New parallel randomized algorithms for the traveling salesman problem
Computers and Operations Research - Special issue on the traveling salesman problem
A new hybrid optimization algorithm
Computers and Industrial Engineering - Special issue on computational intelligence for industrial engineering
Future Generation Computer Systems
A Genetic Algorithm for the Multidimensional Knapsack Problem
Journal of Heuristics
Nested Partitions Method for Global Optimization
Operations Research
Ant Colony Optimization
A new ant colony optimization algorithm for the multidimensional Knapsack problem
Computers and Operations Research
Nested Partitions Method, Theory and Applications
Nested Partitions Method, Theory and Applications
A hybrid approach for the 0-1 multidimensional knapsack problem
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
The hyper-cube framework for ant colony optimization
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Hybrid metaheuristics in combinatorial optimization: A survey
Applied Soft Computing
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This work presents a hybrid algorithm of Nested Partition (NP), Binary Ant System (BAS), and Linear Programming (LP) to solve the multidimensional knapsack problem (MKP). The hybrid NP+BAS+LP algorithm takes advantage of the global search strategies of the NP algorithm; the ability of BAS to quickly generate good solutions and incorporates information obtained from solving a LP relaxation of the MKP to help guide the search. It thus incorporates both the lower bounds (LB), found by the BAS, and the upper bounds (UB), found by solving the relaxed LP, into the search by embedding both in the NP framework. An adjustable computation budget is implemented where the number of samples increases if the LB and the UB point to different promising subregions. The proposed hybrid is compared to state-of-the-art solution techniques and is found to be one of the best algorithms in terms of the quality of solutions obtained and CPU time requirements.