Analytical Evaluation of Multi-Criteria Heuristics

This paper considers the problem of evaluating the solution quality of multi-criteria heuristics. By assuming an additive multi-attribute value structure, efficient and heuristic solutions can be translated into value measures that depend only on the relative importance assigned to the criteria of interest. Approximation errors are then defined as the value penalty incurred by approximating an efficient solution with its heuristic alternative. Results are derived which can be used to eliminate solutions that cannot represent the best available alternative among the set of efficient and heuristic solutions. For the bicriterion case, a polynomial algorithm for determining the mean and maximum relative heuristic error for a given problem instance is presented. For more general multi-criteria problems, the maximum relative approximation error can be determined by solving a series of linear programming problems.