在專案中風險的發生，對經理人員而言，降低其風險程度和相關的偶發成本是一個具挑戰性的工作，尤其是具負面後果的風險，因為過度的意外會導致工程的獲勝策略產生損失。然而，降低偶發也需要風險處理成本，此會造成預算將增加一些額外的費用。受到預算限制的影響，管理人員應在緊縮預算限制下，盡量減少偶發費用和風險處理成本的增加。因具有不同等級的多個風險專案，也使調整更加複雜。為了能表現其複雜性並尋求最佳解決方案，本研究提出了一種與風險矩陣函數相結合的數學模型，並使用粒子群最佳化（PSO）演算法進行求解。
如一些文獻中提到的，PSO演算法已被應用於許多工程領域及專案管理，特別是風險偶發。然而，後者是相對較新的，仍然有待進一步的研究。本研究已顯示PSO演算法可以在不會違反限制下解決調整的問題。所提出的模型可以同時最小化總預算及風險偶發，並提供適當的風險應對策略（接受、緩解、轉移或迴避）的建議。
此外，本研究還觀察到PSO參數的影響，並獲得最佳參數組合。另一方面，還對模型中限制式的影響進行觀察，其可提供真實管理決策的洞察力。

The presence of risks, especially that come with negative consequence, in a project becomes a challenging task for managers to reduce the risks level and the associated contingency cost, since excessive contingency can lead to bidding loss in new project winning strategy. However, lowering the contingency also needs risk-handling cost, from which some additional amount will be borne to project’s budget. Being exposed to limited budget, managers should make an optimum adjustment between reduction of contingency and increment of risk-handling cost within tight budget limitation. Multiple risk items with different levels also make the adjustment more complex. To represent that complexity and search for best solutions, this study has proposed a mathematical model in combination with risk matrix function and performed the computation using Particle Swarm Optimization (PSO) algorithm.
As mentioned in some literatures, PSO algorithm has been applied in many engineering fields as well as in project management, especially risk contingency. The latter, nonetheless, is relatively new and still promising for further researches. This study has demonstrated that PSO can solve the adjustment problem without any violation to given constraints. The proposed model can minimize both total budget and risk contingency and provide recommendations for appropriate risk response strategy (either acceptance, mitigation, transference or avoidance).
In addition, this study has also observed PSO parameters and obtained best parameter combination. On the other hand, effect of constraint in the model has been also examined to give insight for real management decision making.

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