Multi-objective Optimization Formulation Research Articles

A novel design optimization framework to sustain remanufacturability

The ever-increasing global carbon emissions have urged the need for environmentally conscious/sustainable product design, for which the design for remanufacturing (DfRem) is one potential approach. DfRem targets at designing products that have multiple life cycles, thus significantly reducing raw material usage, energy consumption, and carbon emissions. In this paper, we develop a three-stage framework that consists of (1) systematic design space exploration and a multi-objective optimization formulation to minimize the likelihood of failure causes (such as fatigue and wear) and environmental footprint, (2) topology optimization to further reduce material usage without significantly affecting the load-carrying capability of the product, and (3) post-topology optimization design verification to ensure the proposed design satisfies all design constraints. The environmental impact can be assessed at varying comprehensiveness levels (e.g., design and manufacturing phase, use phase) and in terms of carbon or GHG emission, energy use, and waste generation. Because the novel design framework predominantly adjusted the geometry, we focused on mass-based change and energy savings due to sustained remanufacturability. The multi-objective optimization formulation in the first step results in a Pareto optimal set of possible design solutions that the designer can use for the second step. We demonstrate the utility of this framework through a case study of an engine cylinder head subjected to thermo-mechanical loads, where we find that about 5% of the product mass can be conserved with only about a 3% increase in surface area that has a fatigue life less than 10,000 cycles.

Piezoelectric impedance-based high-accuracy damage identification using sparsity conscious multi-objective optimization inverse analysis

Two elements are essential in structural health monitoring utilizing dynamic responses: response measurement with high-frequency contents, i.e., small characteristic wavelengths, that can adequately reflect damage features, and effective inverse identification analysis that is however oftentimes under-determined. The advancement of smart structure integration has led to active interrogation through frequency-sweeping piezoelectric impedance measurement at high frequency range. In this research we develop a multi-objective optimization formulation for the identification of damage location and severity utilizing piezoelectric impedance. While one optimization objective is to match the response measurement with finite element model prediction in the damage parametric space, the other is the number of locations of damage, i.e., the sparsity of damage index as the solution vector, since damage usually occurs within a small number of locations. This multi-objective formulation fits well the under-determined nature of damage identification, as it naturally provides multiple solutions as basis for further elucidation. The challenge remaining is how to find a small solution set that can include the actual damage scenario. Here we develop a novel inverse identification framework utilizing the intelligent swarm optimizer which possesses flexibility for enhancement. We first embed a sparsity enforcement process into the population generation of the optimizer, which yields a solution repository intrinsically possessing sparsity. We then apply reinforcement learning so the agents can adaptively opt for local strategies with the aim of enriching the searching patterns to diversify the solutions. Through the incorporation of a Q-table, searching toward more promising directions will be rewarded. Our case analyses employing experimental data indicate that this sparsity-conscious multi-objective particle swarm optimization technique can lead to a small solution set which generally encompasses the true damage scenario. This effectively solves the structural damage identification problem with piezoelectric impedance measurement.

Exploring optimal pathways of the high-CO2 content natural gas source to chemicals and fuels using superstructure multi-objective optimization

This study aims to develop a mathematical formulation of superstructure multi-objective optimization to find optimal pathways of high-CO2 natural gas and PV-hydrogen to chemicals and fuels integrated with CO2 sequestration. A mixed-integer nonlinear programming optimization model is used to compete along 56 pathways in the superstructure optimization network. The model was developed with the general algebraic modeling system and computed with the standard branch and bound (SBB) solver to maximize annual net profit and minimize annual net CO2 emissions. The result shows the selected products in 2020 are liquefied natural gas, methanol, dimethyl ether, formic acid, and acetic acid, with annual net profits and net CO2 emissions of 38.17 million $/year and −8.47 million tons of CO2/year, respectively. In the projection analysis, the annual net profit growth results at a compounding annual growth rate of 7.85% per year between 2020 and 2060, while annual net CO2 emissions decrease until −16.37 million tons of CO2/year in 2060. In 2030, blue acetic acid will be selected via all separation processes. For 2050, the synfuel via partial membrane separation is selected. The other products, formic acid, methanol, and acetic acid via membrane separation (full and partial), will always be selected between 2020 and 2060. Therefore, this could be a future strategy for monetizing high–CO2–content natural gas sources with low-carbon process development.

