DOI: 10.3303/CET2188094 
 

 
 

 

 
 
 

 
 
 

 
 
 

 
 
 

 
 

 

 
 

 
 
 

 
 
 

 
 
 

 
 
 

 
 
 

 
 

 
 
 

Paper Received: 29 June 2021; Revised: 21 July 2021; Accepted: 6 October 2021 
Please cite this article as: Solis C.M., Juan J.L.S., 2021, Multi-Objective Target-Oriented Robust Optimization of Algal Biofuel Production 
Integrating Resource Recirculation, Chemical Engineering Transactions, 88, 565-570  DOI:10.3303/CET2188094 

CHEMICAL ENGINEERING TRANSACTIONS

VOL. 88, 2021 

A publication of

The Italian Association
of Chemical Engineering
Online at www.cetjournal.it 

Guest Editors: Petar S. Varbanov, Yee Van Fan, Jiří J. Klemeš

Copyright © 2021, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-86-0; ISSN 2283-9216

Multi-Objective Target-Oriented Robust Optimization of Algal
Biofuel Production Integrating Resource Recirculation

Celine Marie Solis*, Jayne Lois San Juan
De La Salle University, Manila, Philippines
celine_solis@dlsu.edu.ph

The production of algal biofuels has long-time been proven as an applicable alternative for fossil fuels. Yet, its
economic performance is challenged by the inexpensive costs of fossil fuels. To address this, integrating various
processes to the system yields high-value bioproducts to increase profitability and sustainability. Looking
towards a circular economy perspective, the recirculation of resource flows is utilized to meet economic and
environmental sustainability through the reduction of waste. Since the recovery of resources used within the
production system is unpredictable in terms of output, uncertainty regarding resource recovery is assessed.
Previous modelling studies have not looked into the opportunity of integrating continuous recirculation and reuse
of resources along with its corresponding output uncertainty. In this work, a novel multi-objective target-oriented
robust optimization model is developed centered on an algal biofuel production system that simultaneously
optimizes profit and environmental impact, integrates inputs and processes aimed towards a closed-loop
system, adopts the principle of resource recovery and recirculation along with the uncertainty of resource
recovery outputs. A case study is solved as proof of concept and to illustrate the design methodology, optimal
solutions based on economic and environmental performance are analyzed. Scenario analysis is also performed
to analyze system behavior under varying conditions. Results show that to get a minimum profit, the robustness
index is greater than one indicating the model is very much flexible to sudden changes in demand.

1. Introduction

The continuous rise of worldwide energy consumption, being heavily dependent on fossil fuel usage, has
become a global environmental concern due to its greenhouse gas emissions. This is an indication that more
research into sustainable energy sources such as solar, wind, and biofuels is necessary. Biodiesel has been
considered the main substitute for fossil fuel (Ahmad et al., 2011). Microalgae is recognised as one of the most
valuable feedstock in the production of biofuel given its high productivity and carbon sequestration capabilities
(Singh and Gu, 2010). Yet, the associated production costs of microalgal biofuels are much higher than that of
fossil fuels and the biofuel process flow typically generate lots of waste including leftover biomass waste. To
maximize biomass utilization, other bioproducts that can be produced from microalgae are introduced into the
microalgal production system (Budzianowski, 2017). Existing studies have already investigated the integration
of various processes to a microalgal biorefinery production system.
Although having been introduced to various conceptual models for a microalgal biorefinery, the mentioned
studies have not presented a mathematical assessment of the zero-waste aspect of the biofuel production
process. Wu and Chang (2019) looked into an integrated microalgal biorefinery with process system engineering
standpoint using life cycle assessment (LCA) and techno-economic assessment (TEA) methodologies to
evaluate the economic and environmental indicators for the system. Their proposed biorefinery system consists
of bioenergies and bioalcohols with materials that are meant to ultimately cycle back as inputs to the current
process. However, their study simply contributes an algorithm for multi-objective optimization yet does not
include the outcome of the methodology. Looking into present optimization models regarding microalgal
biorefineries, various researchers have investigated on resource recirculation. García Prieto et al. (2017)
incorporated methanol recovery as well as leftover hexane from lipid extraction. This study focused on single
objective minimization with profit as the main priority. Aside from that, wastewater, flocculant, and catalyst
recovery processes were considered in a multi-objective optimization study by Solis et al. (2021). This study

