CET-vol 105 DOI: 10.3303/CET23105033 Paper Received: 18 January 2023; Revised: 3 June 2023; Accepted: 27 September 2023 Please cite this article as: Acosta Pavas J.C., Robles-Rodríguez C.E., Morchain J., Corrales D.C., Dumas C., Cockx A., Aceves-Lara C.A., 2023, Economic Multi-Objective Dynamic Optimization (EMODO) as a Decision-Making tool in Biomethanation Process, Chemical Engineering Transactions, 105, 193-198 DOI:10.3303/CET23105033 CHEMICAL ENGINEERING TRANSACTIONS VOL. 105, 2023 A publication of The Italian Association of Chemical Engineering Online at www.cetjournal.it Guest Editors: David Bogle, Flavio Manenti, Piero Salatino Copyright © 2023, AIDIC Servizi S.r.l. ISBN 979-12-81206-04-5; ISSN 2283-9216 Economic Multi-Objective Dynamic Optimization (EMODO) as a Decision-Making tool in Biomethanation Process Juan C. Acosta-Pavasa, Carlos E. Robles-Rodrígueza, Jérôme Morchaina, David Camilo Corralesb, Claire Dumasa, Arnaud Cockxa, César A. Aceves-Laraa* aTBI, Université de Toulouse, CNRS, INRAE, INSA, Toulouse, France bINRAE, UMS (1337) TWB, 135 Avenue de Rangueil, 31077 Toulouse, France aceves@insa-toulouse.fr In biological methanation, the methane produced by anaerobic digestion (AD) is upgraded with the addition of syngas. The successful implementation of biomethanation requires the optimization of the production to be competitive in economic terms against chemical processes. Optimization is an arduous task, especially when it is desired to optimize multiple objectives that can be conflicting, such as yields, productivities, process times, and profit gains, among others. This work aims to implement an Economic Multi-Objective Dynamic Optimization (EMODO) approach as a decision-making tool for adequately operating the biomethanation process. The proposed EMODO strategy was based on a previously developed dynamic model for biomethanation. This strategy effectively optimized the 𝐺𝑎𝑖𝑛 and the 𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛 by manipulating the inlet flow rates of gas (𝑞𝑔𝑎𝑠 𝑖𝑛 ) and liquid (𝑞𝑙𝑖𝑞 𝑖𝑛 ). The strategy also highlights the conflicting behavior of economic objectives and the dependence on substrates. The dynamic optimization improves the response time of the model smoothing the transitions between stages and achieving well adaptation to disturbances regarding the cost of the substrates and the selling prices of the products. 1. Introduction The successful implementation of biological processes requires optimization to be competitive against chemical processes in economic terms. Emerging bioprocesses such as biological methanation can benefit from multi- objective optimization by maximizing or minimizing multiple variables of interest simultaneously. Biological methanation or Biomethanation is a process in which the biogas produced through the well-known Anaerobic Digestion (AD) is upgraded by the biological conversion of CO2 using syngas (a combination of H2, CO, and CO2) to obtain high-purity CH4 (Rafrafi et al., 2020). The biogas produced in the AD contains between 50 - 75% of CH4, 25 – 50 % of CO2, and 2–7% water vapor (Laguillaumie et al., 2022). Through biomethanation, the biogas can be upgraded