Model Predictive Control for Matrix Converters in Grid-Interactive Applications

Model Predictive Control (MPC) is a promising control strategy for matrix converters in grid-interactive applications. MPC optimizes a cost function over a finite time horizon, considering system constraints like voltage and current limits, grid codes, and power factor requirements. This enables effective grid synchronization, power quality regulation, and efficient power conversion. Advancements in MPC include predictive modelling techniques, adaptive algorithms, optimization algorithm integration, hybrid control strategies, and multi-objective optimization formulations. Benefits include fast response to changes in grid conditions, robustness in handling uncertainties, and extended time-horizon optimization. This study provides insights into MPC techniques and highlights the potential for further research.

Joint Data Transmission and Energy Harvesting for MISO Downlink Transmission Coordination in Wireless IoT Networks.

The advent of simultaneous wireless information and power (SWIPT) has been regarded as a promising technique to provide power supplies for an energy sustainable Internet of Things (IoT), which is of paramount importance due to the proliferation of high data communication demands of low-power network devices. In such networks, a multi-antenna base station (BS) in each cell can be utilized to concurrently transmit messages and energies to its intended IoT user equipment (IoT-UE) with a single antenna under a common broadcast frequency band, resulting in a multi-cell multi-input single-output (MISO) interference channel (IC). In this work, we aim to find the trade-off between the spectrum efficiency (SE) and energy harvesting (EH) in SWIPT-enabled networks with MISO ICs. For this, we derive a multi-objective optimization (MOO) formulation to obtain the optimal beamforming pattern (BP) and power splitting ratio (PR), and we propose a fractional programming (FP) model to find the solution. To tackle the nonconvexity of FP, an evolutionary algorithm (EA)-aided quadratic transform technique is proposed, which recasts the nonconvex problem as a sequence of convex problems to be solved iteratively. To further reduce the communication overhead and computational complexity, a distributed multi-agent learning-based approach is proposed that requires only partial observations of the channel state information (CSI). In this approach, each BS is equipped with a double deep Q network (DDQN) to determine the BP and PR for its UE with lower computational complexity based on the observations through a limited information exchange process. Finally, with the simulation experiments, we verify the trade-off between SE and EH, and we demonstrate that, apart from the FP algorithm introduced to provide superior solutions, the proposed DDQN algorithm also shows its performance gain in terms of utility to be up to 1.23-, 1.87-, and 3.45-times larger than the Advantage Actor Critic (A2C), greedy, and random algorithms, respectively, in comparison in the simulated environment.

Single-Loop Multi-Objective Reliability-Based Design Optimization Using Chaos Control Theory and Shifting Vector with Differential Evolution

Multi-objective reliability-based design optimization (MORBDO) is an efficient tool for generating reliable Pareto-optimal (PO) solutions. However, generating such PO solutions requires many function evaluations for reliability analysis, thereby increasing the computational cost. In this paper, a single-loop multi-objective reliability-based design optimization formulation is proposed that approximates reliability analysis using Karush-Kuhn Tucker (KKT) optimality conditions. Further, chaos control theory is used for updating the point that is estimated through KKT conditions for avoiding any convergence issues. In order to generate the reliable point in the feasible region, the proposed formulation also incorporates the shifting vector approach. The proposed MORBDO formulation is solved using differential evolution (DE) that uses a heuristic convergence parameter based on hypervolume indicator for performing different mutation operators. DE incorporating the proposed formulation is tested on two mathematical and one engineering examples. The results demonstrate the generation of a better set of reliable PO solutions using the proposed method over the double-loop variant of multi-objective DE. Moreover, the proposed method requires 6×–377× less functional evaluations than the double-loop-based DE.

