开更多
为了改善高压直流系统的故障后的恢复性能,在研究低压限流单元(voltage dependent current order limiter,VDCOL)对直流系统无功功率消耗和电压稳定性影响的基础上,提出了一种分段变速率低压限流单元(piecewise-variable-rate VDCOL,PVR...为了改善高压直流系统的故障后的恢复性能,在研究低压限流单元(voltage dependent current order limiter,VDCOL)对直流系统无功功率消耗和电压稳定性影响的基础上,提出了一种分段变速率低压限流单元(piecewise-variable-rate VDCOL,PVR-VDCOL)的控制方法,该方法通过将电压下降或恢复过程划分为几个不同的阶段,并在每个阶段根据电压水平的不同而设置不同的功率恢复速率。推导了控制器初值的计算公式,制定了利用Simplex算法优化控制器参数的流程,并重点分析了分段数目对控制器性能的影响及其确定方法。在PSCAD/EMTDC中对提出的PVR-VDCOL和传统线性VDCOL的控制效果进行了对比仿真,并对不同分段数目下的仿真结果进行了对比分析,仿真结果表明提出的PVR-VDCOL能够有效改善直流系统的恢复性能。展开更多
The traditional genetic algorithm(GA)has unstable inversion results and is easy to fall into the local optimum when inverting fault parameters.Therefore,this article considers the combination of GA with other non-line...The traditional genetic algorithm(GA)has unstable inversion results and is easy to fall into the local optimum when inverting fault parameters.Therefore,this article considers the combination of GA with other non-linear algorithms in order to improve the inversion precision of GA.This paper proposes a genetic Nelder-Mead neural network algorithm(GNMNNA).This algorithm uses a neural network algorithm(NNA)to optimize the global search ability of GA.At the same time,the simplex algorithm is used to optimize the local search capability of the GA.Through numerical examples,the stability of the inversion algorithm under different strategies is explored.The experimental results show that the proposed GNMNNA has stronger inversion stability and higher precision compared with the existing algorithms.The effectiveness of GNMNNA is verified by the BodrumeKos earthquake and Monte Cristo Range earthquake.The experimental results show that GNMNNA is superior to GA and NNA in both inversion precision and computational stability.Therefore,GNMNNA has greater application potential in complex earthquake environment.展开更多
The solutions of dynamic optimization problems are usually very difficult due to their highly nonlinear and multidimensional nature. Genetic algorithm (GA) has been proved to be a feasible method when the gradient is ...The solutions of dynamic optimization problems are usually very difficult due to their highly nonlinear and multidimensional nature. Genetic algorithm (GA) has been proved to be a feasible method when the gradient is difficult to calculate. Its advantage is that the control profiles at all time stages are optimized simultaneously, but its convergence is very slow in the later period of evolution and it is easily trapped in the local optimum. In this study, a hybrid improved genetic algorithm (HIGA) for solving dynamic optimization problems is proposed to overcome these defects. Simplex method (SM) is used to perform the local search in the neighborhood of the optimal solution. By using SM, the ideal searching direction of global optimal solution could be found as soon as possible and the convergence speed of the algorithm is improved. The hybrid algorithm presents some improvements, such as protecting the best individual, accepting immigrations, as well as employing adaptive crossover and Gaussian mutation operators. The efficiency of the proposed algorithm is demonstrated by solving several dynamic optimization problems. At last, HIGA is applied to the optimal production of secreted protein in a fed batch reactor and the optimal feed-rate found by HIGA is effective and relatively stable.展开更多
A new genetic algorithm is presented based on the musical performance.The novelty of this algorithm is that a new genetic algorithm, mimicking the musical process of searching for a perfect state of harmony, which inc...A new genetic algorithm is presented based on the musical performance.The novelty of this algorithm is that a new genetic algorithm, mimicking the musical process of searching for a perfect state of harmony, which increases the robustness of it greatly and gives a new meaning of it in the meantime, has been developed. Combining the advantages of the new genetic algorithm, simplex algorithm and tabu search, a hybrid algorithm is proposed. In order to verify the effectiveness of the hybrid algorithm, it is applied to solving some typical numerical function optimization problems which are poorly solved by traditional genetic algorithms. The experimental results show that the hybrid algorithm is fast and reliable.展开更多