into biomethane (95 – 99 %) while removing CO2 with the addition of H2 or syngas (CO/H2) (Sun et al., 2021). The hydrogenotrophic methanogens with CO2 consumption transform the H2. The CO can be transformed indirectly into H2 by carboxydotrophic hydrogenogenesis, then into acetate by CO- acetogenesis and CO-homoacetogenesis, and finally transformed into CH4 through hydrogenotrophic and acetoclastic methanogenesis (Guiot et al., 2011). Other works have shown that biomethanation can also be used to produce acetate (Laguillaumie et al., 2022), a molecule of interest that could help make this process more economically profitable. Based on this complex biological system, managing the biomethanation process is still an arduous task. Therefore, achieving desired objectives such as high productivities, high-profit margins, or low flow rates remains difficult at an industrial scale, especially when it is desired to optimize several variables simultaneously. Multi-Objective Optimization (MOO) involves optimizing problems where there is more than one objective to be optimized simultaneously, and these objectives are usually conflictive. The use of dynamic models plays a crucial role in designing control strategies. For instance, Model Predictive Control (MPC) (Morales-Rodelo et al., 2020) is implemented to maintain or optimize several variables simultaneously (e.g., productivities and yields). MPC refers to control actions that optimize a criterion in the 193 system's future behavior, which is determined by the dynamic model (Camacho & Bordons, 2007). Economic MPC (EMPC) has recently been proposed incorporating a general cost function or performance index in its formulation to consider economic criteria in process optimization (Ellis et al., 2017). MOO has been applied in bioprocess to find the trade-off between yields and productivities (Nimmegeers et al., 2018). In the AD considering the determination of Pareto fronts to find the trade-off between the environmental impact and net present value as economic aspect (Li et al., 2018). In biomethanation, MOO has been applied to minimize energy consumption and maximize the green degree and CH4 production (Yan et al., 2016). However, these works not consider the dynamic optimization of the process, improving the performance of economic objectives. This work aims at implementing an Economic Multi-Objective Dynamic Optimization (EMODO) strategy as a decision-making tool for the biomethanation process to guarantee the maximization of the 𝐺𝑎𝑖𝑛 and 𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛. The 𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛 was calculated based on changes in market prices using as substrates glucose, H2, and CO and as products CH4 and acetate. The 𝐺𝑎𝑖𝑛 was calculated with the price of CH4 and acetate production. Pareto optimal sets associated with three process stages were determined through MOO. Each Pareto fronts solution is considered a Pareto Optimal Point (POP). The Pareto optimal set is considered the first part of the decision-making tool, where it is necessary to select the best POP that maximizes the 𝐺𝑎𝑖𝑛 and 𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛. In dynamic optimization is used an MPC, which is referred to as the second part of the decision-making tool that optimizes the performance of economic objectives with two control variables corresponding to 𝑞𝑔𝑎𝑠 𝑖𝑛 and 𝑞𝑙𝑖𝑞 𝑖𝑛 . To verify the efficacy of the EMODO strategy, the biomethanation process is simulated considering disturbances of ±20 % in the substrates, sugar, H2, and CO cost, and the selling price of the products CH4 and acetate. 