1. Method description

This software is used to solve constrained optimization problems using a novel genetic algorithm. The main steps of the algorithm are: The algorithm uses a population of chromosomes to solve the constraint optimization problem. Every member of the population is a trial solution expressed as a vector of n double numbers. The proposed algorithm has the following steps:

1. Initialization step.

(a) Set the maximum number of generations ITERMAX.

(b) Set the number of chromosomes K.

(c) Set the selection rate pc

(d) Set the mutation rate pm

(e) Set the number of chromosomes for the global search procedure gc

(f) Set the number of iterations for the global search procedure gI

(g) Initialize the chromosomes as random vectors in the range [a,b]

(h) Set iter=0

2. Evaluation step.

(a) For every chromosome C calculate the fitness of C using penalties to enforce the constraints

3. Application of genetic operators.

(a) Selection procedure: The chromosomes are sorted in descending order according to their fitness value. The first (1-ps)*K chromosomes are transferred to the next generation. The rest of the chromosomes are substituted by offsprings created through crossover.

(b) Mutation procedure: perform mutation to the population with mutation probability pm

(c) Replace the ps * K worst chromosomes in the population with the offsprings created by the genetic operators.

4. Set iter=iter+1

5. If iter MOD gI=0, then

(a) Apply the global search procedure, that will described below

(b) Apply the local search procedure Cobyla to the best chromosome of the population.

6. Check for termination. If the termination criteria met then goto Local search step, else goto Evaluation step.

7. Local search step. Apply the local search procedure Cobyla to the best chromosome of the population.