Abstract
The knapsack problem is one of the most widely researched NP-complete combinatorial optimization problems and has numerous practical applications. This paper proposes a quantum-inspired differential evolution algorithm with grey wolf optimizer (QDGWO) to enhance the diversity and convergence performance and improve the performance in high-dimensional cases for 0-1 knapsack problems. The proposed algorithm adopts quantum computing principles such as quantum superposition states and quantum gates. It also uses adaptive mutation operations of differential evolution, crossover operations of differential evolution, and quantum observation to generate new solutions as trial individuals. Selection operations are used to determine the better solutions between the stored individuals and the trial individuals created by mutation and crossover operations. In the event that the trial individuals are worse than the current individuals, the adaptive grey wolf optimizer and quantum rotation gate are used to preserve the diversity of the population as well as speed up the search for the global optimal solution. The experimental results for 0-1 knapsack problems confirm the advantages of QDGWO with the effectiveness and global search capability for knapsack problems, especially for high-dimensional situations.
Highlights
The 0-1 knapsack problem (KP01) is a classical combinatorial optimization problem.It has many practical applications, such as project selection, investment decisions, and complexity theory [1,2]
To assess the performance of the proposed QDGWO algorithm, two groups of datasets are used for solving the KP01
Where wi is the weight of the ith item xi ; pi is the value of xi ; C is the weight capacity of the knapsack; and m is the number of items
Summary
The 0-1 knapsack problem (KP01) is a classical combinatorial optimization problem. It has many practical applications, such as project selection, investment decisions, and complexity theory [1,2]. The first class of approaches includes exact methods based on mathematical programming and operational research. It is possible to obtain the exact solutions of smallscale KP01 problems by exact methods such as branching and bound algorithm [4] and dynamic programming [5]. The second class contains approximate methods based on metaheuristic algorithms [6]. Metaheuristic algorithms are shown to be effective approaches to solving complex engineering problems in a reasonable time when compared with exact methods [7]. The application of metaheuristic algorithms has drawn a great deal of attention in the field of optimization
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