Particle swarm optimization (PSO) and Sine Cosine algorithm (SCA) have been widely used optimization methods but these methods have some disadvantages such as trapped local optimum point. In order to solve this problem and obtain more successful results than others, a novel logistic dynamic weight based sine cosine search algorithm (LDW-SCSA) is presented in this paper. In the LDW-SCSA method, logistic map is used as dynamic weight generator. Logistic map is one of the famous and widely used chaotic map in the literature. Search process of SCA is modified in the LDW-SCSA. To evaluate performance of the LDW-SCSA, the widely used numerical benchmark functions were utilized as test suite and other swarm optimization methods were used to obtain the comparison results. Superior performances of the LDW-SCSA are proved success of this method.
Deep Dive into LDW-SCSA: Logistic Dynamic Weight based Sine Cosine Search Algorithm for Numerical Functions Optimization.
Particle swarm optimization (PSO) and Sine Cosine algorithm (SCA) have been widely used optimization methods but these methods have some disadvantages such as trapped local optimum point. In order to solve this problem and obtain more successful results than others, a novel logistic dynamic weight based sine cosine search algorithm (LDW-SCSA) is presented in this paper. In the LDW-SCSA method, logistic map is used as dynamic weight generator. Logistic map is one of the famous and widely used chaotic map in the literature. Search process of SCA is modified in the LDW-SCSA. To evaluate performance of the LDW-SCSA, the widely used numerical benchmark functions were utilized as test suite and other swarm optimization methods were used to obtain the comparison results. Superior performances of the LDW-SCSA are proved success of this method.
The name of the age we live in is the information age. In this age, information technologies are frequently used to solve real world problems. Some of the real world problems do not have a mathematical solution. To solve these, optimization methods have been used in the literature and real world applications. Optimization is the process of searching a global optima solution of a problem in a finite search space. Optimization algorithms consist of two sub-classes and these are gradient based optimization and metaheuristic optimization algorithms. In the real-world applications, some problems cannot be solved by using mathematically approaches. In order to solve these problems, meta-
The main aim of swarm optimization algorithms to calculate best solution but some of them trapped local best solutions. To solve this problem, chaotic maps have been used to calculate velocity of these algorithms [16]. CDW-PSO [16] clearly demonstrated that, dynamic weights were increased performance of the PSO. In this paper, chaotic dynamic weights are used in the SCA and logistic map is utilized as weight generator. The proposed method called as Logistic Dynamic Weights based Sine-Cosine Search Algorithm (LDW-SCSA). LDW-SCSA is a mathematical heuristic optimization method and the experiments clearly demonstrated that, this method is a successful meta-heuristic search method.
In this section, the related methods of LDW-SCSA are mentioned.
PSO is the most used swarm optimization method in the literature and it has several variations. In this method, the movements of bird and fish swarms are modeled in order to find global optimum value. In the PSO, firstly particles are generated randomly in range of search space and all particles are updated until to reach global optimum value or maximum iteration. Eq. 1 and 2 describe mathematically particles updating of the PSO.
Where ๐ 1 , ๐ 2 are acceleration of the particles, ๐ค is weight, ๐ฃ is velocity, ๐๐๐๐ 1 and ๐๐๐๐ 2 are uniformly generated random numbers in range of [0,1], ๐ ๐๐๐ ๐ก is position of pest particle, ๐ฅ is position of particle, ๐ refers i th value, d is dimension index and t is time.
Shi and Eberhart [17] proposed weighted PSO to increase success of the PSO and steps of this method are given below.
Step 1: Initialization. Generate particles randomly in range of lower and upper bound.
Step 2: Evaluate each particle by using objective function and calculate gbest and pbest.
Step 3: Update position of particles by using Eq. 1-2.
Step 4: Update gbest and pbest.
Step 5: Repeat steps 3-4 until the global optimum value or maximum iterations is reached.
Sine-cosine optimization method is a mathematic based swarm optimization and this method was proposed by Mirjalili in 2015 [18]. Mathematical description of SCA is given Eq. 3 [18][19].
In Eq. 3, r1, r2, r3 and r4 are randomly generated. r1 determines direction of movements particles, r2 determines how far to move inward or outward to reach the global optimum, r3 determines stochastic weight and r4 provides the transition between sine and cosine components.
Steps of SCA are given below.
Step 1: Initialization. Generate particles randomly in range of lower and upper bound.
Step 2: Evaluate each particle by using objective function and calculate pbest.
Step 3: Update position of particles by using Eq. 3.
Step 4: Update pbest.
Step 5: Update r1, r2, r3 and r4.
Step 6: Repeat steps 3-5 until the global optimum value is found or maximum iterations is reached.
Chaos is one of the phenomena of nonlinear mathematics. In particular, chaotic maps and chaotic fractals are frequently used in information technologies. The computer sciences researchers generally use chaos in the information security and optimization algorithms.
In the optimization algorithms, chaos provides many advantages because it provides uniform distributions. In the literature, many chaotic maps have been presented, one of the most known chaotic map is logistic map. Logistic map is a basic and effective chaotic map and Eq. 4 mathematically define logistic map [20][21].
Seed values of this map are r and t1 values. Random number are generated by using these values. In Eq. 4, r is chaos multiplier, t1 is initial value and t is randomly generated sequence.
In this paper, a novel chaotic weighted SCA is proposed and this method is a mathematical based metaheuristic search method. In the LDW-SCSA, weights are generated dynamically by using logistic map. The main aim of LDW-SCSA is to achieve more successful results than SCA. The LDW-SCSA consists of dynamic weight generation, weight based particle updating and optimal particle selection. The steps of LDW-SCSA are given below.
Step 1: Generate initial positions of the particles randomly.
Step 2: Evaluate all particles and select pbest.
Step 3: Calculate initial weight by using Eq. 6 and 7.
Where w(1) is initial weight and eps is 2.2204 x 10 -16 . Eps is a constant ant it has widely used in the MATLAB for de
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