CET-vol 105 DOI: 10.3303/CET23105006 Paper Received: 25 February 2023; Revised: 20 June 2023; Accepted: 22 April 2023 Please cite this article as: Blaiech K., Acosta Pavas J.C., Davidsond S., Ben Gaida L., Gannoun H., Liebgott P.-P., Aceves-Lara C.A., 2023, Multi-objective Optimization of Thermophilic Biohydrogen Production, Chemical Engineering Transactions, 105, 31-36 DOI:10.3303/CET23105006 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 Multi-Objective Optimization of Thermophilic Biohydrogen Production Khadija Blaiecha, Juan C. Acosta-Pavasb, Sylvin Davidsonda,Lamia Ben Gaidac, Hana Gannounc, Pierre-Pol Liebgotta, César A. Aceves-Larab,* aAix-Marseille Université, Université de Toulon, IRD, CNRS MIO UMR235, Marseille, France F-13288 bUniversité de Toulouse; UPS, INSA, INP, F-31077; INRA, UMR792, Toulouse Biotechnology Institute, Bio & Chemical Engineering; CNRS TBI UMR5504, 135 avenue de Rangueil, Toulouse, France F-31077 cUniversité de Tunis El Manar, Laboratoire de Recherche de Bioressources Environnement et Biotechnologies (BeB LR22ES04), Institut Supérieur des Sciences Biologique Appliquées de Tunis (ISSBAT), 9 Avenue Zouhaïer Essafi, 1006 Tunis, Tunisia aceves@insa-toulouse.fr Dynamic optimization of thermophilic hydrogen and by-product production requires the use of robust models coupled with control strategies. In this work, a model was used to optimize biohydrogen (bioH2) and acetate production using Thermotoga maritima (T. maritima) with a Multi-Objective Optimization (MOO). The aim was to find the trade-off between the maxima of yield and productivity of the hydrogen production and acetate in a continuous dark fermentation process by modifying the inlet liquid flow rate. A dynamic mass balance model was used to optimize thermophilic bioH2 and acetate production using T. maritima MSB8 (DSMZ 3109) strains. In this study, the simulations were run using an Intel® Core™ i7-9750 H @ 2.60 GHz, 16 GB RAM computer. The paretosearch integrated function from MATLAB® was used to obtain Pareto Optimal Sets (POSs) for each inlet substrate concentration (𝑆𝑖𝑛). Some constraints were used to fit to the model dynamics of dark fermentation performed by T. maritima. using glucose as a substrate; the maximum theoretical hydrogen yield was 4 𝑚𝑜𝑙 𝐻2 𝑚𝑜𝑙⁄ 𝑔𝑙𝑢𝑐𝑜𝑠𝑒 at 80 °C. The MOO was performed for five different substrate concentrations. The maximum Euclidean distance (𝑑𝑚𝑎𝑥) from the origin of the normalized coordinates was used to select the Pareto Optimal Points (POPs). The simulation results indicate that an 𝑆𝑖𝑛 equal to 70 × 10−3𝑚𝑜𝑙 𝐿⁄ is optimum to significantly maximize/minimize 𝑌 at 3.48 and 0.33 𝑚𝑜𝑙 𝑚𝑜𝑙𝐺𝑙𝑢𝑐𝑜𝑠𝑒𝑖𝑛⁄ and 𝑃 at 3.49 × 10−3 and 1.66 × 10−3 𝑚𝑜𝑙 𝐿 𝐿𝑟𝑒𝑎𝑐𝑡𝑜𝑟⁄⁄ . ℎ simultaneously, respectively, for hydrogen and acetate production. 