Model-based Multi-objective Optimization Research Articles

Multi-objective optimization and energy efficiency improvement for rotor duct in integrated energy recovery-pressure boost device

To reduce the volumetric mixing rate of the integrated energy recovery-pressure boost device, a novel symmetrical duct structure with diversion surface was proposed. The surrogate model-based multi-objective optimization framework was established, and obtained the optimal ducts V1 and V2 combined with computational fluid dynamics simulation. Numerical results indicate that optimized duct structure could promote the formation of plug flow and effectively improve the collision efficiency between high-pressure brine and low-pressure seawater, and the volumetric mixing rate corresponding to the ducts V1 and V2 was reduced by 31.52% and 22.18%, and the duct volume efficiency was increased by 16.04% and 19.56%, respectively. Finally, the performance of optimized device was verified through seawater reverse osmosis desalination system under actual working conditions. Experimental results showed that the mixing rate of optimized ducts had a significant decrease of 30.86% and 20.53% in the applicable range, and the energy recovery efficiency improved at most 5.41% and 7.55%, respectively. The optimized ducts could significantly reduce the specific energy consumption of the desalination system by 26.01% and 18.22%, respectively, and the specific energy consumption reached the lowest level of 3.02 kWh/m3, demonstrating the superiority of the structure and the accuracy and effectiveness of the optimization strategy.

Interpretable GBDT model-based multi-objective optimization analysis for the lateral inlet/outlet design in pumped-storage power stations

ABSTRACT The uneven velocity distribution formed at the lateral inlet/outlet poses a significant risk of damaging the trash racks. Reasonable design of the inlet/outlet structures requires the consideration of two major aspects: the average velocity (Vm) and the coefficient of unevenness (Uc). This paper developed an optimization framework that combines an interpretable Gradient Boosting Decision Tree (SOBOL-GBDT) with a Non-dominated Sorting Genetic Algorithm (NSGA-II). 125 conditions are simulated by performing CFD simulations to generate the dataset, followed by GBDT implemented to establish a nonlinear mapping between the input parameters including vertical (α) and horizontal (β) diffusion angles, diffusion segment length (LD), channel area (CA), and the objectives Uc and Vm. The SOBOL analysis reveals that in Uc prediction, CA and α play more significant roles in the model development compared to β and LD. Besides, GBDT is observed to better capture interactive effects of the input parameters compared with other machine learning models. Subsequently, a multi-objective optimization framework using GBDT-NSGA-II is developed. The framework calculates the optimal Pareto front and determines the best solution using a pseudo-weight method. The results demonstrate that this framework leads to significant improvements in flow separation reduction in the diffusion segment and the normalized velocity distribution. The SOBOL-GBDT-NSGA-II framework facilitates a rational and effective design of the inlet/outlet.

Local machine learning model-based multi-objective optimization for managing system interdependencies in production: A case study from the ironmaking industry

Modeling interdependencies in a production process is a vital aspect of process engineering. Being built on the fundamental understanding of the process and capturing underlying physical and chemical mechanisms, this task is traditionally carried out through first-principle modeling. However, due to various assumptions and parameter approximation, such approach sometimes struggles to accurately model process dynamics. This is partially due to the requirements for process stability in mission-critical scenarios, where it is not viable to conduct extensive experiments that would enable the development of comprehensive models, and hence, the process control is still partially dependent on the experience of the process operator. In this paper, a data-driven approach based on production data is introduced to address the challenge of discovering, understanding, and modeling interdependencies in a production process by constructing a constrained multi-objective optimization problem. The applicability of the proposed approach is demonstrated through a case study in the ironmaking industry, whereby a set of Machine Learning and causality-based methods is provided while highlighting the significance of transparency and use of domain knowledge in the development of data-driven models. Based on the real data from a Sintering plant, interdependencies are quantified between five key process parameters, which, when supplemented with other control parameters, result in a higher overall process output leading to reductions in operational costs and environmental impact. Such approach shows potential for applications in a broader context across other fields of science and engineering, where it can be used to improve the discovery of interdependencies in complex real-world industrial settings.

