本文提出一以多目標粒子群聚最佳化法(MOPSO)為基礎之混合式演算法，藉由結合NM單體搜尋法(NM simplex search)與粒子群聚最佳化法，針對多目標最佳化問題求得可能的Pareto最佳解。作法上係將NM單體搜尋法嵌入粒子群聚最佳化演算法中，充分利用粒子群聚最佳化法在搜尋空間中做探索(exploration)搜尋，輔以改良式NM單體搜尋法在區域鑽探(exploitation)搜尋的能力，進一步提升多目標最佳化演算法之多樣性及精確性。在控制系統方面，我們以MOPSO應用在解決最佳PID控制器設計的問題。作法上係對PID控制器參數作實數編碼後，再與受控系統作結合，以閉迴路系統之性能做考慮，並以平方誤差與時間乘積之積分(ITSE)以及干擾拒絕(disturbance rejection)為適合度評定機制之指標，找出理想的PID控制器參數。 This paper proposes a hybrid multi-objective particle swarm optimizer incorporation (MOPSO) an enhanced Nelder-Mead simplex search scheme to solve multi-objective optimization problems. Because of the strength of PSO in explorative search and NM simplex search in exploitative search to locate promising particles closest to the optimum during the optimization process, both diversity and accuracy of the proposed optimization algorithm can be significantly improved. To demonstrate its application on solving control system problem, the proposed MOPSO is applied to design an optimal PID controller, optimizing the ITSE and disturbance objection specifications.