1. Introduction Dynamic models are commonly used to understand and predict the outcomes of biological processes in various industries, such as wastewater treatment, food production, and bioenergy production (Kim et al., 2018). One of the most important biological processes in bioenergy production is the conversion of organic matter into biogas using microorganisms. Dark fermentation of microorganisms leading to bioH2 production is an example that has been actively investigated for many years for its reported high energy yields (Chandrasekhar et al., 2015). However, many challenges are hindering the full control of the process for scale-up and industrialization perspectives due to the complex nature of the system and the presence of multiple variables that heavily impact the outcomes. A variety of ways have been identified to improve the bioH2 production of microorganisms, including process optimization through predictive and dynamic models. Such models can help further overcome the challenges faced by the bioH2 production industry by informing control strategies that can optimize multiple variables simultaneously. A popular optimization strategy is Multi-Objective Optimization (MOO), which involves optimizing multiple variables that are usually conflicting, such as yield and productivity. MOO is commonly used in the industry to optimize processes where there are multiple objectives, such as reducing energy consumption, minimizing waste, and maximizing profitability (Chang et al., 2015; Vertovec et al., 2021). 31 MOO generates a Pareto Optimal Set (POS), which is a set of optimal solutions, Pareto Optimal Points (POP), for different objectives that cannot be improved without sacrificing the performance of other objectives. This simulation outputs a Pareto front that predicts chosen parameters of a bioprocess (Islam et al., 2021). In this work, a mathematical model describing dark fermentation was combined with MOO dynamics. A published model of a hyperthermophile strain has been used and a previously reported MOO methodology was followed (Auria et al., 2016; Acosta-Pavas et al., 2022). Auria et al. (2016) model has been validated experimentally on a variety of substrates and has proven its capability to simulate and predict the conversion of organic matter into bioH2 with high accuracy. This study proposes a MOO approach to find the trade-off between the maximum yield and productivity of the biogas and a by-product production process, using a POS. Next, following the desired criteria, POPs are selected from the set and used as a reference trajectory for experimental applications and a tool for improving day-to-day performance management at a laboratory or industrial scale. 2. Biohydrogen Model Extension Proposal Dark fermentation by biomass conversion is considered the most promising method, and the most understood process for bioH2 production (Froio and Bezerra, 2021). Dark fermentation is a process in which complex organic substrates are converted in the absence of light, by anaerobic heterotrophic microorganisms, to bioH2, CO2, and various Volatile Fatty Acids (VFAs) (Eq(1) and Eq(2)) (Patel et al., 2018). The theoretical maximum yield of 4 𝑚𝑜𝑙 𝐻2 𝑚𝑜𝑙⁄ ℎ𝑒𝑥𝑜𝑠𝑒 (Thauer et al. 1977) can be achieved when 2 moles of acetate is produced during dark fermentation (see Eq(1)). 