Reducing the Dimensionality of Criteria in Multi-Objective Optimisation of Biomass Energy Supply Chains
Lidija Čuček, Jiří J. Klemeš, Petar S. Varbanov, Zdravko Kravanja
2012 Abstract
In order to obtain economically viable, environmentally benign, and socially just system solutions, different criteria have to be simultaneously considered within a multi-objective optimisation approach, usually by applying either weighted objective or ɛ-constraint methods.
In the former method all different kinds of criteria are composed within a single objective function by some weights, and within the latter an economic criterion, e.g. annual profit, is maximised against a sustainability index in which different environmental and social indicators or footprints are composed by some weights. A set of Pareto optimal solutions can thus be obtained. However, by doing so, subjective weighting between different environmental and/or social indicators (footprints etc.) cannot be avoided.
This contribution presents a novel approach, by which the number of environmental footprints is reduced to a minimum of “independent” footprints through correlations among footprints that show similar behaviour. The correlations are investigated from among carbon footprint (CF), energy footprint (EF), water footprint (WF), water pollution footprint (WPF), land footprint (LF), nitrogen footprint (NF), and phosphorus footprint (PF). Those footprints that show similar behaviour can be grouped in subsets of correlated footprints. In each subset only one footprint, an “independent” one, can be taken into the multi-objective optimisation, whilst the rest of the “dependent” footprints are evaluated after the optimisation from the
“independent” ones. In this way, the dimensionality of the criteria within the multi-objective optimisation can be significantly reduced, so that a multi-parametric optimisation can be performed with independent footprints as parameters, thus avoiding the subjective weighting of environmental and social indicators or footprints.
This approach is applied to different biomass energy supply chains in order to illustrate the novel approach and correlations.
