An investigation of linear convolution of criteria in multicriteria discrete programming

The relation between the effective solutions ofmulticriteria discrete programming problems and the solutions of the single-criterion problem with linear convolution of the criteria is examined. A general formula for the effective solutions that can be found by linear convolution is obtained. The computational complexity of the problems is investigated. A computational experiment is performed for covering tree, 1-tree and assignment problems. On average, linear convolution finds 20% of the effective solutions for MINSUM-MINMAX problems and 60% for MINSUM-MINMAX problems.