未來發展

未來的研究方向包括：套用不同的方案評價方法，探討與歸納其如何影響機 制的決策結果，然後整合不同方案評價方法，使機制可以因應不同的決策需求，

啟用適當的評價方法，更具彈性，應用範圍更寬廣；在資源分配機制方面，可以 嘗詴以本論文提出的遞增邊界改善法作為其他啟發式演算法之後段修正的方式，

可以有效避免單純使用遞增邊界搜尋的問題且提升最佳化率；情境資訊的運用能 力可以進一步擴充，納入更多情境因素並實作相對應的運算以考量更多現實層面 的影響因素，使得決策依憑的資訊更貼近真實情況；最後可以將機制導入真實的

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應用系統中，如實際運作於智慧家庭中，調控智慧家庭的家電設備，滿足使用者 的家居生活需求。

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附錄一 C_HEU部分演算法虛擬碼

snf: 指出current_sol是否為可行解

penalty: penalty 向量，多維度資源耗用轉換之用

Feasible( ): 檢查解之資源耗用是否在資源限制內，是為可行解，否則反之 Utility( ): 計算解之總價值

initial_penalty( ): penalty向量初始化函數，如第二章介紹 adjust_penalty( ): penalty向量調整函數，如第二章介紹 inc_frontier: 該群體二維空間中位於遞增邊界之所有線段 p1,p2: 二維空間中某線段的兩端點，各自對應著一個物件

Begin Procedure C_HEU ()

1. current_sol ← The item with lowest value from each group;

2. if feasible(current_sol)=false then 3. snf←true //Solution not yet found 4. endif

5. penalty = initial_penalty()//initialize penalty

6. for repeat ← 1 to 3 do //only three iterations for finding solution 7. saved_sol ← current_sol //saving the current solution

8. u ←Utility(current_sol) //saving utility 9. for each group in the MMKP do

10. Transform each resource consumption vector of each item to single dimension using vector penalty

11. ch_frontier ← efficient convex hull frontier of the items of the group 12. list_of_frontier_segments ← list_of_frontier_segments + ch_frontier 13. endfor

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14. Sort the segments of list_of_frontier_segments in descending order according to the angle of each segment

15. for each segment in the list_of_frontier_segments do 16. p1, p2 ← The items associated with the segment.

17. adjust_selected_item(p1)//hope to find a feasible solution including p1 18. adjust_selected_item(p2)//hope to find a feasible solution including p2 19. end for.

20. if Utility(current_sol)< u then // New solution is inferior than the saved one 21. current_sol ← saved_sol

22. endif

23. penalty ← adjust_penalty(penalty) //adjust penalty for the next iteration 24. end for

25. if snf = true then 26. Solution Not found 27. else

28. current_sol is the final solution.

29. endif end Procedure.

Algorithm 1 C_HEU procedure

資料來源：”Solving the Multidimensional Multiple-choice Knapsack Problem by Constructing Convex Hulls” [2]

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附錄二 IF_HEU部分演算法虛擬碼

snf: 指出current_sol是否為可行解

penalty: penalty 向量，多維度資源耗用轉換之用

Feasible( ): 檢查解之資源耗用是否在資源限制內，是為可行解，否則反之 Utility( ): 計算解之總價值

initial_penalty( ): penalty向量初始化函數，如第二章介紹 adjust_penalty( ): penalty向量調整函數，如第二章介紹 inc_frontier: 該群體二維空間中位於遞增邊界之所有線段 p1,p2: 二維空間中某線段的兩端點，各自對應著一個物件

Begin Procedure IF_HEU ( )

1. current_sol ← The item with lowest value from each group;

2. if feasible(current_sol) =false then 3. snf←true //Solution not yet found 4. endif

5. penalty = initial_penalty( )

6. for round ← 1 to 3 do //only three iterations for finding solution 7. saved_sol ← current_sol //saving the current solution

8. u ←Utility(current_sol) //saving utility 9. for each group in the MMKP do

10. Transform each resource consumption vector of each item to single dimension using vector penalty.

11. if round =1 do

12. frontier ←efficient convex hull frontier of the items of the group 13. else do

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14. frontier ←increasing frontier of the items of the group 15. list_of_frontier_segments ← list_of_frontier_segments + frontier 16. endfor

17. Sort the segments of list_of_frontier_segments in descending order according to the angle of each segment

18. for each segment in the list_of_frontier_segments do 19. p1, p2 ← The items associated with the segment.

20. adjust_selected_item (p1) 21. adjust_selected_item (p2) 22. end for.

23. penalty ← adjust_penalty(penalty) //adjust penalty for the next iteration 24. end for

25. if snf = true then 26. Solution Not found

27. current_sol ← The item with lowest value from each group;

28. else

29. current_sol is the final solution.

30. endif end Procedure.

Algorithm 1 IF_HEU procedure

Begin Procedure adjust_selected_item (p)

1. current_group ← the group that contains the item corresponding to p.

2. current_item ← the currently selected item of group current_group.

3. p_item ← item of group current_group denoted by point p.

4.change the selection of group current_group from current_item to p_item

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5. feassibility ← feasibility of the resource consumption of current_sol 6. if (feassibility = false and snf = true) then

7. change the selection of group current_group from current _item to p_item 8. update saved_sol

9..else if(feasibility = false and snf = false or Utility(current_sol)<u ) then 10. current_sol ← saved_sol

11.else

12. snf ← false //solution found

13. change the selection of group current_group from current_item to p_item 14. update saved_sol

15. u=Utility(current_sol) 16.endif

Algorithm 2 adjust_selected_item procedure