2. Economic Multi-Objective Dynamic Optimization (EMODO) Several variables can be optimized in the biomethanation process: yields, productivities, process times, etc. Most of these variables are often conflicting. A Multi-Objective Dynamic Optimization (MODO) strategy was proposed in previous work (Acosta-Pavas et al., 2022) in order to address the mentioned problem. However, this methodology does not consider any information about market evolution. Formulating a cost function could directly or indirectly reflect the process economics to consider economic optimization. Therefore, in this study, the MODO strategy is modified to consider economic aspects such as substrates costs or prices market through the Economic Multi-Objective Dynamic Optimization (EMODO) as the following five steps: Step 1 - Model definition Biological methanation was modeled by a dynamic model based on an extension of the Anaerobic Digestion Model No. 1 (ADM1_ME) (Acosta-Pavas et al., 2023). This model considers the uptake of sugar, volatile fatty acids, such as butyrate, propionate, and acetate, the uptake of H2 and CO, and the decay of biomass and in- situ syngas addition. The ADM1_ME describes three types of variables: soluble (𝑆𝑙𝑖𝑞,𝑗), particulated biomass (𝑋𝑘) and gas (𝑆𝑔𝑎𝑠,𝑖) components. The ADM1_ME is summarized as Eqs. (1) – (3). 𝑑𝑆𝑙𝑖𝑞,𝑗 𝑑𝑡 = 𝑞𝑙𝑖𝑞 𝑖𝑛 𝑉𝑙𝑖𝑞 (𝑆𝑙𝑖𝑞,𝑗 𝑖𝑛 −𝑆𝑙𝑖𝑞,𝑗) + ∑ 𝑌𝑘𝑓𝑗,𝑘µ𝑘 𝑘 −𝑁𝑖 (1) 𝑑𝑋𝑘 𝑑𝑡 = 𝑞𝑙𝑖𝑞 𝑖𝑛 𝑉𝑙𝑖𝑞 (𝑋𝑘 𝑖𝑛−𝑋𝑘) + 𝑌𝑘µ𝑘 − µ𝑘,𝑑𝑒𝑐 (2) 𝑑𝑆𝑔𝑎𝑠,𝑖 𝑑𝑡 = 𝑞𝑔𝑎𝑠 𝑖𝑛 𝑉𝑔𝑎𝑠 𝑆𝑔𝑎𝑠,𝑖 𝑖𝑛 +𝑁𝑖 ( 𝑉𝑙𝑖𝑞 𝑉𝑔𝑎𝑠 ) − 𝑞𝑔𝑎𝑠 𝑉𝑔𝑎𝑠 𝑆𝑔𝑎𝑠,𝑖 (3) Sub-index 𝑗 ϵ [1,8] represents glucose, butyrate, propionate, acetate, H2, CH4, CO, and CO2 in the liquid phase. The H2, CH4, and CO are expressed in 𝑔𝐶𝑂𝐷/𝐿, and CO2 is expressed in 𝑚𝑜𝑙/𝐿. Chemical Oxygen Demand (COD) is the amount of oxygen needed to degrade the organic matter into CO2 and H2O. It is important to mention that CO2 is expressed in 𝑚𝑜𝑙 instead of 𝐶𝑂𝐷, as suggested by Batstone et al. (2002). Sub-index 𝑘 ϵ [1,6] denotes for the biomass that degrade glucose, butyrate, propionate, acetate, H2, and CO, respectively. For the gas phase, the sub-index 𝑖 ϵ [1,4] corresponds to H2, CH4, CO, and CO2. The inlet flow rates of liquid and gas are represented by 𝑞𝑙𝑖𝑞 𝑖𝑛 and 𝑞𝑔𝑎𝑠 𝑖𝑛 , respectively, while 𝑞𝑔𝑎𝑠 denotes the outlet gas flow rate. 𝑉𝑙𝑖𝑞 and 𝑉𝑔𝑎𝑠 are the liquid and gas volumes, respectively. 𝑆𝑙𝑖𝑞,𝑗 𝑖𝑛 , 𝑆𝑔𝑎𝑠,𝑖 𝑖𝑛 and 𝑋𝑘 𝑖𝑛 represent the inlet concentration of the component 𝑗 in the liquid phase, the inlet concentration of component 𝑖 in gas phase, and the inlet concentration of biomass 194 𝑘 in the liquid phase, respectively. 