Radio resource management in energy harvesting cooperative cognitive UAV assisted IoT networks: A multi-objective approach

Cooperative communication through energy harvested relays in Cognitive Internet of Things (CIoT) has been envisioned as a promising solution to support massive connectivity of Cognitive Radio (CR) based IoT devices and to achieve maximal energy and spectral efficiency in upcoming wireless systems. In this work, a cooperative CIoT system is contemplated, in which a source acts as a satellite, communicating with multiple CIoT devices over numerous relays. Unmanned Aerial Vehicles (UAVs) are used as relays, which are equipped with onboard Energy Harvesting (EH) facility. We adopted a Power Splitting (PS) method for EH at relays, which are harvested from the Radio frequency (RF) signals. In conjunction with this, the Decode and Forward (DF) relaying strategy is used at UAV relays to transmit the messages from the satellite source to the CIoT devices. We developed a Multi-Objective Optimization (MOO) framework for joint optimization of source power allocation, CIoT device selection, UAV relay assignment, and PS ratio determination. We formulated three objectives: maximizing the sum rate and the number of admitted CIoT in the network and minimizing the carbon dioxide emission. The MOO formulation is a Mixed-Integer Non-Linear Programming (MINLP) problem, which is challenging to solve. To address the joint optimization problem for an epsilon optimal solution, an Outer Approximation Algorithm (OAA) is proposed with reduced complexity. The simulation results show that the proposed OAA is superior in terms of CIoT device selection and network utility maximization when compared to those obtained using the Nonlinear Optimization with Mesh Adaptive Direct-search (NOMAD) algorithm.

Exact and approximate determination of the Pareto front using Minimal Correction Subsets

Recently, it has been shown that the enumeration of Minimal Correction Subsets (MCS) of Boolean formulas allows solving Multi-Objective Boolean Optimization (MOBO) formulations. However, a major drawback of this approach is that most MCSs do not correspond to Pareto-optimal solutions. In fact, one can only know that a given MCS corresponds to a Pareto-optimal solution when all MCSs are enumerated. Moreover, if it is not possible to enumerate all MCSs, then there is no guarantee of the quality of the approximation of the Pareto frontier. This paper extends the state of the art for solving MOBO using MCSs. First, we show that it is possible to use MCS enumeration to solve MOBO problems such that each MCS necessarily corresponds to a Pareto-optimal solution. Additionally, we also propose two new algorithms that can find a (1+ɛ)-approximation of the Pareto frontier using MCS enumeration. Experimental results in several benchmark sets show that the newly proposed algorithms allow finding better approximations of the Pareto frontier than state-of-the-art algorithms, and with guaranteed approximation ratios.

A spatial superstructure approach to the optimal design of modular processes and supply chains

Modularity is a design principle that aims to provide flexibility for spatio-temporal assembly/disassembly and reconfiguration of systems. This design principle can be applied to multiscale (hierarchical) manufacturing systems that connect units, processes, facilities, and entire supply chains. Designing modular systems is challenging because of the need to capture spatial interdependencies that arise between system components due to product exchange/transport between components and due to product transformation in such components. In this work, we propose an optimization framework to facilitate the design of modular manufacturing systems. Central to our approach is the concept of a spatial superstructure, which is a graph that captures all possible system configurations and interdependencies between components. The spatial superstructure is a generalization of the notion of a superstructure and of a p-graph used in process design, in that it encodes spatial (geographical) context of the system components. We show that this generalization facilitates the simultaneous design and analysis of processes, facilities, and of supply chains. Our framework aims to select the system topology from the spatial superstructure that minimizes design cost and that maximizes design modularity. We show that this design problem can be cast as a mixed-integer, multi-objective optimization formulation. We demonstrate these capabilities using a case study arising in the design of a plastic waste upcycling supply chain.

Simultaneous consideration of relative density, energy consumption, and build time for selective laser melting of Inconel 718: A multi-objective optimization study on process parameter selection

Additive manufacturing (AM) is regarded as sustainability friendly thanks to its significantly reduced production steps and simplified supply chain at the system level, but it is often not energy efficient at the process level. In this study, we propose that the optimization of AM process parameters should not only maximize build quality, but also minimize environmental impact and build time. A multi-objective optimization problem of maximizing relative density (RD), minimizing energy consumption and build time per unit volume (ev and tv respectively) is formulated and solved for selective laser melting (SLM) of Inconel 718 alloy. A high accuracy RD prediction model with R2 of 93.23% is obtained by fitting SLM experiment data from wide ranges of laser power (P), scanning speed (SS), hatch spacing (HS), and layer thickness (LT). The ev and tv models are created considering printing area utilization rate (U) based on laser scanning and powder coating process. The two approaches of Pareto front and global criterion method are adopted for solving the multi-objective optimization problem. It is found that the highest RD of close to 100% can be obtained at the expense of high ev and tv of close to 500 J/mm3 and 0.3 s/mm3, respectively, and about three times ev and tv are needed to increase RD from about 95% to 100% than from 85% to 95%. At the same U level, the solutions obtained from prioritizing ev and tv are consistent, while those from prioritizing RD show smaller process parameter values. The multi-objective optimization formulation provides an enabling tool for industry to obtain high quality SLM-ed parts with improved sustainability and efficiency at the process level. The methodology developed is applicable to selective laser melting of other materials, and such consideration can be readily expanded to other AM processes as well.