𝐻𝑒𝑥𝑜𝑠𝑒 + 2 𝐻2𝑂 → 2 𝐴𝑐𝑒𝑡𝑎𝑡𝑒 + 4 𝐻2 + 2 𝐶𝑂2 (1) 𝐻𝑒𝑥𝑜𝑠𝑒 → 𝐵𝑢𝑡𝑦𝑟𝑎𝑡𝑒 + 2 𝐻2 + 2 𝐶𝑂2 (2) However, this maximum yield (or Thauer limit) can only be achieved with thermophilic H2-producing microorganisms. Most of these thermophilic microorganisms can hydrolyze various polysaccharides and ferment the released hexoses and pentoses. So far, the hydrogen-producing (hyper)thermophilic microbial species studied belong essentially to the classes Clostridia, Thermotoga, and Thermococcales (Pradhan et al., 2015). Thermotoga, hyperthermophile marine bacteria, are considered the preferred option for bioH2 production and industrial purposes since they can produce high H2 yields (2.4 to 3.85 𝑚𝑜𝑙 𝐻2 𝑚𝑜𝑙⁄ ℎ𝑒𝑥𝑜𝑠𝑒) from many organic wastes (Saidi et al., 2018). Overall, H2 production yields from dark fermentation by pure cultures such as T. maritima has been reported to reach up to 3.05 𝑚𝑜𝑙 𝐻2 𝑚𝑜𝑙⁄ ℎ𝑒𝑥𝑜𝑠𝑒. T. maritima. is a hyperthermophile bacterium found in marine environments and is known to produce hydrogen yields close to the thermodynamic limit (Thaeur limit) from a large variety of substrates (Boileau et al., 2016). However, acetate, but also lactate, are the main organic products of the fermentation performed by T. maritima. Indeed, when the culture conditions are not optimal, T. maritima redirects the reoxidation of its cofactors towards the production of lactate, thus limiting the production of bioH2. T. maritima has been extensively studied and a modeling approach to various batch experiments was carried out by Auria et al. (2016) (Auria et al., 2016). The batch experiments were carried out in a 2 𝐿 bioreactor with a working volume (𝑉𝑙𝑖𝑞) of 1.5 𝐿 and lasted for 10.1 ℎ operating at 80 °𝐶. The initial substrate concentrations were: 14 × 10−3 𝑚𝑜𝑙 𝐿⁄ of glucose, 1𝑔 𝐿⁄ of yeast extract, and 0.12 𝑔 𝐿⁄ of thiosulfate. These values are reported in Table 1. The inlet gas flow rate and stirring were maintained constant throughout the entire experiment at 8.33𝑚3 𝑠⁄ and 36.65 𝑟𝑎𝑑 𝑠⁄ , respectively. Table 1: Experimental data from the literature (Auria et al., 2016) Biomass Substrate concentration × 10−3(𝑚𝑜𝑙 𝐿⁄ ) ; (𝑔 𝐿⁄ ) Product concentration in the liquid phase × 10−3(𝑚𝑜𝑙 𝐿⁄ ) Product concentration in the gas phase × 10−3(𝑚𝑜𝑙 𝐿⁄ ) Time (ℎ) X (𝑔 𝐿⁄ ) Glucose Yeast Extract Thiosulfate Acetate Lactate H2 CO2 0 0.053 14 1 0.12 - - - - 10.1 0.155 0 22 - 22 9 35 79 Following a previously published methodology, an extension of the Auria et al. (2016) model is proposed to convert the operational reactor mode from a batch to a continuous culture. Adjustments of the dynamic model were carried out and the inlet liquid flow rate with respect to the component concentration change was added to the equations. This was a necessary step to be able to apply a MOO strategy. 32 To present and simplify the changes made, we have defined the gas (𝑆𝑔𝑎𝑠, 𝑖) liquid (Sliq, j) and biomass growth (𝑋) phases as state variables represented in Eq(1), Eq(2), and Eq(3), respectively as, dSgas,i dt = Ni ( Vliq Vgas ) − qgas Vgas Sgas,i (3) dSliq,j dt = qliq, in Vliq (Sj, in l −Sliq,j) +∑𝛽jµX− Ni (4) 𝑑𝑋 𝑑𝑡 = − 𝑞𝑙𝑖𝑞, 𝑖𝑛 𝑉𝑙𝑖𝑞 𝑋 + (µ − µd)𝑋 (5) where the sub-indexed variables are: 𝑖 = H2, CO2, and H2S in the gas phase; 𝑗 = glucose, yeast extract, thiosulfate, acetate, lactate, extracellular polysaccharides, H2, CO2, and H2S in the liquid phase. 