Surrogate model-based multi-objective optimization algorithm for train-ballast turnout system: Balancing safety and vibration damping in parameter design

In rail transportation structural parameter design, multi-objective optimal algorithms (MOOAs) have advanced significantly in safety, comfort, and aerodynamics domain. However, the vital factor of environment vibration remains neglected, impeding depot cover technology advancements. To address this challenge, with a focus on both safety and vibration damping. Firstly, the mechanistic models are constructed to establish a surrogate modeling database. Subsequently, a surrogate model is proposed, integrating stacked denoising autoencoders (SdAEs), self-attention (SA), and the gated recurrent unit (GRU). In addition, A novel MOOA, Dynamic Population-Multi-Objective Harris Hawks Optimization-Crowding Distance-Elitist Learning Strategy (D-MOHHO-CD-ELS), is proposed and its efficacy is validated against five existing MOOAs using the CTP1∼CTP7 test functions. Moreover, the train-ballast No.12 turnout system is considered as an engineering case. Importantly, the accuracy of both the mechanistic model and surrogate model is thoroughly validated. Among them, the performance of the data preprocessing and prediction algorithms is substantiated through a comparison of the proposed SdAEs-SA-GRU model against simulation results and eight other algorithms. Furthermore, the surrogate-based D-MOHHO-CD-ELS method, applied to tackle a multi-objective optimization problem with nine optimization parameters and four optimization objectives, demonstrates an efficiency improvement of 1 to 2 orders of magnitude compared to traditional methods. Consequently, following optimization, the wheel load reduction rate, derailment coefficient, capsizing coefficient and vibration damping effect are improved by 15.5%, 11.1%, 5.5% and 24.8% respectively, which reveals the effectiveness of enhancements in both the safety and damping efffect. the study offers a novel perspective for parameter design of TBT.

Surrogate model-based multi-objective design optimization of vibration suppression effect of acoustic black holes and damping materials on a rectangular plate

The acoustic black hole (ABH) is a ground-breaking passive technology for vibration reduction and noise attenuation, characterized by its ability to manipulate flexural waves. When multiple two-dimensional ABHs are embedded in an irregular shaped complex plate structure used in engineering, such as the support plate of a refrigerator compressor, its vibration characteristics often cannot be solved through analytical or semi-analytical methods, resulting in the inability to carry out subsequent ABH optimization design. To address this issue, we propose a high-precision modelling method that combines surrogate models with finite element methods to construct a vibration characteristic database of the compressor support plate embedded with multiple ABHs in all design spaces of the ABH and damping materials geometric parameters using limited sample data. A high-precision surrogate model was constructed based on the vibration response data of the ABH plate under 50 parameter combinations of ABH and damping layer, and the fitting accuracy of the surrogate model was verified through vibration response data under another 25 parameter combinations. Based on the constructed surrogate model, the Multi-objective Genetic Algorithm (MOGA) was employed to optimize the five parameters of ABH and damping layer simultaneously, aiming to maximize the vibration reduction effect of the ABHs. Our investigation reveals that the optimized ABH and damping materials significantly improve the vibration suppression effect in a wide frequency range compared to the unoptimized structures. Finally, experimental verification was conducted to solidify the accuracy and efficacy of our approach in enhancing vibration reduction effect for irregular shaped complex plate structures using acoustic black holes.

Pushing the boundaries of phosphorylase cascade reaction for cellobiose production II: Model-based multiobjective optimization.

The inherent complexity of coupled biocatalytic reactions presents a major challenge for process development with one-pot multienzyme cascade transformations. Kinetic models are powerful engineering tools to guide the optimization of cascade reactions towards a performance suitable for scale up to an actual production. Here, we report kinetic model-based window of operation analysis for cellobiose production (≥100 g/L) from sucrose and glucose by indirect transglycosylation via glucose 1-phosphate as intermediate. The two-step cascade transformation is catalyzed by sucrose and cellobiose phosphorylase in the presence of substoichiometric amounts of phosphate (≤27 mol% of substrate). Kinetic modeling was instrumental to uncover the hidden effect of bulk microviscosity due to high sugar concentrations on decreasing the rate of cellobiose phosphorylase specifically. The mechanistic-empirical hybrid model thus developed gives a comprehensive description of the cascade reaction at industrially relevant substrate conditions. Model simulations serve to unravel opposed relationships between efficient utilization of the enzymes and maximized concentration (or yield) of the product within a given process time, in dependence of the initial concentrations of substrate and phosphate used. Optimum balance of these competing key metrics of process performance is suggested from the model-calculated window of operation and is verified experimentally. The evidence shown highlights the important use of kinetic modeling for the characterization and optimization of cascade reactions in ways that appear to be inaccessible to purely data-driven approaches.