FRF 기반 부분구조합성법을 이용한 차량 진동성능 강건설계

In this study, a robust design procedure using the FRF-based substructuring (FBS) method was proposed for vehicle vibration performance. In the robust design procedure, global sensitivity analysis was used to obtain the design information of elastomers in structural systems considering uncertainties. The global sensitivity method combines the random balance design method for variance-based sensitivity information and the FRF-based substructuring (FBS) method for the calculation of vibrational responses, which establishes an efficient tool even in complex real structures. Moreover, a multi-objective optimization formulation was applied to obtain the optimal design of elastomers that give robust vibration responses. The objective functions were set to the mean and variance of the vibration responses. The Pareto optimal front was calculated using the non-dominated sorting genetic algorithm-II (NSGA-II). The genetic algorithm design variables were screened using the global sensitivity analysis results for the elastomers. These formulations were applied to a passenger car problem to obtain the optimal design of the engine mount systems. The numerical results showed that the newly introduced feature enhanced the calculation performance and the proposed procedure can be applied successfully in real complex structural problems.

A Novel Reliability-Based Robust Design Multiobjective Optimization Formulation Applied in Chemical Engineering

Mathematical models simulate various events under different conditions, enabling an early overview of the system to be implemented in practice, reducing the waste of resources and in less time. In project optimization, these models play a fundamental role, allowing to obtain parameters and attributes capable of enhancing product performance, reducing costs and operating time. These enhancements depend on several factors, including an accurate computational modeling of the inherent characteristics of the system. In general, such models include uncertainties in their mathematical formulations, which affect the feasibility of the results and their practical implementation. In this work, two different approaches capable of quantifying uncertainties during the optimization of mathematical models are considered. In the first, robust optimization, the sensitivity of decision variables in relation to deviations caused by external factors is evaluated. Robust solutions tend to reduce deviations due to possible system changes. The second approach, reliability-based optimization, measures the probability of system failure and obtains model parameters that ensures an established level of reliability. Overall, the fundamental objective is to formulate a multi-objective optimization problem capable of handling robust and reliability-based optimizations, to obtain solutions that are least sensitive to external noise and that satisfy prescribed reliability levels. The proposed formulation is analyzed by solving benchmark and chemical engineering problems. The results show the influence of both methodologies for the analysis of uncertainties, the multi-objective approach provides a variety of feasible optimizers, and the formulation proves to be flexible, so that the uncertainties can be incorporated into the problem considering the needs of each project.

Multi-Objective Collaborative Flexibility Optimization Design of the Strengthening Layer of a Flexible Riser

Abstract Marine flexible risers are widely used in ocean oil and gas extraction, and need to withstand environment loads (wave and current) and the large offset of the floater. Therefore, the flexible riser is subjected to tension, bending, and torsion loads, which are mainly resisted by the key strengthening layer. Small bending stiffness of a cross section of the strengthening layer with larger tension and torsion stiffness are required to be compliant with the ocean environment. The traditional design of the key strengthening layer is partially rigid with larger cross-sectional stiffnesses. Therefore, the innovative configurations of the strengthening layer are imperative to make sure that the flexible riser is reliable and safe during the installation and operation. The strengthening layer of the flexible riser is treated as the cylindrical shell composed of periodic unit-cell beam structures, which is a hypothetical model. The optimization design is conducted through the novel implementation of the asymptotic homogenization (NIAH) method. The multi-objective collaborative flexibility optimization formulation of cylindrical shell structure is proposed, considering the ratio of cross-sectional tensile torsion stiffness to bending stiffness of the strengthening layer as the objectives. The optimal configuration results, the helically wound structures, are obtained, which are the alternative strengthening components of flexible risers. Finally, the optimal structures are compared with the commonly used marine flexible riser, which gives a great verification of the methodology feasibility and explains why the strengthening layer is designed as the type of helically wound structure.

