Single Objective Genetic Computation (EC) Techniques

35.3 Single Objective Genetic Computation (EC) Techniques

Optimization Search Algorithm (SOGA)

A comparison between Conventional Optimization Techniques and evolutionary algorithms (like GA and PSO) is presented in GAs are an evolutionary optimization approach which is an Table 35.1 [1].

alternative to traditional optimization methods. GA is most

TABLE 35.1 Comparison between conventional optimization procedures and evolutionary algorithms Property

Evolutionary

Traditional

Search space

Trajectory by a single point Motivation

Population of potential solutions

Mathematical properties (gradient, Hessian) Applicability

Natural selection and Social adaptation

Applicable to a specific problem domain Point Transition

Domain independent, Applicable to variety of problems

Deterministic Prerequisites

Probabilistic

Auxiliary knowledge such as gradient vectors Initial guess

An objective function to be optimized

Provided by user Flow of control

Automatically generated by the algorithm

Mostly parallel

Mostly serial

CPU time

Local optimum, dependant of initial guess Advantages

Global optimum more probable

Convergence proof Drawbacks

Global search, parallel, speed

No general formal convergence proof

Locality, computational cost

35 Novel AI-Based Soft Computing Applications in Motor Drives 995 appropriate for complex nonlinear models where the location

2. [Fitness] Evaluate the fitness f (x) of each chromosome of the global optimum is a difficult task. It may be possible

x in the population

to use GA techniques to consider problems which may not be

3. [New population] Create a new population by repeat- modeled as accurately using other approaches.

ing the following steps until the new population is Therefore, GA appears to be a potentially useful approach.

complete:

GA is particularly applicable to problems which are large, (a) [Selection] Select two parent chromosomes nonlinear, and possibly discrete in nature, features that tradi- from a population according to their fitness (the tionally add to the degree of complexity of solution. Due to better fitness, the bigger chance to be selected). the probabilistic development of the solution, GA does not (b) [Crossover] With a crossover probability cross guarantee optimality even when it may be reached. However, over the parents to form a new offspring (chil- they are likely to be close to the global optimum. This prob- dren). If no crossover was performed, the off- abilistic nature of the solution is also the reason they are not

contained by local optima. The GA procedure is based on the spring is an exact copy of parents. (c) [Mutation] With a mutation probability mutate

Darwinian principle of survival of the fittest. An initial popu- new offspring at each locus (position in chro- lation is created containing a predefined number of individuals

mosome).

(or solutions), each represented by a genetic string (incorporat- (d) [Accepting] Place the new offspring in a new ing the variable information). Each individual has an associated

population.

fitness measure, typically representing an objective value. The concept that fittest (or best) individuals in a population will

4. [Replace] Use new generated population for a further produce fitter offspring is then implemented in order to repro-

run of algorithm

duce the next population. Selected individuals are chosen for

5. [Test] If the end condition is satisfied, stop, and return reproduction (or crossover) at each generation, with an appro-

the best solution in current population priate mutation factor to randomly modify the genes of an

[Loop] Go to step 2

individual, in order to develop the new population. The result GAs can be applied to many scientific, engineering problems, is another set of individuals based on the original subjects lead- once solutions of a given problem can be encoded to chromo- ing to subsequent populations with better (min. or ma35.) somes in GA, and compare the relative performance (fitness) of individual fitness. Therefore, the algorithm identifies the indi- solutions. An effective GA representation and meaningful fit- viduals with the optimizing fitness values, and those with lower ness evaluation are the keys of the success in GA applications. fitness will naturally get discarded from the population [2]. The appeal of GAs comes from their simplicity and elegance as Figure 35.1 shows the general flow chart of the GA algorithm robust search algorithms as well as from their power to discover based on the total error iterative minimum search. The steps of good solutions rapidly for difficult high-dimensional prob- the GA are depicted as follows: lems. The main advantage of GA is that models which cannot

be developed using other solution methods without some form somes (suitable solutions for the problem)

1. [Start] Generate random population of n chromo-

of approximation can be considered in an un-approximated form. Size of the model, i.e., number of probabilistic variables, has a significant effect on the speed of solution therefore model

specification can be crucial. Unlike other solution methods, integer variables are easier to accommodate in GA than con- tinuous variables. This is due to the resulting restricted search

Start

Generation of initial population space. Further, variable bound values can be applied to achieve similar results. GAs can be used for problem-solving and for

modeling when the search space is large, complex, or poorly understood, domain knowledge is scarce or expert knowledge is difficult to encode to narrow the search space, no mathemat-

ical analysis is available, and traditional search methods fail.

Mutation