𝑌𝑘 is the yield of biomass k, 𝑓𝑗,𝑘 corresponds the stoichiometric coefficients; µ𝑘 and µ𝑘,𝑑𝑒𝑐 refer to the growth and decay rate of biomass k, and 𝑁𝑖 to the mass transfer rate of component 𝑖. The simulations of the biomethanation process were carried out using the ADM1_ME considering a bubble column reactor (BCR) with a working volume of 37.5 𝐿 and a hydraulic retention time (𝐻𝑅𝑇) of 20 days operating at 37°C for 330 days. The organic loading rate (𝑂𝐿𝑅) was varied over time in all stages, according to Table 1. The reference stage corresponded to the simulation without gas addition, with a 𝑞𝑙𝑖𝑞 𝑖𝑛 of 1.88 𝐿 𝑑⁄ . The flow rates 𝑞𝑙𝑖𝑞 𝑖𝑛 , 𝑞𝑔𝑎𝑠 𝑖𝑛 , and the gas loading rate (𝐺𝐿𝑅) will be optimized by the EMODO strategy for stages I – III. Table 1:Stages and OLR simulated with the ADM1_ME. Stage Time (Day) 𝑶𝑳𝑹 (𝒈𝑪𝑶𝑫/𝑳/𝒅) Reference 1-30 0.53 I 30-130 1.07 II 130-230 1.60 III 230-330 2.13 To propose economic variables, literature values of 3.40×10-4,1.63×10-4, 5.96×10-4, and 1.63×10-3 𝐸𝑈𝑅/𝑔𝐶𝑂𝐷 were suggested for the cost of sugar, syngas, the selling price of CH4, and selling price of acetate, respectively. Then, to verify the efficacy of the EMODO strategy, selling prices were simulated, considering disturbances in the price. First, an increase of 20% (+20%) in the selling price of CH4 and a reduction of 20% (-20%) in the selling price of acetate were considered from 70-100 days (Disturb 1). Then, an increase of 20% in the cost of syngas was simulated from 190-210 days (Disturb 2). Finally, a decrease of 20% in the selling price of CH4 and an increase of 20% in the cost of syngas were considered from 260-290 days (Disturb 3). Step 2 - Definition of the optimization problem The definition of economic optimization corresponds to the maximization of the gain of CH4 and acetate (𝐺𝑎𝑖𝑛), and the profit margin of CH4 and acetate (𝑝𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛) by modifying the 𝑞𝑔𝑎𝑠 𝑖𝑛 and 𝑞𝑙𝑖𝑞 𝑖𝑛 . The economic multi- objective optimization to find the Pareto optimal set was proposed as, 𝑚𝑎𝑥 {𝑞𝑔𝑎𝑠 𝑖𝑛 , 𝑞𝑙𝑖𝑞 𝑖𝑛 } (𝐺𝑎𝑖𝑛, 𝑝𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛) (4) 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 { 𝑑𝑦 𝑑𝑡⁄ = ξ(𝑥, 𝑢, 𝑝, 𝑣) 1 ≤ 𝑞𝑔𝑎𝑠 𝑖𝑛 ≤ 100 𝐿 𝑑⁄ 1.875 ≤ 𝑞𝑙𝑖𝑞 𝑖𝑛 ≤ 10 𝐿 𝑑⁄ (5) The objective variables are, 𝐺𝑎𝑖𝑛 = 𝑎𝑐𝑒𝑡𝑎𝑡𝑒 𝑠𝑒𝑙𝑙𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 ∙ 𝑆𝑙𝑖𝑞,𝑎𝑐 𝐻𝑅𝑇 + 𝐶𝐻4 𝑠𝑒𝑙𝑙𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 ∙ 𝑞𝑔𝑎𝑠,𝐶𝐻4 ∙ 64 22.4 ∙ 𝑉𝑙𝑖𝑞 (6) 𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛 = (𝐶𝐻4 𝑠𝑎𝑙𝑒𝑠 + 𝑎𝑐𝑒𝑡𝑎𝑡𝑒 𝑠𝑎𝑙𝑒𝑠 ) − 𝑆𝑢𝑏𝑠𝑡𝑟𝑎𝑡𝑒𝑠 𝑐𝑜𝑠𝑡 𝐶𝐻4 sales + 𝑎𝑐𝑒𝑡𝑎𝑡𝑒 𝑠𝑎𝑙𝑒𝑠 ∙ 100% (7) In these equations, ξ(𝑥, 𝑢, 𝑝, 𝑡) represents the ADM1_ME, which depends on the state variables 𝑥, the control variables 𝑢, the parameters 𝑝, and the disturbances in the inputs 𝑣. 𝑆𝑢𝑏𝑠𝑡𝑟𝑎𝑡𝑒𝑠 𝑐𝑜𝑠𝑡 refers to the cost of glucose and syngas (Eq (8)). 𝐶𝐻4 𝑠𝑎𝑙𝑒𝑠 and 𝑎𝑐𝑒𝑡𝑎𝑡𝑒 𝑠𝑎𝑙𝑒𝑠 are the gains in 𝐸𝑈𝑅 for selling all the CH4 and acetate produced, Eq (9)-(10). 