A machine learning strategy for optimal path planning of space robotic manipulator in on-orbit servicing

The present study addresses the problem of automatic path planning of a manipulator-like spacecraft in orbit. Based on the concept of optimal control and off-line establishment of optimal trajectories, the study proposes a formulation of multiobjective optimization that accounts for multiple aspects of motion. The effect of manipulator mass is analyzed. Then, the effect of multiple objectives on the optimal path, such as the satellite displacement, arm manipulability and maximum torque, are evaluated. In addition, the end-effector positioning, avoidance of collision between the arm and the spacecraft, and minimization of torque requirements are considered as objectives to be minimized, subject to uncertainty inside the berthing box. The numerical procedure includes a machine learning strategy that is able to learn from both training data and mission tasks. It is used during inverse kinematics analysis, when the Cartesian position is the input parameter and the joint angle estimate is the output. This information improves the convergence rate of the optimization procedure, which leads to the precise value of the angle of the joint. The learning strategy is effective for estimating the solution when five or more samples are available, and the result is improved as new data is added to the analysis. The diversity of scenarios, metrics and parameters considered in the numerical experiments confirms the viability and robustness of the proposed methodology.

Multi-scale sustainable engineering: Integrated design of reaction networks, life cycles, and economic sectors

Efforts toward sustainable engineering have expanded the system boundary to consider the life cycle along with economic and environmental objectives. Many design problems involve selection of reactions from many alternatives, and systematic methods for choosing reaction pathways have also been developed. To prevent burden shifting, selection of reaction pathways needs to consider activities at larger scales of the life cycle and economy. In this work we develop such a framework. The resulting P2P-RNFA framework combines Reaction Network Flux Analysis (RNFA) and Process-to-Planet (P2P) frameworks by means of a novel multi-scale multi-objective optimization formulation. This framework is capable of designing chemical reaction pathways, life-cycle value-chains, and economic cash flows in an integrated manner from a superstructure network containing alternative solutions. Application to synthesizing industrial biofuel, 3-methyl-tetrahydrofuran, demonstrates the method and its features. The P2P-RNFA framework can design novel chemical pathways while being mindful about shifting impacts to larger scales.

A systems engineering framework for the optimization of food supply chains under circular economy considerations

The current linear “take-make-waste-extractive” model leads to the depletion of natural resources and environmental degradation. Circular Economy (CE) aims to address these impacts by building supply chains that are restorative, regenerative, and environmentally benign. This can be achieved through the re-utilization of products and materials, the extensive usage of renewable energy sources, and ultimately by closing any open material loops. Such a transition towards environmental, economic and social advancements requires analytical tools for quantitative evaluation of the alternative pathways. Here, we present a novel CE system engineering framework and decision-making tool for the modeling and optimization of food supply chains. First, the alternative pathways for the production of the desired product and the valorization of wastes and by-products are identified. Then, a Resource-Task-Network representation that captures all these pathways is utilized, based on which a mixed-integer linear programming model is developed. This approach allows the holistic modeling and optimization of the entire food supply chain, taking into account any of its special characteristics, potential constraints as well as different objectives. Considering that typically CE introduces multiple, often conflicting objectives, we deploy here a multi-objective optimization strategy for trade-off analysis. A representative case study for the supply chain of coffee is discussed, illustrating the steps and the applicability of the framework. Single and multi-objective optimization formulations under five different coffee-product demand scenarios are presented. The production of instant coffee as the only final product is shown to be the least energy and environmental efficient scenario. On the contrary, the production solely of whole beans sets a hypothetical upper bound on the optimal energy and environmental utilization. In both problems presented, the amount of energy generated is significant due to the utilization of waste generated for the production of excess energy.