A robust phase-only Direct Data Domain Least Squares (D3LS) algorithm based on gen- eralized Rayleigh quotient optimization using hybrid Genetic Algorithm (GA) is presented in this letter. The optimization efficiency ...A robust phase-only Direct Data Domain Least Squares (D3LS) algorithm based on gen- eralized Rayleigh quotient optimization using hybrid Genetic Algorithm (GA) is presented in this letter. The optimization efficiency and computational speed are improved via the hybrid GA com- posed of standard GA and Nelder-Mead simplex algorithms. First, the objective function, with a form of generalized Rayleigh quotient, is derived via the standard D3LS algorithm. It is then taken as a fitness function and the unknown phases of all adaptive weights are taken as decision variables. Then, the nonlinear optimization is performed via the hybrid GA to obtain the optimized solution of phase-only adaptive weights. As a phase-only adaptive algorithm, the proposed algorithm is sim- pler than conventional algorithms when it comes to hardware implementation. Moreover, it proc- esses only a single snapshot data as opposed to forming sample covariance matrix and operating matrix inversion. Simulation results show that the proposed algorithm has a good signal recovery and interferences nulling performance, which are superior to that of the phase-only D3LS algorithm based on standard GA.展开更多
文摘The purpose of this paper is to introduce a new pivot rule of the simplex algorithm. The simplex algorithm first presented by George B. Dantzig, is a widely used method for solving a linear programming problem (LP). One of the important steps of the simplex algorithm is applying an appropriate pivot rule to select the basis-entering variable corresponding to the maximum reduced cost. Unfortunately, this pivot rule not only can lead to a critical cycling (solved by Bland’s rules), but does not improve efficiently the objective function. Our new pivot rule 1) solves the cycling problem in the original Dantzig’s simplex pivot rule, and 2) leads to an optimal improvement of the objective function at each iteration. The new pivot rule can lead to the optimal solution of LP with a lower number of iterations. In a maximization problem, Dantzig’s pivot rule selects a basis-entering variable corresponding to the most positive reduced cost;in some problems, it is well-known that Dantzig’s pivot rule, before reaching the optimal solution, may visit a large number of extreme points. Our goal is to improve the simplex algorithm so that the number of extreme points to visit is reduced;we propose an optimal improvement in the objective value per unit step of the basis-entering variable. In this paper, we propose a pivot rule that can reduce the number of such iterations over the Dantzig’s pivot rule and prevent cycling in the simplex algorithm. The idea is to have the maximum improvement in the objective value function: from the set of basis-entering variables with positive reduced cost, the efficient basis-entering variable corresponds to an optimal improvement of the objective function. Using computational complexity arguments and some examples, we prove that our optimal pivot rule is very effective and solves the cycling problem in LP. We test and compare the efficiency of this new pivot rule with Dantzig’s original pivot rule and the simplex algorithm in MATLAB environment.
基金National Natural Science Foundation of China(Grant No.50278006)
文摘Evolutionary computation based on the idea of biologic evolution is one type of global optimization algorithm that uses self-adaptation, self-organization and random searching to solve optimization problems. The evolutionary-simplex algorithm is introduced in this paper. It contains floating encoding which combines the evolutionary computation and the simplex algorithm to ovcrcomc the problems encountered in the genetic algorithm and evolutionary strategy methods.Numerical cxpcrimcnts arc performed using seven typical functions to verify the algorithm. An inverse analysis method to identify structural physical parameters based on incomplete dynamic responses obtained from the analysis in the time domain is prcscntcd by using the evolutionary-simplex algorithm. The modal evolutionary-simplex algorithm converted from the time domain to the modal domain is proposed to improve the inverse efficiency. Numerical calculations for a 50-DOF system show that whcn compared with other methods, the evolutionary-simplex algorithm offers advantages of high precision,cfficient searching ability, strong ability to resist noise, independence of initial value, and good adaptation to incomplete information conditions.
文摘Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic feasible solution is not easily at hand and the later method needs to an initial dual basic feasible solution. In this paper, we develop a novel approach namely the primal-dual simplex algorithm to overcome mentioned shortcomings. A numerical example is given to illustrate the proposed approach.
