Automatic design of algorithms for optimization problems

The design of efficient algorithms for difficult combinatorial optimization problems remains a challenging field. Many heuristic, meta-heuristic and hyper-heuristic methods exist. In the specialized literature, it is observed that for some problems, the combined algorithms have better computational performance than individual performance. However, the automatic combination of the existing methods or the automatic design of new algorithms has received less attention in the literature. In this study, a method to automatically design algorithms is put into practice for two optimization problems of recognized computational difficulty: the traveling salesman problem and the automatic clustering problem. The new algorithms are generated by means of genetic programming and are numerically evaluated with sets of typical instances for each problem. From an initial population of randomly generated algorithms, a systematic convergence towards the better algorithms is observed after a few hundred generations. Numerical results obtained from the evaluation of each of the designed algorithms suggest that for each set of instances with similar characteristics, specialized algorithms are required.