Interactive nonlinear multiobjective optimal design of water distribution systems using Pareto navigator technique

Sustainable water distribution systems comprise complex combinations of critical components that are simultaneously optimized. The trade-offs and interactions that exist among these components, however, will introduce difficult challenges to optimization algorithms. In this paper, a multiobjective optimization formulation is proposed to scrupulously manage the demand, leakage, and age of water, as well as energy consumption of water distribution systems. Pareto navigator approach, a learning-oriented algorithm, is used to attain the final Pareto optimal solution for water network. The optimal power consumption, leakage, demand, and water age are used as inputs to the upper level energy resource allocation to optimize the energy demand and operational cost of integrated water–energy system. Numerical results show 76.6%, 95.4%, 13.14%, and 27.4% reduction in leakage, water age, water usage, and energy consumption of water network over 24 h, respectively, while the daily cost of electricity generation reduces by 3.7%. The energy system is designed based on isolated energy units, also known as microgrids, with minimum dependency on the fossil-fuel-based power plants. As such, the proposed multiobjective bi-level optimization model will also improve the carbon footprint of water distribution systems and their impact on climate change.

Multiobjective Optimization of Mixed-Integer Linear Programming Problems: A Multiparametric Optimization Approach.

Industrial process systems need to be optimized, simultaneously satisfying financial, quality and safety criteria. To meet all those potentially conflicting optimization objectives, multiobjective optimization formulations can be used to derive optimal trade-off solutions. In this work, we present a framework that provides the exact Pareto front of multiobjective mixed-integer linear optimization problems through multiparametric programming. The original multiobjective optimization program is reformulated through the well-established ϵ-constraint scalarization method, in which the vector of scalarization parameters is treated as a right-hand side uncertainty for the multiparametric program. The algorithmic procedure then derives the optimal solution of the resulting multiparametric mixed-integer linear programming problem as an affine function of the ϵ parameters, which explicitly generates the Pareto front of the multiobjective problem. The solution of a numerical example is analytically presented to exhibit the steps of the approach, while its practicality is shown through a simultaneous process and product design problem case study. Finally, the computational performance is benchmarked with case studies of varying dimensionality with respect to the number of objective functions and decision variables.

A Bayesian-reliability based multi-objective optimization for tolerance design of mechanical assemblies

Tolerances significantly affect the assemblability of components, the product's performance, and manufacturing cost in mechanical assemblies. Despite the importance of product reliability assessment, the reliability-based tolerance design of mechanical assemblies has not been previously considered in the literature. In this paper, a novel method based on Bayesian modeling is proposed for the tolerance-reliability analysis and allocation of complex assemblies where the explicit assembly functions are difficult or impossible to extract. To reach this aim, a Bayesian model is developed for tolerance-reliability analysis. Then, a multi-objective optimization formulation is proposed for obtaining the optimum tolerances of components to minimize cost and maximize product performance. Subsequently, Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed for solving multi-objective optimization. Then, the enhanced TOPSIS is used to find the best optimum tolerances from the optimum Pareto solutions. Using the importance vector concept, a sensitivity analysis approach is used to determine the effects of design variables on the product reliability level and improve assembly reliability to the desired level. Finally, to exhibit the applicability of the proposed method, a transmission planetary gear system is considered, and the obtained results are compared and discussed for verification.

Self-connected multi-domain topology optimization of structures with multiple dissimilar microstructures

Multi-domain topology optimization allows the design of lattice structures with multiple dissimilar microstructures. However, how to handle the connectivity issue between the dissimilar microstructures is a very important and difficult topic. In this paper, a self-connected material interpolation is proposed to handle the topology optimization of structures with multiple dissimilar-but-connected microstructures. Due to this interpolation, the material in the interface domains between the dissimilar microstructures can be separately defined, which enables us to carefully design the material of interface to guarantee good connectivity. An advantage of this way is that the connectivity requirement is only considered for these microstructures in the small interface domain while other microstructures can be freely designed in the remaining relatively much bigger design domain. In this paper, the connectivity requirement is realized by simply using a non-design solid domain in the interface microstructures. Based on the proposed interpolation, a two-scale multi-objective optimization formulation is proposed for concurrently designing the topologies and the lattice materials. In addition to the traditional mechanical performance, a geometric feature, i.e., the mass of the interface, is also taken as an objective in this method to control the material usage of interface. Several examples with parameterized lattice microstructures are provided to illustrate the effectiveness of the proposed method.