22nd European Symposium on Computer Aided Process Engineering, Vol. 30, Suppl (C), July 2012

ISSN: 1570-7946

doi: 10.1016/B978-0-444-59519-5.50001-0

Objective reduction in multi-criteria optimization of integrated bioethanol-sugar supply chains

Andrei Kostina, Gonzalo Guillén-Gozálbeza, Fernando D. Meleb, Laureano Jiméneza

a Departament d'Enginyeria Química, Universitat Rovira i Virgili, Tarragona, Spain

b Ingeniería de Procesos y Gestión Industrial, Universidad Nacional de Tucumán, Tucumán, Argentina

E-mail address: gonzalo.guillen@urv.cat

Abstract

The design of more sustainable bioethanol supply chains (SCs) has recently emerged as an active area of research. Most of the approaches presented so far focus on minimizing the emitted greenhouse gases (GHG) as unique criterion, neglecting the damage caused in other impact categories. In this work, we address the multi-objective design of integrated sugar/bioethanol SCs considering several life cycle assessment (LCA) impacts. To overcome the numerical difficulties of dealing with several objective functions, we apply a rigorous MILP-based dimensionality reduction method that minimizes the error of omitting objectives.

Keywords

multi-objective optimization, dimension reduction, bioethanol supply chain, life cycle assesment

1 Introduction

Energy security and environmental concerns have boosted the large-scale substitution of fossil fuels with bio-based sources of energy. By now, bioethanol is the world's leading transportation biofuel, with a worldwide production in 2010 that reached 23 billion gallons. In this context, the economic and environmental concerns related to bioethanol supply chains (SCs) become more important than ever. By far, most studies have focused on economical enhancement of bioethanol SCs.

A limited number of mathematical models have been proposed to optimize the environmental performance of bioethanol SCs. These approaches have mainly focused on reducing the GHG emissions of the bioethanol infrastructure.Zamboni et al.(2009) formulated a bi-objective optimization model that minimizes the GHG emissions associated with the future corn-based Italian bioethanol network. Mele et al.(2011) developed a bi-criteria model that maximizes the profit and minimizes the life cycle environmental impact of combined sugar/bioethanol SCs. The latter criterion was measured using two environmental indicators: the global warming potential and the eco-indicator 99.

The eco-indicator 99 is an aggregated environmental metric constructed by attaching weights and normalization values to a set of single environmental indicators. The use of aggregated metrics is motivated by the fact that increasing the number of objectives leads to computationally expensive problems whose solutions are difficult to visualize and analyze. The weakness of this aggregation is that it uses fixed normalization and weighting parameters that may not represent the decision-makers' interests. Moreover, Brockhoff and Zitzler (2010) showed that aggregated metrics may change the dominance structure of the problem in a manner such that some solutions may be left out of the analysis.

An alternative approach to overcome the computational difficulties associated with optimizing a large number of objectives is to reduce the problem dimensionality, i.e., to remove the redundant objectives of the model and keep the conflicting ones.

In this work, we integrate multi-objective optimization (MOO) with an MILP-based dimensionality reduction technique previously presented by the authors to address the environmentally conscious design of bioethanol network. The capabilities of this method are tested through a real case study based on the Argentinean sugar cane industry. The existence of redundant and conflicting LCA metrics in the context of the SC design problem is discussed in detail, suggesting a procedure to omit non-essential objectives without changing the dominance structure of the problem. The proposed method makes it possible to reduce the number of environmental indicators, thereby facilitating the calculation and analysis of the Pareto solutions.

2 MILP-based dimension reduction method

We consider the following general multi-objective minimization problem MO(X):

where k objective functions are optimized. N is the number of inequality constraints, and N' is the number of equality constraints. X is the search space, x is a vector of decision variables, and F(x) denotes the vector of objective functions fk(x).

The aim of any objective reduction method is to identify a subset of objectives of a MOO problem such that the error of omitting them (known as d-error) is minimum. The concept of d-error was first proposed by Brockhoff and Zitzler (2006).

The d-error is defined as the difference between the value of objective fk in solutions si and si´. In the context of the MILP presented in REF, this value is determined as follows:

(1)

where the binary variable ZOk is equal to 1 if objective fk is fk removed from F, and 0 otherwise, while binary variable ZDi,i' takes the value of 1 if solution si´ dominates solution si in the reduced Pareto space and 0 otherwise.

The binary parameter YPi,i',k takes the value of 1 if solution si is better than solution si' in objective function fk (i.e., fk(si)= fk(si´)) and 0 otherwise. The definition of ZDi,i' is enforced via the following constraint:

(2)

(3)

Eq.(1) can be linearized as follows:

(4)

(5)

(6)

(7)

For minimizing the number of objectives OB for a given error, we impose an upper bound on variable di,i´,k:

(8)

The model for solving the k-MOSS problem (i.e., finding the maximum number of objectives that can be removed while still keeping the delta error below a given threshold) is then expressed as follows:

3 Case study

The optimal design and planning of integrated sugar/bioethanol SCs in Argentina is considered (Mele et al., 2011). We aim to determine the structure of a three-echelon SC (production-storage-market) that includes a set of plants and a set of storage facilities, where products are stored before being delivered to the final customers. The production and storage facilities can be installed in a set of subregions defined according to the administrative division of Argentina.

We consider all possible configurations of the ethanol-sugar SC as well as all technological aspects associated with its performance, such as production and storage technologies, waste disposal, and transportation alternatives for raw materials and products. Five different technologies, two for sugar production and three types of distilleries, are studied. Sugar mills use sugar cane juice to produce both white and raw sugar. One type of sugar mill (T1) generates molasses as a byproduct, whereas the other one (T2) produces a secondary honey in addition to sugars. Anhydrous ethanol can be produced by fermentation and subsequent dehydration of different process streams: molasses (T3), honey (T4), and sugar cane juice (T5).

Two different types of storage facilities, warehouses for liquid products (S1) and warehouses for solid materials (S2), are considered. It is assumed that materials can be transported by three different types of trucks: heavy trucks with open-box bed for sugar cane (TR1), medium trucks for sugar (TR2), and tank trucks for liquid products (TR3). The economic performance was measured via the NPV, whereas the environmental damage was quantified according to 5 environmental metrics: global warming potential (GWP100), eco-indicator 99 (EI99), damage to human health (DHH), damage to ecosystem quality (DEQ), and damage to resources (DR).

4 Numerical results

To solve the resulting MOO problem, we implemented the e-constraint method considering 7 e-values for each environmental metric. The model was written in GAMS and solved with the MILP solver CPLEX 12.0 on a HP Compaq DC5850 desktop PC with an AMD Phenom 8600B, 2.29 GHz triple-core processor, and 2.75 Gb of RAM. This led to 16,807 iterations, 4,941 of which were feasible. Only 40 solutions were finally identified after removing the repeated ones. The total CPU time spent was 58,669 seconds.

The NPV values were next normalized as follows:

(9)

where and denote the maximum and minimum values of objective fk among all the Pareto solutions. The normalized values of the environmental indicators were calculated as follows:

(10)

Figure 1 is a parallel coordinate plot that depicts the 40 normalized Pareto points. The figure shows in the bottom axis the different objective functions, while in the vertical axis it depicts the performance attained by each solution in every objective. Hence, each line in the plot...