Efficiency coefficient method to solve interval multi-objective linear optimization problems

Based on the efficiency coefficients, a new interval model and its correlative method for solving multi-objective optimization problems with uncertain parameters in the engineering field were proposed. A group of supplementary variables were introduced to transform the interval objective functions into the forms with deterministic parameters. In terms of the evaluation function deduced from efficiency coefficients, the original multi-objective optimization problem was converted into one with a single objective function. The simplified model was solved respectively under the best case and worst case of the interval constraints, and then the ranges of optimal solution and optimal values were easily obtained. Two numerical examples were given to demonstrate the effectiveness of proposed model and algorithm by comparing their results with probabilistic method.