A computational study of a genetic algorithm to solve the set covering problem
Abstract A Genetic Algorithm to solve the Set Covering Problem has been proposed by K. Iwamura, T. Sibahara, M. Fushimi and H. Morohoshi [14, 15]. In their algorithm, they have made some improvements in getting some better feasible solutions, i.e. better chromosomes at the first starting population, taking full account of Domain Specific Knowledge with sound programming skill. Here, we have carried out a systematic computational study of the algorithm to show its efficiency. We show computing time dependency on problem size, parameters of the Genetic Algorithm. And finally we make a computational comparison between the Genetic Algorithm and the commercial software code LINGO4 concerning approximation ratio and computing time.
Abstract The case of exact first-order saturated designs with N ≡ 1 mod 4 observations [ N ≠ 2 s ( s + 1) + 1, s = 1,2,…] is considered. Conditions are found for the A- optimality of such designs, when the first r rows of the corresponding design matrix have a known structure. By modifying the method of Sathe and Shenoy (1989) for the case N ≡ 1 mod 4, the structure of the information matrix of the A- optimal design is found. Then, by exhaustive search, it is proved that the known D- optimal saturated design for N = 9 (Ehlich, 1964) is also A- optimal.