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involved life cycle assessment (LCA) as the environmental impact calculation methodology. Yet, this research
focused on a deterministic approach regarding the cost and environmental aspects of the biorefinery. Since
production system behavior are subject to different factors, a steady production flow is unlikely and shall yield
specific effects to the economic and environmental performance of the biorefinery. To address this, the target-
oriented robust optimization methodology (TORO), developed by Ng and Sy (2014), has been applied by Sy et
al. (2018) to an algal biorefinery to achieve robust optimal solutions that are immune to uncertainties in
parameters. However, the study does not look into the reuse and recoveries of resources within the biofuel
production system which can add more complexity to the production process and presents a different behavior
with regards to flow of materials within the biorefinery. Based on the review conducted on present algal biofuel
optimization studies, there is a need to develop a target-oriented robust optimization model on an integrated
algal biorefinery that optimizes profit and environmental impact, and incorporates resource recirculation focusing
on a zero-waste process flow.

2. System definition

The microalgal biorefinery system and the other components of the mathematical model are defined.

2.1 Microalgal biorefinery 

The microalgal biofuel process network involves the main processes necessary for biofuel production, biochar
production and anaerobic digestion processes for usage of leftover biomass, and recovery processes for the
different input materials as presented in Figure 1.

Figure 1: Microalgal biorefinery process network 

The algal biofuel process flow to be considered in this study is divided into two main stages. The first stage is
focused on microalgal biomass cultivation and the conversion of biomass into algal oil to be used in biofuel
production. The main processes involved in this stage are microalgae cultivation, harvesting, oven drying, and
lipid extraction. The second stage includes the downstream processes of the biorefinery focusing on the
conversion of the biomass into end products such as biodiesel, glycerol, biochar, and digestate. The extraction
process produces algal lipid which is transformed into biodiesel and glycerol through transesterification.
Generated waste from the extraction process in the forms of solid and liquid residues. These residues are then
converted into bioproducts such as biochar and digestate through pyrolysis and anaerobic digestion.

2.2 Resource recirculation 

For the integrated algal biorefinery, material inputs such as water, flocculant, solvent, and catalyst are those
that are involved in the resource recirculation consideration. This is because these are resources that simply
assist in microalgal biomass development for biofuel conversion. Resource recovery process units are added
to biorefineries to be able to recover materials if the model chooses to do so. Decisions shall then be made
regarding the yield of the waste input determining whether the material is reused in the production system, sold
for a given price per kg, or led to waste.

2.3 Multi-periodicity 

The optimization model considers multiple time periods to incorporate long term biorefinery operations. Capital
and operating costs shall be properly accounted for the microalgal biorefinery with multiple period consideration.

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2.4 Cost components 

For the optimization model, the following cost components will be included namely: inventory costs, initial
investment costs, operating costs, and material purchasing costs. Given that the optimization model considers
multiple time periods, inventory costs are included for each material expressed as a periodic cost per kg material.
Investment costs refer to the initial capital expenses incurred to construct the microalgal biorefinery process
units expressed at a cost per facility basis. Operating costs include labor, overhead, and material costs
associated with each process expressed as a cost per time period. Material purchase costs are set for every
material input that is purchased for microalgal production expressed as a cost per kg unit.

2.5 Environmental impact components 

The environmental impact values used for the minimization objective are greenhouse gas (GHG) emissions
from the process units. Emission counts for each process are estimated at a rate of GHG emissions per output.

3. Model formulation

The mathematical optimization model is formulated with the objective functions and constraints are evaluated.