𝑆𝑢𝑏𝑠𝑡𝑟𝑎𝑡𝑒𝑠 𝑐𝑜𝑠𝑡 = ((𝑆𝑢𝑔𝑎𝑟 𝑐𝑜𝑠𝑡 ∙ 𝑂𝐿𝑅) + (𝑆𝑦𝑛𝑔𝑎𝑠 𝑐𝑜𝑠𝑡 ∙ 𝐺𝐿𝑅) ) ∙ 𝑉𝑙𝑖𝑞 (8) 𝐶𝐻4 𝑠𝑎𝑙𝑒𝑠 = 𝐶𝐻4 𝑠𝑒𝑙𝑙𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 ∙ 𝑞𝑔𝑎𝑠,𝐶𝐻4 ∙ 64 22.4 (9) 𝑎𝑐𝑒𝑡𝑎𝑡𝑒 𝑠𝑎𝑙𝑒𝑠 = 𝑎𝑐𝑒𝑡𝑎𝑡𝑒 𝑠𝑒𝑙𝑙𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 ∙ 𝑆𝑙𝑖𝑞,𝑎𝑐 ∙ 𝑉𝑙𝑖𝑞 𝐻𝑅𝑇 (10) 195 Step 3 - Selection of the Pareto optimal point (POP) In this study, the simulations were run using an Intel® Core i7 8665U 2.11 GHz, 16 GB RAM computer. The paretosearch function from MATLAB® was used to obtain the Pareto optimal set for each stage. Figure 1 presents the three Pareto fronts computed for each stage, where 60 POP were calculated. Figure 1: Pareto optimal sets for stages I-III, and maximum Euclidean length. At each stage, one POP was selected, which corresponded to the maximization of the Euclidean length (𝑑𝑚𝑎𝑥) for the 𝐺𝑎𝑖𝑛 and the 𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛 (red squares in Figure 1). For all the stages, 𝑑𝑚𝑎𝑥 was calculated as the distance from the origin, using a normalization as in Eq. (11). 𝑑𝑚𝑎𝑥 = 𝑚𝑎𝑥 (√( 𝐺𝑎𝑖𝑛∗ − 𝑚𝑖𝑛(𝐺𝑎𝑖𝑛∗) 𝑚𝑎𝑥(𝐺𝑎𝑖𝑛∗) − 𝑚𝑖𝑛(𝐺𝑎𝑖𝑛∗) ) 2 + ( 𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛∗ − 𝑚𝑖𝑛( 𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛∗) 𝑚𝑎𝑥( 𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛∗) − 𝑚𝑖𝑛( 𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛∗) ) 2 ) (11) Step 4 - Definition of the dynamic problem with a single weighted objective In order to consider a dynamic optimization, the two previously defined objectives and their optimal points (POP) were merged into one objective function and solved based on an MPC problem. The proposed dynamic optimization determines the input variables that minimize the following objective function, 𝑚𝑖𝑛 {𝑞𝑔𝑎𝑠 𝑖𝑛 , 𝑞𝑙𝑖𝑞 𝑖𝑛 } ( ∑ ( |𝐺𝑎𝑖𝑛∗ − 𝐺𝑎𝑖𝑛(𝑡)| 𝐺𝑎𝑖𝑛∗ ) 2 𝑡+𝐻𝑝 𝑗=𝑡 + ( |𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛∗ − 𝑃𝑟𝑜𝑓𝑖𝑡 𝑔𝑎𝑖𝑛(𝑡)| 𝑃𝑟𝑜𝑓𝑖𝑡 𝑔𝑎𝑖𝑛∗ ) 2 + ∑ 𝑊𝑢,1 ∆𝑞𝑔𝑎𝑠 𝑖𝑛 (𝑡)2 + 𝑊𝑢,2 ∆𝑞𝑙𝑖𝑞 𝑖𝑛 (𝑡)2 𝑡+𝐻𝑐 𝑗=𝑡 ) (12) Eq. (12) is subject to the constraints in Eq (5). 𝐺𝑎𝑖𝑛∗ and 𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛∗ denote the POP values for 𝐺𝑎𝑖𝑛 and 𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛 computed by the MOO, ∆𝑞𝑔𝑎𝑠 𝑖𝑛 (𝑡)2 and ∆𝑞𝑙𝑖𝑞 𝑖𝑛 (𝑡)2 are the differences between 𝑞𝑔𝑎𝑠 𝑖𝑛 and 𝑞𝑙𝑖𝑞 𝑖𝑛 , respectively, before and after each step of the dynamic optimization. 𝑊𝑢,1 and 𝑊𝑢,2 are the parameters that weight the importance of the control effort term in the optimization. The initial values for both manipulated variables, 𝑞𝑔𝑎𝑠 𝑖𝑛 and 𝑞𝑙𝑖𝑞 𝑖𝑛 were 1 𝐿 𝑑⁄ and 1.875 𝐿 𝑑⁄ , respectively. Step 5 - Implementation of the optimization Two cases were analyzed. Case 1 corresponded to the use of the POP identified in step 3 and applied directly in the simulation with the ADM1_ME (Pareto results). Case 2 referred to dynamic optimization as a control strategy (Dynamic opt). The weights 𝑊𝑢,1 and 𝑊𝑢,2 were manually adjusted to values of 1 × 10−7. The prediction (𝐻𝑝) and control (𝐻𝑐) horizons were considered with equal values and equivalent to the time length of each stage (Table 1). Optimization was performed with the patternsearch algorithm in MATLAB®. 