Designing a Unique Single Point Cross Over Method

The idea behind genetic algorithms is to extract optimization strategies nature uses successfully - known as Darwinian Evolution - and transform them for application in mathematical optimization theory to find the global optimum in a defined phase space. One could imagine a population of individual 'explorers' sent into the optimization phase-space. Each explorer is defined by its genes, what means, its position inside the phase-space is coded in his genes. Every explorer has the duty to find a value of the quality of his position in the phase space. (Consider the phase-space being a number of variables in some technological process, the value of quality of any position in the phase space - in other words: any set of the variables - can be expressed by the yield of the desired chemical product.) Then the struggle of 'life' begins. The three fundamental principles are selection, mating/crossover, and mutation. Only explorers (= genes) sitting on the best places will reproduce and create a new population. This is performed in the second step (mating/crossover). The 'hope' behind this part of the algorithm is, that 'good' sections of two parents will be recombined to yet better fitting children. In fact, many of the created children will not be successful (as in biological evolution), but a few children will indeed fulfill this hope. These good sections are named in some publications as building blocks. Now there appears a problem. Repeating these steps, no new area would be explored. The two former steps would only exploit the already known regions in the phase space, which could lead to premature convergence of the algorithm with the consequence of missing the global optimum by exploiting some local optimum. The third step, mutation, ensures the necessary accidental effects. One can imagine the new population being mixed up a little bit to bring some new information into this set of genes. Whereas in biology a gene is described as a macro-molecule with four different bases to code the genetic information, a gene in genetic algorithms is usually defined as a bitstring (a sequence of b 1's and 0's).