3.1 Assumptions 

The production outputs of the biorefinery are assumed to be transported to customers instantaneously. The
processing of microalgal biomass in all process units is instantaneous. Capacities for all facilities are fixed
throughout the entire study period.

3.2 Objective functions 

The objectives involved in the mathematical model are profit maximization and environmental impact
minimization. The equation for profit is the difference between the revenue from all biorefinery products and the
total costs incurred, presented in Eq(1). The total costs are broken down into capital costs, operating costs,
purchase costs, and inventory costs. The environmental impact objective is defined in Eq(2).

Profit = ∑ ∑ 𝑆𝑃𝑝𝑡 ∙ 𝑇𝑃𝑝𝑡𝑝𝑡 − ∑ 𝐹𝐶𝑖 ∙ 𝐵𝑃𝑖𝑖 − ∑ ∑ 𝑂𝐶𝑖𝑡 ∙ 𝑃𝑂𝑖𝑡𝑖𝑡 − ∑ ∑ 𝑃𝐶𝑎𝑡 ∙ 𝑀𝐼𝑎𝑡𝑎𝑡 − ∑ ∑ 𝐼𝐶𝑎𝑡 ∙ 𝐸𝐼𝑎𝑡𝑎𝑡 (1)

Environmental Impact = ∑ ∑ 𝐸𝑁𝑖𝑡 ∙ 𝑃𝑂𝑖𝑡𝑖𝑡 (2)

Given that the model has two objectives, there must be a balance between the economic and environmental
objectives to generate the optimal solution. The objective function is defined as the maximization of the least
desired value to balance the two objectives as seen in Eq(3) (San Juan et al., 2019). Since the objective function
is nonlinear, linearizing constraints are necessary to make sure that the optimization model generates the
optimal solution. The objective function is defined as the maximization of efficiency as seen in Eq(4). Eq(5) and
Eq(6) indicate that the value for efficiency must be the minimum of the efficiencies of the two objectives.

Max Z = 𝑚𝑖𝑛 [ 𝑃𝑟𝑜𝑓𝑖𝑡𝑤𝑜𝑟𝑠𝑡−𝑃𝑟𝑜𝑓𝑖𝑡
𝑃𝑟𝑜𝑓𝑖𝑡𝑤𝑜𝑟𝑠𝑡−𝑃𝑟𝑜𝑓𝑖𝑡𝑏𝑒𝑠𝑡

,
𝐼𝑚𝑝𝑎𝑐𝑡𝑤𝑜𝑟𝑠𝑡−𝐼𝑚𝑝𝑎𝑐𝑡

𝐼𝑚𝑝𝑎𝑐𝑡𝑤𝑜𝑟𝑠𝑡−𝐼𝑚𝑝𝑎𝑐𝑡𝑏𝑒𝑠𝑡
 ] (3)

Max Z = Efficiency (4)

Efficiency ≤ 𝑃𝑟𝑜𝑓𝑖𝑡𝑤𝑜𝑟𝑠𝑡−𝑃𝑟𝑜𝑓𝑖𝑡
𝑃𝑟𝑜𝑓𝑖𝑡𝑤𝑜𝑟𝑠𝑡−𝑃𝑟𝑜𝑓𝑖𝑡𝑏𝑒𝑠𝑡

(5)

Efficiency ≤ 𝐼𝑚𝑝𝑎𝑐𝑡𝑤𝑜𝑟𝑠𝑡−𝐼𝑚𝑝𝑎𝑐𝑡
𝐼𝑚𝑝𝑎𝑐𝑡𝑤𝑜𝑟𝑠𝑡−𝐼𝑚𝑝𝑎𝑐𝑡𝑏𝑒𝑠𝑡

(6)

3.3 Constraints 

The demand constraint for the different products of the biorefinery are presented in Eq(7). The total product
outputs must be greater than or equal to the demand for each product namely, biodiesel, glycerol, biochar, and
digestate. The capacity constraints define the processing capability of each facility as defined in Eq(8). The
production output of each process must be less than or equal to the sumproduct of its process capacity and the
binary variable for that process.

