Multitask Knapsack Problems with Scalable Objective and Constraint Similarities: Behavioral Analysis of Evolutionary Multi-Factorial Algorithms

This paper proposes a multitask knapsack problem framework as a discrete test suite that allows for the independent adjustment of both objective and constraint similarities among tasks. The proposed multitask knapsack problem framework introduces objective and constraint covariance matrices for multiple tasks. These covariance matrices influence the setting of profit and weight values in each knapsack problem. By adjusting the elements of the covariance matrices, both objective and constraint similarities among tasks can be precisely controlled. Experiments were conducted to observe the perfromance of multi-factorial evolutionary algorithms, MFEA and MFEA/TS, as well as a single-task evolutionary algorithm, SOEA, on multitask knapsack problems. Results revealed that estimating task similarities based on the distribution of solution sets and integrating this information into parent selection led to improved objective values for feasible solutions, thereby enhancing overall multitask optimization performance.