文摘The computation of the basis inverse is the most time-consuming step in simplex type algorithms. This inverse does not have to be computed from scratch at any iteration, but updating schemes can be applied to accelerate this calculation. In this paper, we perform a computational comparison in which the basis inverse is computed with five different updating schemes. Then, we propose a parallel implementation of two updating schemes on a CPU-GPU System using MATLAB and CUDA environment. Finally, a computational study on randomly generated full dense linear programs is preented to establish the practical value of GPU-based implementation.
文摘The algorithm under this name, together with the variants, is a method that solves the problems of optimal flow and costs. Examples of such problems are planning and procurement, scheduling by contractors, distribution and supply systems, transport on the road or rail network, electricity transmission, computer and telecommunications networks, pipe transmission systems (water, oil, …), and the like. The main goal of any business organization is to increase profits and satisfy its customers. Because business is an integral part of our environment, their goals will be limited by certain environmental factors and economic conditions. The out-of-kilter algorithm is used to solve a complex allocation problem involving interactive and conflicting personal choices subject to interactive resource constraints. The paper presents an example of successful use of this algorithm and proposes an extension to the areas of corporate and social planning. Customer demand, warehousing, and factory capacity were used as input for the model. First, we propose a linear programming approach to determine the optimal distribution pattern to reduce overall distribution costs. The proposed model of linear programming is solved by the standard simplex algorithm and the Excel-solver program. It is noticed that the proposed model of linear programming is suitable for finding the optimal distribution pattern and total minimum costs.
文摘In this papers we propose two new perturbation simplex variants. Solving linear programming problems without introducing artificial variables, each of the two uses the dual pivot rule to achieve primal feasibility, and then the primal pivot rule to achieve optimality. The second algorithm, a modification of the first, is designed to handle highly degenerate problems more efficiently. Some interesting results concerning merit of the perturbation are established. Numerical results from preliminary tests are also reported.
基金Supported by National Natural Science Foundation of P.R.China(60474069)
文摘In this paper, a hybrid simplex-improved genetic algorithm (HSIGA) which combines simplex method (SM) and genetic algorithm (GA) is proposed to solve global numerical optimization problems. In this hybrid algorithm some improved genetic mechanisms, for example, non-linear ranking selection, competition and selection among several crossover offspring, adaptive change of mutation scaling and stage evolution, are adopted; and new population is produced through three ap-proaches, i.e. elitist strategy, modified simplex strategy and improved genetic algorithm (IGA) strategy. Numerical experi-ments are included to demonstrate effectiveness of the proposed algorithm.
基金supported by the National Natural Science Foundation of China (Nos. 61473165 and 61134012)the National Key Basic Research and Development (973) Program of China (No. 2012CB720505)
文摘This paper works on a modified simplex algorithm for the local optimization of Continuous Piece Wise Linear(CPWL) programming with generalization of hinging hyperplane objective and linear constraints. CPWL programming is popular since it can be equivalently transformed into difference of convex functions programming or concave optimization. Inspired by the concavity of the concave CPWL functions, we propose an Objective Variation Simplex Algorithm(OVSA), which is able to find a local optimum in a reasonable time. Computational results are presented for further insights into the performance of the OVSA compared with two other algorithms on random test problems.
文摘The purpose of this research paper is to introduce Easy Simplex Algorithm which is developed by author. The simplex algorithm first presented by G. B. Dantzing, is generally used for solving a Linear programming problem (LPP). One of the important steps of the simplex algorithm is to convert all unequal constraints into equal form by adding slack variables then proceeds to basic solution. Our new algorithm i) solves the LPP without equalize the constraints and ii) leads to optimal solution definitely in lesser time. The goal of suggested algorithm is to improve the simplex algorithm so that the time of solving an LPP will be definitely lesser than the simplex algorithm. According to this Easy Simplex (AHA Simplex) Algorithm the use of Big M method is not required.
文摘为了改善高压直流系统的故障后的恢复性能,在研究低压限流单元(voltage dependent current order limiter,VDCOL)对直流系统无功功率消耗和电压稳定性影响的基础上,提出了一种分段变速率低压限流单元(piecewise-variable-rate VDCOL,PVR-VDCOL)的控制方法,该方法通过将电压下降或恢复过程划分为几个不同的阶段,并在每个阶段根据电压水平的不同而设置不同的功率恢复速率。推导了控制器初值的计算公式,制定了利用Simplex算法优化控制器参数的流程,并重点分析了分段数目对控制器性能的影响及其确定方法。在PSCAD/EMTDC中对提出的PVR-VDCOL和传统线性VDCOL的控制效果进行了对比仿真,并对不同分段数目下的仿真结果进行了对比分析,仿真结果表明提出的PVR-VDCOL能够有效改善直流系统的恢复性能。
基金This manuscript is supported by the National Natural Science Foundation of China(No.42174011,41874001 and 42174011).