Hybrid Surrogate Model-Based Multi-Objective Lightweight Optimization of Spherical Fuel Element Canister

A number of canisters need to be lightweight designed to store the spherical fuel elements (SFE) used in high-temperature gas-cooled reactors (HTGR). The main challenge for engineering is pursuing high-accuracy and high-efficiency optimization simultaneously. Accordingly, a hybrid surrogate model-based multi-objective optimization method with the numerical method for the lightweight and safe design of the SFE canister is proposed. To be specific, the drop analysis model of the SFE canister is firstly established where the finite element method—discrete element method (FEM–DEM) coupled method is integrated to simulate the interaction force between the SFE and canister. Through simulation, the design variables, optimization objectives, and constraints are identified. Then the hybrid radial basis function—response surface method (RBF–RSM) surrogate method is carried out to approximate and simplify the accurate numerical model. A non-dominated sorting genetic algorithm (NSGA-II) is used for resolving this multi-objective model. Optimal design is validated using comprehensive comparison, and the reduction of weight and maximum strain can be up to 2.46% and 44.65%, respectively. High-accuracy simulation with high-efficiency optimization is successfully demonstrated to perform the lightweight design on nuclear facilities.

Surrogate Model-Based Multiobjective Optimization of High-Speed PM Synchronous Machine: Construction and Comparison

This article employs surrogate models for large-scale high-speed (HS) electrical machine optimization to reduce heavy computational burden caused by the finite-element method (FEM) based on nondominated sorting genetic algorithm II. Three artificial neural networks, namely, multilayer perceptron (MLP), support vector regression (SVR), and generalized regression neural network (GRNN), and the classical Kriging model are developed based on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> -fold crossing validation method. To find out the most suitable surrogate model, a HS permanent magnet synchronous machine (PMSM) applied in electrically assisted turbocharger (EATC) considering its multiphysics characteristics is optimized by different models. A detailed comparison is provided in terms of prediction accuracy and modeling time consumption. The optimal design is verified to guarantee the accuracy of optimization results. The key contributions of this article include an automatic HSPMSM optimization process is proposed, where complete modeling and tuning method as well as a reasonable comprehensive evaluation metric of different surrogate models are conducted. It is found that invalid samples from the initial dataset contain useful information to improve prediction accuracy. Hence, an entire surrogate process should benefit from a pretrained classifier. Also, it reveals that MLP, SVR, and Kriging model can greatly improve the design optimization effectiveness with high accuracy, whereas GRNN is not suitable for this specific optimization scenario.

Multi-objective optimization under parametric uncertainty: A Pareto ellipsoids-based algorithm

Model-based multi-objective optimization is a useful tool to compute optimal trade-offs between multiple conflicting objectives such as minimizing energy consumption while maximizing productivity. However, the computational cost of solving such optimization problems is high. In addition, a model approximates the real process, meaning uncertainty is inherently present. To avoid erroneous predictions of process performance and unsafe operation conditions, this uncertainty should be accounted for. Adding uncertainty propagation techniques increases the computational cost even further. In this article, a novel algorithm is presented that efficiently computes relevant Pareto points based on a significance criterion using Pareto ellipsoids. These ellipsoids represent and visualize the uncertainty on the objective functions due to parametric uncertainty. This facilitates the selection of the Pareto points as it allows a decision-maker to easily consider the uncertainty of a solution. The algorithm is showcased using three case studies with different levels of complexity.

Surrogate Model-based Multi-Objective Optimization in Early Stages of Ship Design