𝑇𝑃𝑝𝑡 ≥ 𝐷𝐵𝑝𝑡     ∀𝑝 ∀𝑡 (7)

𝑃𝑂𝑖𝑡 ≤ 𝐵𝑖 𝐶𝑖     ∀𝑖 ∀𝑡  (8)

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The conversion of product input to output is presented in the constraints shown in Eq(9). The product of the
process input materials and the conversion matrix for input and outputs is set to be equal to the overall process
outputs. For the flow of materials within the biorefinery, the relationship between the output of the previous
process and the corresponding inputs for the next process is defined in Eq(10). The equation regarding the
relationship between the total final products of the biorefinery and the outputs of the downstream processes is
presented in Eq(11). The constraint about input ending inventory is defined in Eq(12). The ending inventory for
a given period is equated to the total recovered input material for reuse during the given period. Eq(13) defines
the input beginning inventory constraints per period. The beginning inventory for an input in a given period is
the sum of the ending inventory of the previous period and the total purchased inputs during the current period.

𝑋𝑃𝑎𝑖𝑡 𝐶𝑀𝑎𝑖 = 𝑌𝑃𝑎𝑖𝑡    ∀𝑎 ∀𝑖 ∀𝑡 (9)

∑ 𝑌𝑃𝑎𝑖𝑡𝑖 ≥ ∑ 𝑋𝑃𝑎𝑖𝑡𝑖−1   ∀𝑎 ∀𝑖 ∀𝑡 (10)

∑ 𝑌𝑃𝑎𝑖𝑡𝑖 ≥ 𝑇𝑃𝑝𝑡  ∀𝑎 ∀𝑝 ∀𝑡 (11)

𝐸𝐼𝑎𝑡 = 𝑅𝑅𝐼𝑎𝑡   ∀𝑎 ∀𝑡 (12)

𝐵𝐼𝑎𝑡 = 𝐸𝐼𝑎𝑡−1 + 𝑀𝐼𝑎𝑡    ∀𝑎 ∀𝑡  (13)

The relationship between the total required material input and the input usage for each process is displayed in
Eq(14). Eq(15) displays that the input beginning inventory for each time period is greater than or equal to the
total amount of required material input for production while Eq(16) indicates that the total amount of recovered
material input is equal to the amount recovered going towards reuse, selling, and to waste.

𝑅𝑄𝐼𝑎𝑡 = ∑ 𝑋𝑃𝑎𝑖𝑡𝑖  ∀𝑎 ∀𝑡 (14)

𝐵𝐼𝑎𝑡 ≥ 𝑅𝑄𝐼𝑏𝑡    ∀𝑎 ∀𝑡   (15)

∑ 𝑌𝑅𝑎𝑗𝑡𝑗 ≥ 𝑅𝑅𝐼𝑎𝑡 + 𝑅𝑆𝐼𝑎𝑡 + 𝑅𝑊𝐼𝑎𝑡    ∀𝑎 ∀𝑡 (16)

The equation regarding the relationship between the total purchased material inputs and their corresponding
purchase capacity is displayed in Eq(17). Similarly, Eq(18) presents the relationship between the total ending
inventories of each input material and the corresponding inventory capacities. The equation pertaining to the
binary variables for the process alternatives is displayed in Eq(19). As for the equation for relationship between
binary variables of recovery processes and the corresponding main processes, it is presented in Eq(20). The
equation setting the value for the input binary variables equal to the binary variable for the recovery of the given
input material is presented in Eq(21).

