The Influence of Uncertainty of Parameters on the Solutions of Engineering Optimization Models(1/3)

Engineering optimization models have been widely applied to the field of engineering in order toeffectively help the decision maker solve various engineering optimization problems and obtain the optimaldecisions. However, when facing with practical problems in engineering, there may be some uncertainparameters involved in the optimization model. Since uncertain parameter values are difficult to accuratelyestimate, there are usually errors with these values. If an engineering optimization model is applied withuncertain parameters (i.e., the model input contains errors), then the model solution could have errors (i.e.,the model output has errors) accordingly. Therefore, when the decision maker makes the so-called “optimal”decision based on the model solution that contains errors inherently, he/she may not know that the decisionthat could be improper. Past related studies on evaluating uncertain parameter values mainly employ theestimation or prediction method to search for the most appropriate uncertain parameter values, and then usethem as input data to the model. However, even if some estimation or prediction methods are tried toaccurately evaluate the uncertain parameter values, the errors of the model solutions are still unknown.Because the real optimal solution of a model with uncertain parameters is very difficult to grasp when itcontains uncertain parameters, the evaluation of the model solution in those studies was performed mainly bycomparing with the best solution obtained previously. This means that the difference between the obtainedmodel solution and real optimal solution cannot be clearly understood, indicating that the performance of thesolutions obtained in those studies cannot be objectively validated. In addition, many studies have adoptedapproximation solution algorithms with a solution tolerance error to increase the solution efficiency, but nostudy further discusses the influence of different solution tolerance errors on the model solution with inputerrors. Therefore, in this study we will propose an experimental evaluation method to explore the outputerrors for an engineering optimization model which contains uncertain parameter values with differentcontrollable and random error scenarios, coupled with different solution tolerance errors. In general, theuncertain parameters for an optimal mathematical programming model can be divided into two types: thosefor the objective function and those for the constraint set. Because there may be differences in the erroranalysis results of the two types of parameters, the study will be divided into a three-year project.In the first year, we will propose an experimental evaluation method to explore the output error for theengineering optimization model in which the uncertain parameter values are involved with the objectivefunction, under different controllable and random error scenarios, coupled with different solution toleranceerrors. In the second year, we will also propose an experimental evaluation method to explore the output errorfor the engineering optimization model in which the uncertain parameter values are involved with theconstraint set, under different controllable and random error scenarios, coupled with different solutiontolerance errors. In the third year, we will integrate the approaches of the first two years to propose anexperimental evaluation method to explore the output error for the engineering optimization model in whichthe uncertain parameter values are involved with the objective function and the constraint set, under differentcontrollable and random error scenarios, coupled with different solution tolerance errors. To be able tomutually compare the test results of the three-year project, we will use the same engineering projectoptimization scheduling model in the tests. In addition, we will also perform regression analysis of testresults for each error scenario associated with the three-year project to furt