𝑉𝑔𝑎𝑠 and 𝑉𝑙𝑖𝑞 = volume of the gas and liquid fraction, respectively; 𝛽j = the stoichiometric coefficient of components 𝑗; 𝑗 = Sgas,i and 𝑆𝑗, 𝑖𝑛 𝑙 = outlet and inlet concentrations of component 𝑖 and 𝑗 in the gas and liquid phases, respectively; 𝑋 = is the concentration of biomass; 𝑁i = the mass transfer of component 𝑖; 𝑞𝑔𝑎𝑠 : and qliq, in = the total outlet gas and inlet liquid flowrates, respectively; µ and µd = the specific growth and death rates constants of biomass. 3. Multi-Objective Optimization Multi-Objective Optimization (MOO) implies solving multiple problems simultaneously where more than one variable is to be optimized (Chang, 2015; Vertovec, Ober-Blöbaum Margellos, 2021). Usually, variables to be optimized in a bioprocess are conflicting. Productivities, yields, experimental stage, and process durations are examples of variables that are usually conflicting and therefore difficult to optimize. Ultimately, the goal of MOO dynamics is to find a balance that maximizes the targeted outcomes of the process. The outcome of a MOO model simulation is a Pareto front. A Pareto front allows the visualization of the obtained Pareto Optimal Set (POS). A POS is an optimal solution set composed of multiple Pareto Optimal Points (POPs). Lastly, POPs are parameter values, indicators, or coordinates that fulfill the desired conditions of conflicting variables (Deb et al., 2002). Generally, a MOO can be formulated as, min 𝑥,𝑢,𝑝,𝑡 {𝑌1(𝑥, 𝑢, 𝑝),… , 𝑌𝑚(𝑥, 𝑢, 𝑝)} s𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 { 𝑑𝑥 𝑑𝑡⁄ = 𝑓(𝑥, 𝑢, 𝑝, 𝑡) 𝑡 ∈ [0, 𝑡𝑓] 𝑓𝑖(𝑥, 𝑢, 𝑝, 𝑡) ≤ 0 𝑖 = 1,2,… , 𝑛 𝑔𝑖(𝑥, 𝑢, 𝑝, 𝑡) = 0 𝑖 = 1,2,… , 𝑘 𝑢𝐿 ≤ 𝑢 ≤ 𝑢𝑈 (6) where 𝑌1, … , 𝑌𝑚 = 𝑚 objective functions; 𝑥 = to the state variables; 𝑢 and 𝑝 = the control variables and parameters; 𝑓𝑖 and 𝑔𝑖 = inequality and equality constraints on the variable states; 𝑢𝐿 and 𝑢𝑈 = indicate the control variables’ lower and upper bounds (Tsiantis et al., 2018). Based on the desired outcomes, a MOO strategy is proposed to identify the best possible values for the objective functions. The MOO methodology comprises three main steps: firstly, defining the model that represents the biological process, secondly, specifying the objective functions 𝑌1, … , 𝑌𝑚 to be minimized or maximized, including the control variables 𝑢 and the constraints that are lower and upper bounds 𝑢𝐿 and 𝑢𝑈, selecting the conflicting variables to be optimized for the objective functions 𝑌1 ∗, … , 𝑌𝑚 ∗ .which will be used as a reference in the optimization process. Finally, a POS is obtained from which one or more POPs are selected following certain criteria defined by the end user. 4. Case Study: Multi-Objective Optimization in Dark Fermentation Bioprocess The primary goal of the study was to optimize, independently, H2 and acetate production processes by maximizing their respective yields (𝑌𝐻2𝑎𝑛𝑑 𝑌𝐴𝑐𝑒𝑡𝑎𝑡𝑒) and productivities (𝑃𝐻2 𝑎𝑛𝑑 𝑃𝐴𝑐𝑒𝑡𝑎𝑡𝑒). To reach this goal, it proposes different sets denoted Pareto optimal sets (POS) of POPs following two chosen control variables: the inlet liquid concentration 𝑆𝑖𝑛 and liquid flow rate 𝑞𝑙𝑖𝑞,𝑖𝑛.This would allow the user to minimize experimental costs by developing an experimental design based on the experimental conditions forecasted by the model. To optimize hydrogen production, 𝑌𝐻2 was defined as the amount of hydrogen production rate (𝑞𝑔𝑎𝑠,𝐻2) over 𝑆𝑖𝑛, while 𝑃𝐻2 represents the ratio of 𝑞𝑔𝑎𝑠,𝐻2 to 𝑉𝑙𝑖𝑞, as follows. 