An adaptive step improved fruit fly optimization algorithm

In order to solve the shortcomings of Fruit Fly Optimization Algorithm (FOA), which is slow and easy to fall into local optimum, can not specify the domain, Fruit Fly Optimization Algorithm and logstic function transformation are combined to propose an adaptive step improved fruit fly optimization algorithm with logistic transform (ASFOALT). The algorithm improves the correctness of the optimal solution range by improving the fitness function of the FOA, and improves the overall performance of the algorithm by adding the adaptive step mechanism. The experimental results show that ASFOALT has a large improvement in global search capability, convergence speed, convergence accuracy and reliability.


Introduction
Fruit Fly Optimization Algorithm(FOA) is a grouped intelligence algorithm proposed by Dr. Pan WT in 2011 based on the characteristics of fruit fly foraging behavior and the global optimal solution [1,2] .The algorithm improves the diversity of fruit fly melanogaster by olfactory search, increases the search space of fruit fly individuals, and rapidly converges the fruit flies by visual search to achieve the optimal solution.The algorithm has the characteristics of less parameters, fast calculation speed, strong global optimization ability and easy implementation.It can be widely used in science and engineering field, and can be used together with other data mining techniques, It has been successfully applied to BP neural Network clustering analysis [3] , support vector machine (SVM) parameter optimization [4] , blind source separation [5] and other fields.On the other hand, FOA also has the problem that the domain of optimization can not be specified, the search direction is blind, the optimization is easy to fall into the local optimal, the later convergence speed is slow and the convergence precision is low.Therefore, many scholars have done a different degree of improvement on the FOA.Han JY [6] and others, combining chaos optimization with the fruit fly algorithm, proposed adaptive chaos fruit fly optimization algorithm; Ning Jianping [7] and others, applied the step size of the decreasing algorithm to Fruit Fly Optimization Algorithm, which makes Fruit Fly Optimization Algorithm have strong global search ability at the initial stage, so as to effectively avoid the local optimal problem.Yang Shuquan [8] and others proposed a clustering analysis algorithm(Flow-IFOA) based on the improved fruit fly optimization algorithm and functional flow algorithm, by introducing the fruit fly factor, the search step size of each fruit fly  Step3 Since the food location cannot be known, the distance to the origin is thus estimated first (Dist), then the smell concentration judgment value (Js) is calculated, and this value is the reciprocal of distance.Step7 Enter iterative optimization to repeat the implementation of steps 2-5, then judge if the smell concentration is superior to the previous iterative smell concentration, if so, implement step 6.

Improvement based on Fruit Fly Optimization Algorithm
In the process of overall iterative optimization, FOA substitute the reciprocal of the distance each fruit fly to the origin into Fitness function to get the optimal solution, so the searching range(or call domain) of fruit fly swarm is not domain of Fitness function, the optimal solution obtained by the fitness function is probably not the solution within the specified range.For example, use FOA to get the minimum value of the sine function f(x)=sin(x),x∈ [2,4] will get the global optimal value f(x)=-1 Instead of the optimal value f(x)=-0.7568within domain x∈ [2,4], this means that FOA is unable to specify the search range (or call domain).In order to solve this problem, this paper improves the initial range of the fruit fly swarm, the calculation method of smell concentration judgment value and the fitness function of the FOA.
The proceed of the improved fruit fly optimization algorithm as follows: Step1 Perform the steps 1 to 5 in FOA.
Step2 First, estimated the distance each fruit fly to the origin (Dist), than performs a modulus on 1 to put the value(smell concentration judgment value, Js) in the proper range.Step4 Perform the steps 4 to 7 in FOA.
The improved fruit fly optimization algorithm can overcome the defects in FOA that can not specify the search range by mapping the smell concentration judgment value(Js) within the range [0,1] to the specified domain.In the following experimental section, the effectiveness of this improvement will be verified by multiple functions.

Adaptive step size based on logistic transform
In each iteration, Fruit Fly Optimization Algorithm take the best individual of last iteration as the center and take the random distance(R) as the radius to search the food, but the random distance(R) is a fixed value.If R is a large value, the algorithm will get better performance in global optimization, can quickly locate the approximate range of the optimal solution, but in the process of local optimization, convergence accuracy and search efficiency of the algorithm can not be guaranteed.If R is a smaller value, the algorithm is easily trapped in the local optimum and appeared premature convergence, whole search efficiency is limited even in unimodal functions.
In order to resolve this problem, we have introduced a function based on Logistic Function transformation.20( 0.5) Set the Adaptive step size(RV).
In this formula, R is the initial step size(or call random distance) of FOA, Gen is iterations, Maxgen is maximum number of iterations, function LT is a correction function and the graph as shown in the Fig. 2.
adaptive step size adjustment technology can make Fruit Fly Optimization Algorithm have a larger random step value(RV) in early iterations to avoid premature convergence, as the number of iterations increases RV will decreased by Logistic Function curve; in later iterations, smaller step size make Fruit Fly Optimization Algorithm have powerful local optimization performance.

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In function, but ASFOALT raise 8 orders of magnitude at least than FOA.In addition, the optimal solution obtained of sine Function by FOA is not within the specified domain( [2,4]), but ASFOALT successfully converged to the optimal value, this also proves that FOA is unable to specify the domain.Sine Rate is a multimodal function, because FOA can not specify the domain and the search step is fixed value, this algorithm is not stable and the standard deviation is large, the effect of convergence accuracy far from ideal.Unlike FOA, ASFOALT effectively overcome premature convergence by adaptive step size adjustment technology and increase global optimization capability and precision of solutions. )

Conclusion
For the FOA can not specify the domain of optimization, the optimization accuracy is not high and easy to fall into the local optimal characteristics, by the improved fruit fly optimization algorithm and adaptive step size adjustment techniques combined, proposed an adaptive step improved fruit fly optimization algorithm with logistic transform (ASFOALT).And the experiments show that the proposed algorithm(ASFOALT) can specify the search range and on this basis,it has a lot of improvements than FOA in global search capability, convergence speed, convergence accuracy and reliability.
concentration judgment value (Js) into smell concentration judgment function (or called Fitness function) so as to find the smell concentration (Smell i ) of the individual location of the fruit fly.( ) i i Smell Function Js  Step5 Find out the fruit fly with maximal smell concentration (finding the maximal value Smellbest) among the fruit fly swarm.(Best individual FF best smell concentration judgment value(Js) to the domain([Min,Max]).

The 3rd International Conference on Intelligent Energy and Power Systems (IEPS 2017) Published by CSP © 2017 the Authors
).Step6 Keep the best smell concentration value and x, y coordinate, and at this moment, the fruit fly swarm will use vision to fly towards that location.
best X axis Y axis FF

Table . 1
Test function

Table . 2
Result of the experiment