A contribution-guided discrete differential evolution algorithm for the quadratic multiple knapsack problem

In order to explore and extend the ability and application of Differential Evolution (DE), a Contribution-guided Discrete Differential Evolution (C-DDE) is proposed in this paper for the Quadratic Multiple Knapsack Problem (QMKP), which is a challenging combinatorial optimization problem with NP-Hard and a number of applications. C-DDE extends the traditional standard DE by adopting a novel hybrid mutation operation strategy, which includes “DE/rand/1” mutation and a new contribution-guided mutation operator. They are adopted interchangeably based on a uniform distribution. The definition of contribution for an object to a knapsack is presented, which is applied to guide an individual to evolve into an improved mutant individual and to accelerate the calculation of fitness value for mutant individuals. Traditional “DE/rand/1” is utilized as a dedicated perturbation strategy to ensure a global diversification of the search procedure. The contribution-guided mutation is utilized as self-evolution strategy for intensification of ability in searching for better solutions. The proposed algorithm has been tested on the set of 27 well-known benchmarks. The experimental results demonstrate the efficiency and robustness of our proposed algorithm to reach good results.