0-1 Piecewise linearization approach for interval-parameter nonlinear programming: application to environmental management under uncertainty

Abstract

Interval-parameter nonlinear programming (INP) is an extension of conventional nonlinear optimization methods for handling both nonlinearities and uncertainties. However, challenges exist in its solution method, leading to difficulties in obtaining a global optimum. In this study, a 0-1 piecewise approximation approach is provided for solving the INP, through integration with an interactive algorithm for interval-parameter optimization problems. Thus, the INP model can be transformed into two deterministic submodels that correspond to the lower and upper bounds of the objective-function value. By solving the two submodels, interval solutions can be obtained, which are used for generating a range of decision options. The developed method is applied to a case of long-term municipal solid waste (MSW) management planning. Not only uncertainties expressed as interval values but also nonlinearities in the objective function can be tackled. Moreover, economies of scale (EOS) effects on waste-management cost can also be reflected. The results obtained can be used for generating decision alternatives and thus help waste managers to identify desired policies for MSW management and planning. Compared with the conventional interval-parameter linear and quadratic programs, the developed INP can better reflect system-cost variations and generate more robust solutions.