Inexact Fractional Optimization for Multicriteria Resources and Environmental Management Under Uncertainty

Zhu, Hua
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Faculty of Graduate Studies and Research, University of Regina

A set of inexact-fuzzy nonlinear programming (IFNP) and inexact fractional mathematical programming (IFMP) methods have been developed for the first time for supporting multi-criteria resources and environmental management under various uncertainties. They include the following methods: (a) an interval-parameter fuzzy robust nonlinear programming (IFRNP) approach for water quality management, (b) a simulation-based interval-fuzzy nonlinear programming (SIFNP) approach for seasonal planning of water quality management, (c) a stochastic linear fractional programming (SLFP) method for waste management, (d) a dynamic stochastic fractional programming (DSFP) approach for capacity-expansion planning of an electric power system, (e) an inexact linear fractional programming (ILFP) method for municipal solid waste management, (f) an inexact mixed-integer fractional energy system planning (IMIF-EP) model for sustainable energy management, and (g) a robust inexact-stochastic fractional programming (RISFP) approach for agricultural water management in Jiangxi Province, China. The major contributions of this research are summarized as follows: (i) The proposed IFRNP and SIFNP methods have improved upon the interval nonlinear programming (INP) through introducing concepts of fuzzy boundary intervals and interval-fuzzy membership functions into the INP framework. They can tackle water quality management problems with nonlinear objectives and dual-uncertain information, and provide a linkage between the environmental policies and the associated economic implications. (ii) The proposed SLFP and DSFP methods have improved upon the linear fractional programming (LFP) through introducing chance-constrained programming (CCP) technique into the LFP framework. They can solve ratio-optimization problems associated with random information, and reflect tradeoffs among multiple system criteria under different system-reliability conditions. (iii) The proposed ILFP and IMIF-EP methods can optimize system efficiency under imprecise uncertainty and generate multiple management alternatives. (iv) The proposed RISFP approach can simultaneously handle parameters presented as intervals, fuzzy sets, and probability distribution functions within a fractional programming framework, and thus support quantitative management of multiple criteria under various complexities of system components. (v) Through converting a bi-objective problem into a single-objective one, the proposed inexact fractional optimization approaches can offer desired information regarding tradeoff between the two objectives without the requirement of directly or indirectly setting a weight for each objective.

A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Environmental Systems Engineering, University of Regina. xxi, 431 p.