196 The results of the optimization are displayed in Figure 2. In both cases, the 𝐺𝑎𝑖𝑛 increased at each stage change, while the 𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛 varied between 30 and 35% (Figure 2-C). For both economic variables, it is observed that the dynamic optimization improved the model's response, smoothing the transition between stages, which is ideal in this type of biological process to avoid additional disturbances. Additionally, the EMODO strategy responds satisfactorily to the three proposed disturbances regarding the cost of substrates and the selling price of products, especially with the disturbance presented between 190-210 days, where there was a 20% increase in syngas cost and subsequent transition between stages II and III (Figure 2- A). In Figure 2-B, comparing case 2 to case 1 in terms of control variables, a slight reduction of 3.3×10-2 and 7.5×10- 2 𝐿/𝑑 was observed for 𝑞𝑙𝑖𝑞 𝑖𝑛 in stages I and III, respectively. A slight increase of 3.6 ×10-2 𝐿/𝑑 was observed in stage II. In contrast, 𝑞𝑔𝑎𝑠 𝑖𝑛 showed an increase of 5.85 and 11.15 𝐿/𝑑 in stages I and III, respectively, and a reduction of 9.49 𝐿/𝑑 in stage II. Figure 2: ADM1 ME inputs and outputs. (A) ADM1_ME Economic inputs (B) ADM1_ME inputs (C) ADM1_ME Economic outputs. Case 1: Pareto results, case 2: dynamic optimization as a control strategy (Dynamic opt). Disturbance 1-3 (Disturb 1-3). If the EMODO strategy is considered as a decision-making tool in the biomethanation process, it is necessary to refer to the ADM1_ME inputs (Figure 2-B) and the ADM1_ME outputs at a steady state (Figure 2-C). For stages I and III, there were slight decreases in 𝑞𝑙𝑖𝑞 𝑖𝑛 , while the 𝑂𝐿𝑅 doubled, and the 𝑞𝑔𝑎𝑠 𝑖𝑛 increased from 22 to 25 𝐿/𝑑, respectively, resulting in an increase in 𝐺𝐿𝑅 from 0.60 to 0.97 𝐿 𝐿𝑟/𝑑⁄ . This led to an increase in 𝐺𝑎𝑖𝑛 from 1.27×10-3 to 2.68×10-3 𝐸𝑈𝑅 𝐿𝑟/𝑑⁄ , while the 𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛 slightly increased from 33.8% to 36.0%. From a 𝐺𝑎𝑖𝑛 point of view, it can be increased by maintaining similar 𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛𝑠. However, it should be noted that a significant increase in 𝑞𝑔𝑎𝑠 𝑖𝑛 is needed to achieve these changes, as in stage II, where values of 91 𝐿/𝑑 were obtained. 197 3. Conclusions The EMODO strategy demonstrates to be a good alternative to obtain the best 𝐺𝑎𝑖𝑛 and 𝑃𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑟𝑔𝑖𝑛 by manipulating 𝑞𝑔𝑎𝑠 𝑖𝑛 , and 𝑞𝑙𝑖𝑞 𝑖𝑛 . These variables played a key role and ranged between optimal values of 22 - 91 𝐿 𝑑⁄ and 4.00 and 4.22 𝐿 𝑑⁄ through all stages. The proposed strategy shows the conflicting behavior of both economic objectives and the high dependence of the substrates added to the process (the three Pareto fronts, clearly differentiated for each stage). The application of dynamic optimization improves the response, smoothing the transitions between stages. The efficacy of the EMODO strategy is demonstrated with a successful adaptation to three disturbances in the cost of the substrates and the selling price of the products. These results show the feasibility of the proposed methodology as a decision-making tool and its use for multiple control objectives. Acknowledgments The authors would like to acknowledge the financial support of the Ministerio de Ciencias, Tecnología e Innovación (Minciencias) through the Scholarship Program No. 860. This work has also benefited from a State grant managed by the National Research Agency under the "Investissements d'Avenir" programme with the reference ANR-18-EURE-0021. 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