Risk/dispersion index method

A new sensitivity measure is developed whereby the effects of variations in the nominal conditions describing a given multiobjective problem can be measured and incorporated as a performance index to be minimised. The general nonlinear programming problem provides a framework for examining objective constraint level sensitivities in the ϵ-constraint form of the multiobjective optimisation problem. Investigation of the effects of random variations in the model parameters of the optimal solution to a nonlinear program leads to a new sensitivity measure called the dispersion index Ω. The index is interpreted as a first-order approximation to the standard deviation in the optimal solution of the nonlinear program. A sensitivity trade-off Δ_dΩ is derived for the multiobjective problem yielding an explicit representation of the trade-offs between sensitivity and objective levels. Using the information provided by Ω, the risk/dispersion index method (RDIM) is developed to find solutions to the multiobjective problem that minimise sensitivity and maximise overall utility. The last phase of the study is an application of the RDIM to a simple nonlinear multiobjective optimisation problem.