The abstract is the early stages of ship design, the decision of the ship's main dimensions significantly impacts the ship's performance and the total cost of ownership. This paper focuses on an optimization approach based on surrogate models at the early stages of ship design. The objectives are to minimize power requirements and building costs while still satisfying the constraints. We compare three approaches of surrogate models: Kriging, BPNN-PSO (Backpropagation Neural Network-Particle Swarm Optimizer), and MLP (Multi-Layer Perceptron) in two multi-objective optimization algorithms: MOEA/D (Multi-Objective Evolutionary Algorithm Decomposition) and NSGA-II (Non-Dominated Sorting Genetic Algorithm II). The experimental results show that MLP surrogate models get the best performance with MAE 6.03, and BPNN-PSO gets the second position with MAE 7.2. BPNN-PSO and MLP with MOEA/D and NSGA-II improve the design with around 58% smaller adequate power and 6% less steel weight than the original design. However, BPNN-PSO and MLP have lower hypervolume than Kriging for both optimization algorithms MOEA/D and NSGA-II. On the other hand, Kriging has the most inadequate model accuracy performance, with an MAE of 22.2, but produces the highest hypervolume, lowest computational time, and far lower objective values than BPNN-PSO and MLP for both optimization algorithms, MOEA/D and NSGA-II. Nevertheless, the three surrogate model approaches can significantly improve ship design solutions and reduce work time in the early stages of design.

A Surrogate Model Based Multi-Objective Optimization Method for Optical Imaging System

An optimization model for the optical imaging system was established in this paper. It combined the modern design of experiments (DOE) method known as Latin hypercube sampling (LHS), Kriging surrogate model training, and the multi-objective optimization algorithm NSGA-III into the optimization of a triplet optical system. Compared with the methods that rely mainly on optical system simulation, this surrogate model-based multi-objective optimization method can achieve a high-accuracy result with significantly improved optimization efficiency. Using this model, case studies were carried out for two-objective optimizations of a Cooke triplet optical system. The results showed that the weighted geometric spot diagram and the maximum field curvature were reduced 5.32% and 11.59%, respectively, in the first case. In the second case, where the initial parameters were already optimized by Code-V, this model further reduced the weighted geometric spot diagram and the maximum field curvature by another 3.53% and 4.33%, respectively. The imaging quality in both cases was considerably improved compared with the initial design, indicating that the model is suitable for the optimal design of an optical system.

A Novel Resolution Scheme of Time-Energy Optimal Trajectory for Precise Acceleration Controlled Industrial Robot Using Neural Networks

The surging popularity of adopting industrial robots in smart manufacturing has led to an increasing trend in the simultaneous improvement of the energy costs and operational efficiency of motion trajectory. Motivated by this, multi-objective trajectory planning subject to kinematic and dynamic constraints at multiple levels has been considered as a promising paradigm to achieve the improvement. However, most existing model-based multi-objective optimization algorithms tend to come out with infeasible solutions, which results in non-zero initial and final acceleration. Popular commercial software toolkits applied to solve multi-objective optimization problems in actual situations are mostly based on the fussy conversion of the original objective and constraints into strict convex functions or linear functions, which could induce a failure of duality and obtain results exceeding limits. To address the problem, this paper proposes a time-energy optimization model in a phase plane based on the Riemann approximation method and a solution scheme using an iterative learning algorithm with neural networks. We present forward-substitution interpolation functions as basic functions to calculate indirect kinematic and dynamic expressions introduced in a discrete optimization model with coupled constraints. Moreover, we develop a solution scheme of the complex trajectory optimization problem based on artificial neural networks to generate candidate solutions for each iteration without any conversion into a strict convex function, until minimum optimization objectives are achieved. Experiments were carried out to verify the effectiveness of the proposed optimization solution scheme by comparing it with state-of-the-art trajectory optimization methods using Yalmip software. The proposed method was observed to improve the acceleration control performance of the solved robot trajectory by reducing accelerations exceeding values of joints 2, 3 and 5 by 3.277 rad/s2, 26.674 rad/s2, and 7.620 rad/s2, respectively.

Surrogate model-based multiobjective design optimization for air-cooled battery thermal management systems

ABSTRACT A well-designed battery thermal management system (BTMS) can achieve optimal cooling performance with less power consumption than a poorly-designed system. However, it is difficult to use the computational fluid dynamics (CFD) method to perform an effective and optimal design of BTMSs when there are several structural design parameters and multiple evaluation criteria. In this paper, instead of CFD, a compound surrogate model based on the mixture of experts (MoE) method is developed to accurately approximate the BTMS performance of different structural configurations. Then, the multiple criteria evaluation of the structural design is transformed into a multiobjective optimization (MOO) problem, which is solved by the nondominated sorting genetic algorithm II (NSGA-II). To address the nonuniqueness of the optimal solutions and the contradiction between evaluation criteria, the entropy weight method (EWM) and criteria importance through the intercriteria correlation (CRITIC) method are applied to analyze the weight of each evaluation criterion. Finally, the optimal structural parameters are obtained for the corresponding weights. The results show that the surrogate-based MOO can find a structural design that meets expectations, and this approach can provide guidelines for the design of BTMSs.