𝑀𝐼𝑎𝑡 ≤ 𝑃𝐾𝑎𝑡 ∗ 𝐵𝑀𝑎   ∀𝑎 ∀𝑡 (17)

𝐸𝐼𝑎𝑡 ≤ 𝐼𝐾𝑎𝑡 ∗ 𝐵𝑀𝑎    ∀𝑎 ∀𝑡  (18)

∑ 𝐵𝑃𝑖𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝑡𝑦𝑝𝑒 = 1 (19)

𝐵𝑅𝑗 = ∑ 𝐵𝑃𝑖𝑖    ∀𝑗 (20)

𝐵𝑀𝑎 = 𝐵𝑅𝑗    ∀𝑎 ∀𝑗  (21)

3.4 Target-oriented robust optimization methodology 

To execute the target-oriented robust optimization methodology, the robustness index shall be set as the new
objective to maximize for the model as shown in Eq(22). Profit and environmental impact targets are set for the
two objectives as presented in Eq(23) and Eq(24). The revised demand constraint is presented in Eq(25), which
reflects the new demand values to be calculated using the robustness index. The new demand values are
computed by subtracting the sumproduct of the robustness index and the demand threshold from the base
demand values, as displayed in Eq(26).

Max Z = α (22)

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Profit ≥ 𝑃𝑟𝑜𝑓𝑖𝑡𝑡𝑎𝑟𝑔𝑒𝑡 (23)

Impact ≤ 𝐼𝑚𝑝𝑎𝑐𝑡𝑡𝑎𝑟𝑔𝑒𝑡 (24)

𝑇𝑃𝑝𝑡 ≥ 𝐷𝐵𝑝�̃�     ∀𝑝 ∀𝑡 (25)

𝐷𝐵𝑝�̃� = 𝐷𝐵𝑝𝑡 − α ∙ 𝐷𝐵𝑝�̂�    ∀𝑖 ∀𝑡 (26)

4. Model validation

The mathematical model was validated using the Cplex optimization solver in the software MATLAB R2020a.
The model is deemed valid since it runs according to the production system. For the base run, a study period of
10 years was arbitrarily selected. The process flow is presented in Figure 1.

4.1 Multi-objective optimization 

The profit and environmental impact values for the base run are presented in Table 1. This illustrates the base
values to be referenced for comparison to the target-oriented robust optimization runs. The final production
network generated involves hybrid wastewater photobioreactor cultivation, filtration for harvesting, and
microwave for extraction.

Table 1: Multi-objective optimization base run 

Profit ($) Environmental Impact – GHG (mPt)  Efficiency Biodiesel Output (kg)
1,404,430.80 512.29 58.09 % 76,218.44

4.2 Target-oriented robust optimization 

Upon executing the mathematical model with the additional equations for the TORO methodology, the optimal
results are summarized in Table 2. The minimum set for the profit is set to 0 to indicate a breakeven production
level. The optimal robustness index subject to the constraints and profit target is 1.094493. This indicates that
the model is very flexible to changes in demand since it is greater than 1. It is seen that while there is near no
profit, a significant amount of biodiesel production is still required compared to the base run result.

Table 2: TORO results summary 

Profit ($) Environmental Impact – GHG (mPt)  Efficiency Biodiesel Output (kg) Robustness Index
0.21 418.83 44.35 % 62,312.74 1.0945
1,000,221.03 485.39 53.94 % 72,216.24 0.3149
468,899.07 450.03 48.73 % 66,955.45 0.7290

Targets are set for the profit and environmental impact values to test how the mathematical model generates
the robustness index. For a profit target of $ 1,000,000, the robustness index resulted to 0.31485. When the
environmental impact target was targeted to be 450 mPt, the resulting index was then 0.729. This presents the
effect of the profit target to resulting robustness capabilities of the system. A higher profit target leads to a lower
robustness index which indicates that there is less room for error compared to a lower target.
To further observe the behavior of the optimization model under TORO, different values for the robustness index
are assigned to generate the optimal results. Figure 2 presents the graph of the profit and environmental impact
optimal values under the varying robustness indices. It is still evident that with lower robustness index, a higher
profit value is expected since the model is less susceptible to changes in demand. Given a higher index, profit
results to a lower value which may even lead to a net loss. The environmental impact has a positive correlation
with profit yet a different behavior when the minimization objective is considered. With a higher robustness
index, there is less impact which is desirable for the system. This indicates that it would then be the prerogative
of the stakeholders to decide which objective to prioritize in the long run.

