Thực hiện Một số phương pháp Sử dụng các vấn đề không bị giới hạn Là một nghiên cứu thực hiện số đầu tiên, bốn phương pháp sau đây đã được thực hiện (Elwakeil và Aroraphương pháp xác định; S: phương pháp ngẫu nhiên; G: toàn cầu giai đoạn, L: địa phương giai đoạn. 1 Phụ thuộc vào các thủ tục giảm thiểu địa phương được sử dụng. | TABLE 18-1 Characteristics of Global Optimization Methods Method Can solve discrete problems General constraints Tries to find all x Phases Needs gradients Covering D No No Yes G 1 Zooming D Yes1 Yes No L 1 Generalized No No No G Yes descent D Tunneling D No Yes No L G 1 Multistart S Yes1 Yes Yes L G 1 Clustering S Yes1 Yes Yes L G 1 Controlled Yes No No L G No random S Simulated Yes No No G No annealing S Acceptance- Yes1 Yes No G No rejection S Stochastic No No No G No integration S Genetic S Yes No No G No Stochastic Yes1 Yes No L G 1 zooming S Domain Yes1 Yes Yes L G 1 elimination S D deterministic methods S stochastic methods G global phase L local phase. 1 Depends on the local minimization procedure used. Performance of Some Methods Using Unconstrained Problems As a first numerical performance study the following four methods were implemented Elwakeil and Arora 1996a covering method acceptance-rejection method A-R controlled random search CRS and simulated annealing SA . The numerical tests were performed on 29 unconstrained problems available in the literature. The problems had one to six design variables and only explicit bounds on them. Global solutions for the problems were known. Based on the results it was concluded that the covering methods were not practical because of their inefficiency for problems with n 2. The methods required very large computational effort. Also it was difficult to generate a good estimate for the Lipschitz constant that is needed in the algorithm. Both A-R and CRS methods performed better than simulated annealing and the covering method. The fact that the A-R method does not include any stopping criterion makes it undesirable for practical applications. The method worked efficiently on test problems because it was stopped upon finding the known global optimum point. The CRS method contains a stopping criterion and is more efficient compared with other methods. An attempt to treat general constraints explicitly in the CRS
