多限制式背包問題(Multidimensional Knapsack problem, MKP)，是從一組已知有各自重量及價值的物品中，挑選一組滿足多限制式條件的物品並置於背包中，同時使得背包中物品的總價值最高之模型。0-1多限制式背包問題屬於NP-hard下之組合優化問題，到目前為止尚未能找到一個能在多項式時間內求得最佳解之演算法。因此，各種群體搜尋演算法被用來求解這些問題。
粒子群尋優法(Particle Swarm Optimization, PSO)是根據群居生物之間互動及通訊的特徵所發展出來的一種有效率群體優化演算法(例如，魚群及鳥群)。在古典的PSO演算法中，由於各別粒子的認知學習因子及粒群體的經驗學習因子為固定常數，使得粒子移動過程中容易陷入區域最佳解。因此，在本研究中我們提出三種新穎的二元粒子群演算法(Binary Particle Swarm Optimization, BPSO)，來改善了0-1多限制式背包問題(0-1 Multidimensional Knapsack Problem, 0-1 MKP)的品質。第一種是引入時變加速係數(time-varying acceleration coefficients，TVAC)概念的BPSOTVAC演算法。第二種是引入時變加速係數及混沌(Chaos)概念的CBPSOTVAC演算法。第三種是引入比例加速係數(proportional acceleration coefficient)及代理人資訊(Surrogate information)概念的BPSOSIPAC演算法。從OR-Library之低維度及高維度背包問題的計算結果，證明我們所提出的演算法在合理的時間內能夠找到最佳解或接近最佳解且優於其它已存在的PSO演算法。

A 0-1 multidimensional knapsack problem (MKP) aims to choose a set of items satisfied the m knapsack capacity conditions into the bag from a given group of n items with weights and prices such that the total prices in the bag is maximal simultaneously. The 0-1 MKP is a NP-hard problem; that is, no polynomial algorithm for any NP-hard problem has yet been found. Hence, various population-based search algorithms are applied to solve these problems.
Particle swarm optimization (PSO), which is an efficient population-based optimization algorithm, is based on the metaphors of social interaction and communication (e.g., fish schooling and bird flocking). In the classic PSO model, the cognition learning factor and social learning factor are constant. Thus, it is easy for particles to get trapped in the local optimum. Therefore, this dissertation proposes three novel binary PSO algorithms with dynamic learning factors to prevent particles from being trapped in the local optimum and improves the quality of the solutions of the 0-1 MKPs. The computational results have shown that the proposed algorithms are capable of finding the optimal or near optimal solutions and can outperform the other existing BPSO algorithms in a reasonable time for solving low- and high-dimensional 0-1 MKPs from OR-Library.

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