| Summary: | 碩士 === 國立交通大學 === 資訊管理研究所 === 85 === Knapsack Problem is a well-known problem in Operation
Research. However, Knapsack Problem is a NP-hard problem . If we
solve Knapsack Problem by Exhaustive Enumeration , a problem
with 60 items will need O(2^n) computation time. It is time-
consuming to solve a Knapsack Problem,especially when n is large
. Yang proposed Linear Search Algorithm to solve One-
dimensional Knapsack Problem in 1992. The philosophy behind
Linear Search Algorithm is that if an item with lower cost ( Cj
) or with higher profit ( Pj ) or with higher profit per cost (
Pj / Cj ), it will have a higher probability to get into the
optimal solution set.This thesis adds a new criteria Pj-Cj into
Yang's Linear Search Algorithm in order to improve the
performance of Linear Search Algorithm . Furthermore, this
thesis try to solve Multi-dimensional Knapsack Problem by Linear
Search Algorithm. By verifying a large amount of cases , this
research gets some conclusions listed below:1. It is no obvious
improvement for the performance of Linear Search Algorithm by
adding the criteria Pj-Cj.2. The results of computer simulation
in this research show that the probability to find the optimal
solution of One-dimensional Knapsack Problem is more than 93% by
Linear Search Algorithm.3. For Multi-dimensional Knapsack
Problem , the performance of Linear Search Algorithm is not as
goos as that of One-dimensional Knapsack Problem; however, by
using Linear Search Algorithm , the probability to find the
optimal solution is still more than 82%.4. For either One-
dimensional or Multi-dimensional Knapsack Problem , even if
Linear Search Algorithm can't find the optimal solution , it
won't loss more than two optimal solution items in average.
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