Building Pareto Frontiers for Ecosystem Services Tradeoff Analysis in Forest Management Planning Integer Programs

Decision making in modern forest management planning is challenged by the need to recognize multiple ecosystem services and to address the preferences and goals of stakeholders. This research presents an innovative a posteriori preference modeling and multi-objective integer optimization (MOIP) approach encompassing integer programming models and a new technique for generation and interactive visualization of the Pareto frontier. Due to the complexity and size of our management problems, a decomposition approach was used to build the Pareto frontier of the general problem using the Pareto frontiers of its sub-problems. The emphasis was on the approximation of convex Edgeworth–Pareto hulls (EPHs) for the sub-problems by systems of linear inequalities; the generation of Edgeworth–Pareto hulls by the convex approximation of the Pareto frontier evinced a very small discrepancy from the real integer programming solutions. The results thus highlight the possibility of generating the Pareto frontiers of large multi-objective integer problems using our approach. This research innovated the generation of Pareto frontier methods using integer programming in order to address multiple objectives, locational specificity requirements and product even-flow constraints in landscape-level management planning problems. This may contribute to enhancing the analysis of tradeoffs between ecosystem services in large-scale problems and help forest managers address effectively the demand for forest products while sustaining the provision of services in participatory management planning processes.

MODELLING DESIGN TRADE-OFFS USING A SET THEORY APPROACH: ALTERNATIVE PATHS FOR NAVIGATING TRADE-OFF SITUATIONS

This paper synthesizes concepts from the design creativity and design optimization literatures to develop a conceptual descriptive model of trade-off situations in design. Using a set theory approach, a model of the design space is expanded to formalize the description of trade-offs as Pareto frontiers on this space. The modelling of design process and human biases and limitations on the structure of these design spaces explores the perceptions designers form of these design spaces. The model presented describes how altering the framing and formulation of the design space can be used to alter or bypass the original Pareto frontiers of that space, allowing trade-offs to be navigated outside of the original limitations.