LFOA

If you want to understand the LFOA, You have to read the information below.

Fruit Fly Optimization Algorithm (FFOA) Introduction

The book entitled by “Innovative Computational Intelligence: A Rough Guide to 134 Clever Algorithms”, by “Bo Xing and Wen-Jing Gao, 2014, Springer.

Part II Biology-based CI Algorithms: Fruit Fly Optimization Algorithm (FFOA)

Chapter 11:

In this chapter, we present a novel optimization algorithm called fruit fly optimization algorithm (FFOA) which is inspired by the behavior of fruit flies. We first describe the general knowledge about the foraging behavior of fruit flies in Sect. 11.1. Then, the fundamentals and performance of FFOA are introduced in Sect. 11.2. Finally, Sect. 11.3 summarizes this chapter.

Foreword to this book

Innovative Computational Intelligence: A Rough Guide to 134 Clever Algorithms”

Computational intelligence (CI) is a relatively new discipline, and accordingly, there is little agreement about its precise definition. Nevertheless, most academicians and practitioners would include techniques such as artificial neural network, fuzzy systems, many versions of evolutionary algorithms (e.g. evolution strategies, genetic algorithm, genetic programming, differential evolution), as well as ant colony optimization, artificial immune systems, multi-agent systems, particle swarm optimization, and the hybridization versions of these, under the umbrella of CI.

In contrast to this common trend, Bo and Wen-Jing offer us a brand new perspective in the field of CI research through their book entitled Innovative Computational Intelligence: A Rough Guide to 134 Clever Algorithms.

 This book is unique because it contains in one source an overview of a wide range of newly developed CI algorithms that are normally found in scattered resources.

The authors succeed in identifying this vast amount of novel CI algorithms and grouping them into four large classes, namely, biology-, physics-, chemistry-, and mathematics-based CI algorithms.

 Furthermore, the organization of the book is such that each algorithm covered in the book contains the corresponding core working principles and some preliminary performance evaluations. This style would, no doubt, lead to the further development of these fascinating algorithms. This book will be beneficial to a broad audience: First, university students, particularly those pursuing their postgraduate studies in advanced subjects; Second, the algorithms introduced in this book can serve as foundations for researchers to build bodies of knowledge in the fast growing area of CI research; Finally, practitioners can also use the algorithms presented in this book to solve and analyze specific real-world problems. Overall, this book makes a worthwhile read and is a welcome edition to the CI literature.

By Zbigniew Michalewicz

Adelaide, Australia, September 2013

Read More

Leader and Follower (LF) Optimization Algorithm

Leader and Follower (LF) Optimization Algorithm One and a half years ago we had invented a new method called the Leader and Follower (LF) Optimization Algorithm. It extends the main idea of Fruit Fly Optimization Algorithm. LF can solve any kind of the problems including unconstrained or constrained examples. I will show them more detail in the future.

Read More

Particle Swarm Algorithm (PSO) and Traditional Gradient Methods:

The basic flow of particle swarm algorithm (PSO) is as follows:

1. Initialize the particle swarm: that is, randomly set the initial position of each  particle and initial   velocity.

2. The new positions of the particles are generated from the initial position and the initial velocity.

3. Calculate the fitness value for each particle.

4. For each particle, compare its fitness value with the fitness value of the best position Pid  it has undergone and update the best position Pid .

5. For each particle, compare its fitness value with the fitness value of the best position Pgd the population has experienced. If it is better than Pgd , update the global optimal solution Pgd .

6. Speed-Displacement Model Operator: In the particle algorithm, the particle velocity and position are adjusted according to Equations (1) and (2) for each particle.

Vid(t+1)=ω*Vid(t)+eta1*rand() (Pid-Xid(t))+eta2*rand()(Pgd-Xid(t)) (1)
Xid(t+1)=Xid(t) + Vid(t+1)                                                                     (2)

Where Vid(t+1) denotes the velocity of the i-th particle in the d-dimension of the (t + 1)-th generation, and ω is the inertia weight , eta1 and eta2 are acceleration constants, and rand() is a random variable between 0 and 1. In addition, in order to make the particle velocity not excessively large, we can set speed upper limit Vmax.

7. The termination condition is satisfied (the set condition or the maximum number of iterations is reached), then stop, otherwise go to step 3 and proceed as shown in Fig 1.

Traditional gradient methods:

(1)   Unconstrained Example (Traditional gradient method: fminsearch)

Consider the problem of finding a set of values [ ] that solves

Minimize f(x)= exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1) ;

    

We use fminsearch of the Matlab toolbox to solve this two-dimensional problem by the following two steps:

Step 1: Write on M-file fun.m:

function f=fun(x)

f=exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1) ;

Step 2: invoke optimization routine:

x0=[-1,1]; % Starting guess

x= fminsearch(‘fun’, x0)

You can evaluate the solution below:

% Ans:

x =    0.5000   -1.0000

fval =   5.1425e-10

Elapsed time is 0.071092 second

%%%%%%%%%%%%%%

PSO for this Unconstrained Problem:

*************best PSO  ****************

zbest =    0.4959   -0.9961

fitnesszbest =   5.5972e-05

Elapsed time is 0.060479 seconds.

(2)   Constrained Example (Traditional gradient method: fmincon)

If inequality constraints are added, the resulting problem may be solve by the fmincon function. For example, if you want to find x that solves

Minimize f=exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1) ;

subject to the following constraints:

 x(1)*x(2)-x(1)-x(2)+1.5 <=0  ;  -x(1)*x(2)-10 <=0 ; 

The original M-file is modified to return both the objective function and constraints.

We can also use fmincon of the Matlab toolbox to solve this constraint problem by the following two steps:

Step 1: Write on M-file fmincon.m for the objective function:

x0=[-1,1]; % Starting guess

fun='exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1)';

Step 2: invoke constrainted optimization routine:

%% Program for two constraints:

function[c,ceq]=mycon(x)

 c=[x(1)*x(2)-x(1)-x(2)+1.5,-x(1)*x(2)-10];

ceq=[];

%%%%%%%%%%%%%%%

Main Program:

clear all

clc

tic

x0=[-1,1]; % Starting guess

fun='exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1)';

x0=[-1,1]; % Starting guess

A=[];

b=[];

Aeq=[];

beq=[];

lb=[];

ub=[];

[x,fval]=fmincon('fun',x0,A,b,Aeq,beq,lb,ub,@mycon)

toc

% Ans:

% Local minimum found that satisfies the constraints.

% Optimization completed because the objective function is non-decreasing in

% feasible directions, to within the default value of the function tolerance,

% and constraints are satisfied to within the default value of the constraint tolerance.

% <stopping criteria details>

% x =   -9.5473    1.0474

% fval =    0.0236

% Elapsed time is 0.559910 seconds.

%%%%%%%%%%%%%%%%%%%%%%%%%

FL for Constrained Problem:

One and a half years ago we had invented a new method called the Leader and Follower (LF) Algorithm. It extends the main idea of Fruit Fly Optimization Algorithm. LF can solve any kind of  the problems including unconstrained or constrained  examples.

If readers wants to know much about this algorithm, Please refer to the next  page.

Output:

    Starting parallel pool (parpool) using the 'local' profile ...

best =   -9.5038    1.0517

minSh =    0.0244

Read More