文摘The traditional genetic algorithm(GA)has unstable inversion results and is easy to fall into the local optimum when inverting fault parameters.Therefore,this article considers the combination of GA with other non-linear algorithms in order to improve the inversion precision of GA.This paper proposes a genetic Nelder-Mead neural network algorithm(GNMNNA).This algorithm uses a neural network algorithm(NNA)to optimize the global search ability of GA.At the same time,the simplex algorithm is used to optimize the local search capability of the GA.Through numerical examples,the stability of the inversion algorithm under different strategies is explored.The experimental results show that the proposed GNMNNA has stronger inversion stability and higher precision compared with the existing algorithms.The effectiveness of GNMNNA is verified by the BodrumeKos earthquake and Monte Cristo Range earthquake.The experimental results show that GNMNNA is superior to GA and NNA in both inversion precision and computational stability.Therefore,GNMNNA has greater application potential in complex earthquake environment.
基金Supported by Major State Basic Research Development Program of China （2012CB720500）, National Natural Science Foundation of China （Key Program： Ul162202）, National Science Fund for Outstanding Young Scholars （61222303）, National Natural Science Foundation of China （21276078, 21206037） and the Fundamental Research Funds for the Central Universities.
文摘The solutions of dynamic optimization problems are usually very difficult due to their highly nonlinear and multidimensional nature. Genetic algorithm (GA) has been proved to be a feasible method when the gradient is difficult to calculate. Its advantage is that the control profiles at all time stages are optimized simultaneously, but its convergence is very slow in the later period of evolution and it is easily trapped in the local optimum. In this study, a hybrid improved genetic algorithm (HIGA) for solving dynamic optimization problems is proposed to overcome these defects. Simplex method (SM) is used to perform the local search in the neighborhood of the optimal solution. By using SM, the ideal searching direction of global optimal solution could be found as soon as possible and the convergence speed of the algorithm is improved. The hybrid algorithm presents some improvements, such as protecting the best individual, accepting immigrations, as well as employing adaptive crossover and Gaussian mutation operators. The efficiency of the proposed algorithm is demonstrated by solving several dynamic optimization problems. At last, HIGA is applied to the optimal production of secreted protein in a fed batch reactor and the optimal feed-rate found by HIGA is effective and relatively stable.
基金Supported by the National Natural Science Foun-dation of China (60273075)
文摘A new genetic algorithm is presented based on the musical performance.The novelty of this algorithm is that a new genetic algorithm, mimicking the musical process of searching for a perfect state of harmony, which increases the robustness of it greatly and gives a new meaning of it in the meantime, has been developed. Combining the advantages of the new genetic algorithm, simplex algorithm and tabu search, a hybrid algorithm is proposed. In order to verify the effectiveness of the hybrid algorithm, it is applied to solving some typical numerical function optimization problems which are poorly solved by traditional genetic algorithms. The experimental results show that the hybrid algorithm is fast and reliable.
基金Supported by the Natural Science Foundation of Jiangsu Province (No.BK2004016).
文摘A robust phase-only Direct Data Domain Least Squares (D3LS) algorithm based on gen- eralized Rayleigh quotient optimization using hybrid Genetic Algorithm (GA) is presented in this letter. The optimization efficiency and computational speed are improved via the hybrid GA com- posed of standard GA and Nelder-Mead simplex algorithms. First, the objective function, with a form of generalized Rayleigh quotient, is derived via the standard D3LS algorithm. It is then taken as a fitness function and the unknown phases of all adaptive weights are taken as decision variables. Then, the nonlinear optimization is performed via the hybrid GA to obtain the optimized solution of phase-only adaptive weights. As a phase-only adaptive algorithm, the proposed algorithm is sim- pler than conventional algorithms when it comes to hardware implementation. Moreover, it proc- esses only a single snapshot data as opposed to forming sample covariance matrix and operating matrix inversion. Simulation results show that the proposed algorithm has a good signal recovery and interferences nulling performance, which are superior to that of the phase-only D3LS algorithm based on standard GA.