𝑌𝐻2 = 𝑞𝑔𝑎𝑠,𝐻2 S𝑖𝑛 (7) 33 𝑃𝐻2 = 𝑞𝑔𝑎𝑠,𝐻2 𝑉𝑙𝑖𝑞 (8) As for acetate, 𝑌𝑎𝑐𝑒𝑡 was defined as the final concentration of acetate produced (SA𝑐𝑒𝑡,𝑜𝑢𝑡) over 𝑆𝑖𝑛, while 𝑃𝐴𝑐𝑒𝑡 represents the ratio between SA𝑐𝑒𝑡,𝑜𝑢𝑡 multiplied by 𝑞𝑙𝑖𝑞,𝑖𝑛 and 𝑉𝑙𝑖𝑞 expressed as, 𝑌𝐴𝑐𝑒𝑡 = SA𝑐𝑒𝑡,𝑜𝑢𝑡 S𝑖𝑛 (9) 𝑃𝐴𝑐𝑒𝑡 = SA𝑐𝑒𝑡,𝑜𝑢𝑡 × 𝑞𝑙𝑖𝑞,𝑖𝑛 𝑉𝑙𝑖𝑞 (10) where (𝑞𝑔𝑎𝑠,𝐻2) was calculated as, 𝑞𝑔𝑎𝑠, 𝐻2 = 𝑞𝑔𝑎𝑠 ( 𝑃𝑔𝑎𝑠,𝐻2 𝑃𝑔𝑎𝑠 ) (11) with 𝑃𝑔𝑎𝑠 and 𝑃𝑔𝑎𝑠,𝐻2 = the total pressure in the bioreactor and partial pressure of 𝐻2 in 𝑃𝑎. In this work, multiple simulations were run using an Intel® Core™ i7-9750H @ 2.60 GHz, 16 GB RAM computer. The paretosearch function provided by MATLAB® was used to obtain Pareto optimal set for each 𝑆𝑖𝑛. The MOO was proposed as, 𝑚𝑎𝑥 {𝑞𝑙𝑖𝑞, 𝑖𝑛} (𝑌𝐻2 , 𝑃𝐻2) 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 { 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛𝑠 (3) − (8) 𝑎𝑛𝑑 (11) 𝑌𝐻2 ≤ 4 [𝑚𝑜𝑙 𝐻2 𝑚𝑜𝑙⁄ 𝑔𝑙𝑢𝑐𝑜𝑠𝑒] 1 × 10−3 ≤ 𝑞𝑙𝑖𝑞,𝑖𝑛 ≤ 1 [𝐿/ℎ] (12) 𝑚𝑎𝑥 {𝑞𝑙𝑖𝑞, 𝑖𝑛} (𝑌𝐴𝑐𝑒𝑡 , 𝑃𝐴𝑐𝑒𝑡) 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 { 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛𝑠 (3) − (6) and (9) − (11) 𝑌𝐻2 ≤ 4 [𝑚𝑜𝑙 𝐻2 𝑚𝑜𝑙⁄ 𝑔𝑙𝑢𝑐𝑜𝑠𝑒] 1 × 10−3 ≤ qliq, in ≤ 1 [𝐿/ℎ] (13) where Eq(12) and Eq(13) state the constraints that were used where Eq(3) − Eq(5) represent the model dynamics and 4 𝑚𝑜𝑙 𝐻2 𝑚𝑜𝑙⁄ 𝑔𝑙𝑢𝑐𝑜𝑠𝑒 is the theoretical yield limit (Thauer limit) mentioned previously. The MOO was performed for five 𝑆𝑖𝑛 concentrations such that 𝑆𝑖𝑛 [× 10 −3𝑚𝑜𝑙 𝐿⁄ ] ∈ {14, 42, 70, 90, 110}. The POS was composed of 60 points for every 𝑆𝑖𝑛. 5. Selection of Pareto Optimal Points (POPs) A normalization of POSs [0, 1] was performed in order to perform the selection. Three POPs were chosen to maximize the yield and productivity: the first POP to maximize productivity, the second to maximize Euclidean distance (𝑑𝑚𝑎𝑥) from the origin to the standardized coordinates, and the third to maximize yield. The results are summarized in Table 2. Table 2. Multi-Objective optimization results. Substrate concentration (𝑆𝑖𝑛) (× 10−3𝑚𝑜𝑙 𝐿⁄ ) POP for maximum Yield (𝑌) for hydrogen for acetate 𝑌H2 (𝑚𝑜𝑙𝐻2 𝑚𝑜𝑙𝐺𝑙𝑢𝑐𝑜𝑠𝑒𝑖𝑛⁄ ) 𝑃H2 × 10 −3 (𝑚𝑜𝑙 𝐿𝐻2 𝐿𝑟𝑒𝑎𝑐𝑡𝑜𝑟⁄⁄ . ℎ) 𝑌Acet (𝑚𝑜𝑙𝐴𝑐𝑒𝑡 𝑚𝑜𝑙𝐺𝑙𝑢𝑐𝑜𝑠𝑒𝑖𝑛⁄ ) 𝑃𝐴𝑐𝑒𝑡 × 10 −3 (𝑚𝑜𝑙 𝐿𝐴𝑐𝑒𝑡 𝐿𝑟𝑒𝑎𝑐𝑡𝑜𝑟⁄⁄ . ℎ) 14 3.9906 2.3542 1.4678 0.2141 42 3.8406 3.3605 1.2171 0.2536 70 3.9550 3.4624 0.6380 0.5583 90 3.9302 3.4927 0.4329 0.6313 110 3.9644 3.5074 0.3473 0.6511 for maximum Euclidean distance (𝑑𝑚𝑎𝑥) 14 3.2867 2.4859 1.1690 0.9550 42 3.5509 3.3987 0.7952 1.3254 70 3.5566 3.5125 0.5209 1.3327 90 3.7967 3.4993 0.2684 1.5657 110 3.7917 3.5125 0.2574 1.3517 34 Substrate Concentration (𝑆𝑖𝑛) (× 10−3𝑚𝑜𝑙 𝐿⁄ ) POP for maximum productivity(𝑃) for hydrogen for acetate 𝑌H2 (𝑚𝑜𝑙𝐻2 𝑚𝑜𝑙𝐺𝑙𝑢𝑐𝑜𝑠𝑒𝑖𝑛⁄ ) 𝑃H2 × 10 −3 (𝑚𝑜𝑙 𝐿𝐻2 𝐿𝑟𝑒𝑎𝑐𝑡𝑜𝑟⁄⁄ . ℎ) 𝑌Acet (𝑚𝑜𝑙𝐴𝑐𝑒𝑡 𝑚𝑜𝑙𝐺𝑙𝑢𝑐𝑜𝑠𝑒𝑖𝑛⁄ ) 𝑃𝐴𝑐𝑒𝑡 × 10 −3 (𝑚𝑜𝑙 𝐿𝐴𝑐𝑒𝑡 𝐿𝑟𝑒𝑎𝑐𝑡𝑜𝑟⁄⁄ . ℎ) 14 2.8644 2.5085 0.7319 1.2542 42 2.9857 3.4261 0.5817 1.4420 70 3.4779 3.4857 0.3068 1.6610 90 3.6579 3.5023 0.1872 1.6956 110 3.7199 3.5130 0.1418 1.6949 Figures 1-(A) and (B) show the POSs of hydrogen (left) and acetate (right) for the different initial substrate concentrations tested. The selected POPs were highlighted in orange, yellow, and purple shapes for maximum 𝑌, 𝑑𝑚𝑎𝑥 and 𝑃, respectively. The result of the simulation shows that POSs ranges are narrower as we increase 𝑆𝑖𝑛 and 𝑌𝐻2, 𝑃𝐻2, and 𝑃𝐴𝑐𝑒𝑡 increases in contrast to 𝑌𝐴𝑐𝑒𝑡. However, the rise for 𝑃𝐻2 and 𝑃𝐴𝑐𝑒𝑡 ranges are noticeable from 𝑆𝑖𝑛 ≥ 42 × 10−3𝑚𝑜𝑙 𝐿⁄ and was almost unchanged beyond 70 × 10−3𝑚𝑜𝑙 𝐿⁄ . The same behavior is observed for 𝑌𝐻2and 𝑌𝐴𝑐𝑒𝑡 POS boundaries from 𝑆𝑖𝑛 ≥ 70 × 10 −3𝑚𝑜𝑙 𝐿⁄ . The simulation results indicate that an 𝑆𝑖𝑛 equal to 70 × 10−3𝑚𝑜𝑙 𝐿⁄ is optimum to significantly maximize/minimize 𝑌 and 𝑃 simultaneously for both products. Moreover, studies of continuous-flow dark fermentation reported that at higher carbohydrate (organic) loading rates, bioH2 production is inhibited by the overaccumulation of hydrogen gas in the working volume (Van Ginkel and Logan, 2005). It is important to mention that this parameter is taken into account in our proposed model and during our simulations and therefore could explain our results. Thus, the increase of 𝑆𝑖𝑛 beyond 70 × 10−3𝑚𝑜𝑙 𝐿⁄ indicates that the carbohydrate source, glucose, is not the limiting factor in those conditions and bioH2 production could solely be limited by T. maritima growth rate. 6. Conclusion A MOO strategy for the bioH2 production process based on the mathematical model used for the two objectives (maximization of 𝑌 and 𝑃) was successfully developed for both hydrogen and acetate production. We analyzed 10 cases, where it was observed that maximizing 𝑃 lowers 𝑌 ratio and vice versa. It is observed that by increasing the substrate concentration (𝑆𝑖𝑛) of the inlet liquid, maximum productivity increases whereas maximum yield decreases for acetate. It was also shown that the hydrogen yield is improved by increasing the substrate concentration (𝑆𝑖𝑛) of the inlet liquid. The simulation results indicate that an 𝑆𝑖𝑛 equal to 70 × 10−3𝑚𝑜𝑙 𝐿⁄ is optimum to significantly maximize/minimize 𝑌 and 𝑃 simultaneously for both products. Future work includes the validation of the model using experimental data, the application of the dynamic MOO methodology, and the use of an economic Pareto, allowing the estimations of the purchase price of substrates or the sale of bioH2 or acetate. Figure 1: (A). POSs for 𝑆𝑖𝑛 [× 10 −3𝑚𝑜𝑙 𝐿⁄ ] ∈ {14, 42, 70, 90, 110}, and selected POPs for yield and productivity maximization and maximum Euclidean length for hydrogen and (B). acetate produced. 35 Acknowledgments This publication was made possible through support provided by the IRD. References Acosta-Pavas, J.C., Robles-Rodríguez, C.E., Méndez, C.A.S., Morchain, J., Dumas, C., Cockx, A., Aceves- Lara, C.A., n.d. 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