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Figure 2: Profit and Impact vs. Robustness Index 

5. Conclusions

This study introduced a multi-objective optimization model for an algal biorefinery involving resource
recirculation with the goal of maximizing profit and minimizing environmental impact. The consideration of both
objectives in a multi-objective optimization model strikes a balance between the two objectives. Target-oriented
robust optimization is applied to the mathematical model to enable to it to become flexible to changes in demand.
The optimal robustness index generated under a breakeven profit target is 1.0945 which indicates that the model
is largely flexible to changes in demand given the target. Upon testing different robustness indices for the
optimization model, it was found that a higher index yields a lower profit. On the other hand, a higher robustness
index leads to a lower impact which is desirable for the biorefinery. This indicates that abrupt changes in demand
affect the optimal results significantly which cements the importance of introducing robustness into the model.

Nomenclature

a, p – inputs & final products mPt – millipoint
BMa, BPi, BRj – binary vars (input, process, recovery)
BIat, EIat – beginning and ending inventory
Ci, DKat, IKat – capacity (output, purchase, inventory)
DBpt – demand
FCi, OCit – fixed costs and operating costs
ICat, PCat – purchase costs and inventory costs
SPpt, TPpt – selling price and total product amounts
POit – production outputs

MIat – purchase amounts
XPait, YPait – input and output material usage
CMai – conversion matrix for input/output
RQIat – total required input
RRIat, RSIat, RWIat – recovery decisions
t – time period
α – robustness index
i, j – process unit indices

References 

Ahmad, A. L., Mat Yasin, N. H., Derek, C. J. C., Lim, J. K., 2011, Microalgae as a sustainable energy source for
biodiesel production: A review, Renewable and Sustainable Energy Reviews, 15, 584-593.

Budzianowski, W. M., 2017, High-value low-volume bioproducts coupled to bioenergies with potential to
enhance business development of sustainable biorefineries, Renewable and Sustainable Energy Reviews,
70, 793-804.

García Prieto, C. V., Ramos, F. D., Estrada, V., Villar, M. A., Diaz, M. S., 2017, Optimization of an integrated
algae-based biorefinery for the production of biodiesel, astaxanthin and PHB, Energy, 139, 1159-1172.

Ng, T. S., Sy, C. L., 2014, An affine adjustable robust model for generation and transmission network planning,
International Journal of Electrical Power & Energy Systems, 60, 141-152.

San Juan, J. L., Aviso, K. B., Tan, R. R., Sy, C. L., 2019, A Multi-Objective Optimization Model for the Design
of Biomass Co-Firing Networks Integrating Feedstock Quality Considerations, Energies, 12, 2252-2274.

Singh, J., Gu, S., 2010, Commercialization potential of microalgae for biofuels production, Renewable and
Sustainable Energy Reviews, 14, 2596-2610.

Solis, C. M. A., San Juan, J. L. G., Mayol, A. P., Sy, C. L., Ubando, A. T., Culaba, A. B., 2021, A Multi-Objective
Life Cycle Optimization Model of an Integrated Algal Biorefinery toward a Sustainable Circular Bioeconomy
Considering Resource Recirculation, Energies, 14, 1416.

Sy, C. L., Ubando, A. T., Aviso, K. B., Tan, R. R., 2018, Multi-objective target oriented robust optimization for
the design of an integrated biorefinery, Journal of Cleaner Production, 170, 496-509.

Wu, W., Chang, J., 2019, Integrated algal biorefineries from process systems engineering aspects: A review,
Bioresource Technology, 291, 121939.

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