Chi-Square Matrix: An Approach for Building-Block Identification

This paper presents a line of research in genetic algorithms (GAs), called building-block identification. The building blocks (BBs) are common structures inferred from a set of solutions. In simple GA, crossover operator plays an important role in mixing BBs. However, the crossover probably disrupts the BBs because the cut point is chosen at random. Therefore the BBs need to be identified explicitly so that the solutions are efficiently mixed. Let S be a set of binary solutions and the solution s = b1 . . . b , bi {0, 1}. We construct a symmetric matrix of which the element in row i and column j, denoted by mij, is the chi-square of variables bi and bj . The larger the mij is, the higher the dependency is between bit i and bit j. If mij is high, bit i and bit j should be passed together to prevent BB disruption. Our approach is validated for additively decomposable functions (ADFs) and hierarchically decomposable functions (HDFs). In terms of scalability, our approach shows a polynomi...

• Type: Conference
• Year: 2004
• Where: ASIAN
• Authors: Chatchawit Aporntewan, Prabhas Chongstitvatana
• Keywords: Algorithms, ASIAN 2004, Building-block Identification, Crossover Operator, Decomposable Functions