A fuzzy programming approach to multi-objective optimization for geopolymer product design

Geopolymer is an inorganic polymer binder formed from the alkaline activation of reactive alumino-silicate materials resulting in two- or three-dimensional polymeric network. It is a promising alternative to Portland cement-based materials because of its lower embodied energy and carbon footprint with potential for waste valorization. Studies have been done to develop such material with desired engineering specification by using statistical design of experiment and optimizing the process conditions or mix formulation of waste materials. However, it is not only the engineering properties such as its mechanical and thermal properties, but also other properties pertaining to green materials (e.g., embodied energy and carbon footprint) have to be considered. Conflicting objectives may also have to be satisfied simultaneously to find a compromised solution in the product design such as that of maximizing the strength and minimizing the volumetric weight. This work thus proposes a weighted max-min aggregation approach to multi-objective optimization of the geopolymer product using fuzzy programming approach. The optimization formulation was introduced such that fuzzy sets represent both the aspired product desirability and soft constraints; the optimal mix is then found by maximizing the simultaneous satisfaction of target properties of the desired product. This work also proposes an extension of such fuzzy optimization formulation wherein the nature of trade-off between improving the product desirability and satisfying the fuzzy constraints are made explicit. The relative importance of the properties as represented by priority weights were derived systematically using Analytic Hierarchy Process (AHP). A case study on a ternary blended geopolymer from coal fly ash, coal bottom ash, and rice hull ash is presented to illustrate the proposed method.© 2017 Elsevier B.V