Genetic Algorithm Basic Concepts

A genetic algorithm (GA) is a search technique used in computing to find exact or approximate solutions to optimisation and search problems. Originated by John H. Holland in the 1960s, is based on the principles of

natural selection, this stochastic search algorithm is able to explore good solutions quickly on large and complicated search spaces. The power of the algorithms comes from the mechanism of evolution, which allows searching through a huge number of possibilities for solutions, and its representations and operations simplicity in the GAs is another feature that makes this methodology so popular.

Firstly, a set of individuals are chosen, corresponding to a set of possible solutions. In each generation (iteration), the best members of the population generate new members (sons) from a set of operators. At the end of each iteration the worst sons are removed, forming the population for the next generation with the remaining ones. The aim is to find the values of the parameters so that the overall output of the system is optimum. The decision variables are discrete in nature and the problem at hand is a typical combinatorial optimisation problem. The strength of GA lies in its ability to manipulate many parameters simultaneously, thus making it attractive and suitable for applications as an optimisation meta-heuristic in a wide variety of disciplines (Gonsalves et al., 2007). For many realistic problems, such as manufacturing, communication and network design, GA can often find good solutions (near-optimal) in relatively short search period (Ding et al., 2005).

The basic form of an optimising meta-heuristic can be framed as follows (Reeves, 2003):

As sum a discrete search space χ. Further, assuming that the optimisation problem is one of maximisation, the general problem is to find:

x, x ∈ χ . . . (1) So as to maximise:

f(x) . . . (2) Subject to:

g(x) ≤0 . . . (3) h(x) =0 . . . (4)

where x is a vector of decision variables, f is the objective function, and, g and h represent the inequality and equality constraints, respectively.

Figure 12 Outline of the Genetic Algorithm (Source: Gonsalves et al., 2007).

In the following subsections, the bounds on the decision variables are described, then the objective function and finally the constraints under which the objective function is to be minimised.

A typical genetic algorithm requires two conditions to be defined: a genetic representation of the solution domain and a fitness function to evaluate the solution domain. The procedure of a genetic algorithm is as follows:

1. Generate random populations of feasible solutions for the problem.

2. Evaluate the fitness function of each solution (which, depending on the type of fitness, a function to maximise or minimise).

3. Create a new population by repeating the following step until the population is complete:

- select two parent solutions from a population based on their fitness value (the highest is the fitness the most likely is to be selected);

- crossover the parents to form new spring solutions;

- place new offspring in the new population;

4. Use new generated population for a further run of the algorithm.

5. Evaluate the new chromosomes.

6. If the terminate condition is satisfied, return the best solution; else go to condition 2.

The following parameters can be manipulated to get the desired results in GA:

 Crossover probability (Cp) —indicates how often the crossover will be performed. If this value is zero

then the new generation is made from exact copies of chromosomes from old population, the higher the value of this parameter more offspring are made by the crossover and vice versa.

 Mutation probability (Mp) – indicates how often parts of the chromosome will be mutated. If there is

no mutation the offspring generated just after the crossover or directly copied without any change. If the mutation is performed, than the parts of chromosome are changed. The higher this constant, the higher is the number of times the chromosomes are mutated and vice-versa.

 Population size (P) – indicates how many chromosomes are in the population. If there are too many

chromosomes, the algorithm may slow down.

 Generations (G) – indicates how many generations will be in the population.

The pseudo code of a basic genetic algorithm is shown on Figure 13.

t – actual generation; d – criterion to finish the algorithm; P – population { t := 0; //counter

Starts_population(P,t); //starts a population on n individuals Evaluation (P,t); //evaluates individuals fitness

Repeat until (t = d) //tests criteria (duration, fitness, and so on.) { t := t + 1; //increases the counter of generations Selection_of_parent s (P,t); //selects the couples for crossover Recombination (P, t); //accomplishes selected couples crossover Mutation (P, t); //disturbs the group generated by crossover Evaluation (P,t); //evaluates new fitness

Survive (P, t) //selects survivors }

}

Figure 13 Basic pseudo code of a Genetic Algorithm (Source: Ferrolho & Crisóstomo, 2005).

Genetic algorithms start with a population P of n individuals, where each individual codifies a solution to the problem. The evaluation of each individual’s performance is based on a function of fitness evaluation. The best ones will tend to be the progenitors of the following generation, therefore transmitting their features to the next generations.

There are advantages and disadvantages to the use of GA. The advantages relate to how bad generation proposals are discarded from consideration and hence not affecting negatively the end solution, it can quickly evaluate a large solution area and very complex and loosely defined problems.

Some of the disadvantages relate to the fact that GA does not evolve towards a good solution but evolves away from a bad one so, if not modelled correctly, can get caught in a local optimal solution; the number of iterations can be very high to arrive at near optimum solution, if the problem is not defined correctly; it is very difficult to achieve an optimal solution in very complex scenarios. Moreover, according to Ding et al.

(2005), the differences between GA and other traditional methods are mainly:

• GA uses an encoding of the control variables, rather than the variables themselves.

• GA searches from one population of solutions to another, rather than from individual to individual. It is a great advantage for searching noisy spaces littered with local optima (instead of relying on a single configuration to search through the space).

• GA uses only objective function information to guide itself through the solution space, not derivatives. Once GA knows the value of ‘goodness’ about a configuration, it can use this to continuing to approach the optimum.

• GA is probabilistic in nature, not deterministic. This is a direct result of the randomisation

techniques used by Gas, which is not the case for most existing methods.

• One of the most attractive advantages of using GA as a design tool is its ability to find solutions to problems in a way completely free of preconceptions about what is possible and what is not.