The Adaptive Memory Projection Method for Multidimensional Knapsack problems with generalized Upper Bound Constraints

• Main Authors: Huan-Fu Chang, 張桓輔
• Other Authors: Yun-Chia Liang
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/20673081374091951368

碩士 === 元智大學 === 工業工程與管理學系 === 97 === An adaptive memory projection (referred as AMP) method is developed for multidimensional knapsack problems with generalized upper bound constraints (referred as the GUBMKP). All the variables are divided into several generalized upper bound (referred as GUB) sets and at most one variable can be chosen from each GUB set. The GUBMKP can be applied to many real-world problems, such as capital budgeting, resource allocation, cargo loading, project selection, just to name a few. The GUBMKP is a special case of multidimensional knapsack problems (referred as MKP), a well-known NP-hard problem. Therefore, it is justified to use metaheuristics to approximate the optimal solution for large problem instances. The adaptive memory procedure keeps track of components of good solutions during the search and creates provisional solution by combining components of better solutions. The projection method, which fixes the selected variables while varying the others, is very useful for metaheuristics, especially in large scale optimization. In this study, the AMP method is implemented by incorporating critical event tabu search and the branch and bound method built in a commercial optimization solver. In addition to the diversification effect within critical event tabu search, the pseudo-cut inequalities and an adjusted frequency penalty scalar are also applied to increase opportunities of exploring new regions. This study conducts a comprehensive sensitivity analysis on the parameters and strategies used in the proposed AMP algorithm. The performance of the algorithm is verified using a set of nine instances that consists of small- to large-scale instances. Therefore, this study has provided a fundamental basis for applying the AMP method to solve the GUBMKP.