Multi-Objective Optimization of an Axial Flow Turbine Design Using Surrogate Modeling and Genetic Algorithm

Abstract A surrogate model-based multi-objective design optimization methodology using a nondominated sorting genetic algorithm is used to maximize the power output and efficiency of an axial flow turbine. A set of high-fidelity data obtained from ANSYS-CFD simulations on space-filling samples is used for developing a surrogate model. The methodology uses (i) a Latin hypercube experimental design for selecting space-filling samples, (ii) a genetic algorithm for determining parameters of a Kriging model, and (iii) axial gap, tip clearance, and rotation angle of nozzle profile of turbine as predictor variables. Flow in the turbine is characterized by the presence of jet and wake flow, shock in the rotor blade flow passage, and tip clearance vortex. Study shows that (i) the axial gap controls the mixing of the jet and the wake flows and provides proper blade incidence which reduces the shock strength in the rotor blade flow passages and (ii) an optimum sized tip clearance vortex controls tip clearance leakage. The optimization provided a set of Pareto-optimal solutions that are nondominated in terms of power and efficiency. Verification of a selected design configuration from the Pareto-optimal solution using computational fluid dynamics (CFD) analysis showed that the process of optimization has been able to fine-tune the axial gap and the tip clearance.

Optimal fed-batch bioreactor operating strategies for the microbial production of lignocellulosic bioethanol and exploration of their economic implications: A step forward towards sustainability and commercialization

The enduring adoption of greener technologies from the biofuel manufacturing industries requires the balanced integration of multiple inter-disciplinary concerns (i.e., engineering, business, sustainability, societal) to make production processes more attractive to the industrial sector. From an engineering perspective, the commercial establishment of lignocellulosic bioethanol plants is still hindered by increased production cost. High product concentrations with improved yield and productivity at the fermentation stage seem to be inviolable condition to straightly compete with fossil-based and first-generation bioethanol facilities. This study proposes a model-based multi-objective dynamic optimization approach to systematically derive optimal operating policies for the fermentation bioreactor as a step forward towards enhancing the economic performance of lignocellulosic bioethanol plants. The economic benefit of the derived optimal bioreactor strategies is evaluated via a scalable economic index, linking for the first time the performance of the fermentation bioreactor to the economics of the entire production process. It is demonstrated that high values in productivity and substantial compromises in yield and final bioethanol concentration are conditions which favor economic feasibility with the achieved fermentation performance (3.32 g L−1 h−1, 0.399 g g−1, 106.0 g L−1) being comparable to first-generation bioethanol production. Finally, a global system analysis framework is employed to investigate the robustness of the optimal value of the economic index to the variability of key model parameters, illustrating the impact of model uncertainty on the process economic performance.

A model-based multi-objective optimization of energy consumption and thermal comfort for active chilled beam systems

Active chilled beam (ACB) systems provide two highly-coupled cooling capacities due to its unique structure through combining primary air nozzle and cooling coil, whose energy consumption is difficult to be estimated and balanced against thermal comfort. This study considered the trade-off between energy consumption and thermal comfort as a multi-objective optimization problem and proposed a novel and practical solution by utilizing empirical energy models of the ACB system and an evolutional non-dominated sorting genetic algorithm II. The energy models are established for components of fans, pumps, and chillers based on fundamental equations which are validated by experimental data. The thermal comfort of each room is quantified by the predicted percentage dissatisfied (PPD) model. Chilled water flow rate, primary airflow rate, and room temperature in ACB systems are specifically chosen as control variables due to the control convenience. Besides, a parameterless selection strategy that considers both thermal comfort and energy consumption is proposed to select the most appropriate solution among Pareto optimal solutions. Three steady-state experiments with different heat load conditions are conducted. Compared to experienced operation, the proposed strategy demonstrates a maximum of 39.32% of energy saving and 12.21% of PPD reduction by increasing the water flow rate and room temperature, and reducing the primary airflow rate. Furthermore, this study investigates the distribution of capacities in ACB systems and suggests to assign more capacity to the cooling coil based on energy efficiency considerations. A good trade-off is achieved between energy consumption and thermal comfort through the proposed multi-objective optimization strategy.

Optimization of Agent-Based Models Through Coarse-Graining: A Case Study in Microbial Ecology.

Optimization and control are important objectives across biology and biomedicine, and mathematical models are a key enabling technology. This paper reports a computational study of model-based multi-objective optimization in the setting of microbial ecology, using agent-based models. This modeling framework is well-suited to the field, but is not amenable to standard control-theoretic approaches. Furthermore, due to computational complexity, simulation-based optimization approaches are often challenging to implement. This paper presents the results of an approach that combines control-dependent coarse-graining with Pareto optimization, applied to two models of multi-species bacterial biofilms. It shows that this approach can be successful for models whose computational complexity prevents effective simulation-based optimization.

Methodology to Solve the Multi-Objective Optimization of Acrylic Acid Production Using Neural Networks as Meta-Models

It is paramount to optimize the performance of a chemical process in order to maximize its yield and productivity and to minimize the production cost and the environmental impact. The various objectives in optimization are often in conflict, and one must determine the best compromise solution usually using a representative model of the process. However, solving first-principle models can be a computationally intensive problem, thus making model-based multi-objective optimization (MOO) a time-consuming task. In this work, a methodology to perform the multi-objective optimization for a two-reactor system for the production of acrylic acid, using artificial neural networks (ANNs) as meta-models, is proposed in an effort to reduce the computational time required to circumscribe the Pareto domain. The performance of the meta-model confirmed good agreement between the experimental data and the model-predicted values of the existent relationships between the eight decision variables and the nine performance criteria of the process. Once the meta-model was built, the Pareto domain was circumscribed based on a genetic algorithm (GA) and ranked with the net flow method (NFM). Using the ANN surrogate model, the optimization time decreased by a factor of 15.5.

A Kriging Model-Based Expensive Multiobjective Optimization Algorithm Using R2 Indicator of Expectation Improvement

Most of the multiobjective optimization problems in engineering involve the evaluation of expensive objectives and constraint functions, for which an approximate model-based multiobjective optimization algorithm is usually employed, but requires a large amount of function evaluation. Aiming at effectively reducing the computation cost, a novel infilling point criterion EIR2 is proposed, whose basic idea is mapping a point in objective space into a set in expectation improvement space and utilizing the R2 indicator of the set to quantify the fitness of the point being selected as an infilling point. This criterion has an analytic form regardless of the number of objectives and demands lower calculation resources. Combining the Kriging model, optimal Latin hypercube sampling, and particle swarm optimization, an algorithm, EIR2-MOEA, is developed for solving expensive multiobjective optimization problems and applied to three sets of standard test functions of varying difficulty and comparing with two other competitive infill point criteria. Results show that EIR2 has higher resource utilization efficiency, and the resulting nondominated solution set possesses good convergence and diversity. By coupling with the average probability of feasibility, the EIR2 criterion is capable of dealing with expensive constrained multiobjective optimization problems and its efficiency is successfully validated in the optimal design of energy storage flywheel.

Multiplicity of solutions in model-based multiobjective optimization of wastewater treatment plants

Wastewater treatment process design involves the optimization of multiple conflicting objectives. The detection of different equivalent solutions in terms of objective values is crucial for designers in order to efficiently switch to the new optimal operation policies if changes in the process conditions or new constraints occur. In this work, the dynamic multi-objective optimization of a municipal wastewater treatment plant model is carried out. The aim is to simultaneously optimize an economic cost term and an effluent quality index. The selected process variables for the optimization are (1) an aeration factor in the aerated tank previous to the clarifier, and (2) an internal recycle flow rate. Their time profiles are approximated using the control vector parameterization technique. To solve the multi-objective problem and find the Pareto front, the NSGA-II algorithm has been used. The simulation of different realistic scenarios which impose operational constraints (e.g., maintenance operations) reveals that, indeed, multiple solutions exist at least in some areas of the Pareto front. It is observed that different control profiles can produce nearly identical results in terms of Pareto solutions. The a priori knowledge of these equivalent solutions for different scenarios provides the decision makers with alternative choices to be adapted to their organizations policies when events altering decision variables bounds or adding new constraints to the process model occur.