Multi-objective Design Problem Research Articles

Cellular Gradient Algorithm for Solving Complex Mechanical Optimization Design Problems

In mechanical optimization design problems, there are often some non-continuous or non-differentiable objective functions. For these non-continuous and non-differentiable optimization objectives, it is often difficult for existing optimal design algorithms to find the desired optimal solutions. In this paper, we incorporate the idea of gradient descent into cellular automata and propose a Cellular Gradient (CG) method. First, we have given the basic rules and algorithmic framework of CG and designed three kinds of growth and extinction rules respectively. Then, the three evolutionary rules for cellular within a single cycle are analyzed separately for form and ordering. The best expressions for the cellular jealous neighbor rule and the solitary regeneration rule are given, and the most appropriate order in which the rules are run is selected. Finally, the solution results of the cellular gradient algorithm and other classical optimization design algorithms are compared with a multi-objective multi-parameter mechanical optimization design problem as an example. The computational results show that the cellular gradient algorithm has an advantage over other algorithms in solving global and dynamic mechanical optimal design problems. The novelty of CG is to provide a new way of thinking for solving optimization problems with global discontinuities.

NSGAN: a non-dominant sorting optimisation-based generative adversarial design framework for alloy discovery

The design and discovery of new materials is fundamental to advancing scientific and technological innovation. The recent emergence of the materials genome concept holds great promise in revolutionising materials science by enabling the systematic utilisation of data for efficient prediction and optimisation of ‘superior’ materials. However, the materials genome approach can be stymied by the vast complexity of design spaces, which often demand substantial computational resources and sophisticated data processing capabilities. To address these challenges, this work introduces a generative design framework called the non-dominant sorting optimisation-based generative adversarial networks (NSGAN). Capitalising on the synergies of genetic algorithms (GA) and generative adversarial networks (GANs), NSGAN provides a robust and efficient approach for tackling high-dimensional multi-objective optimisation design problems. To validate the efficacy of the proposed framework, we applied the model to a comprehensive dataset of aluminium alloys. Additionally, an online tool was created as a supplementary resource, offering a brief introduction to this innovative method for the wider scientific community. This study explores the potential of a predictive and data-driven approach in material design, indicating a promising pathway for widespread applications in the field of materials science.

PANDA: A physarum-inspired algorithm to solve the multi-objective discrete network design problem

The Multi-Objective Discrete Network Design Problem (MO-DNDP) describes the optimisation of a transport network across multiple metrics. Due to the impractical processing times of exact solutions, heuristics have been harnessed to solve this problem. However, the scale of the networks, the set of candidate links and the metrics assessed have been limited. This research proposes a MO-DNDP that encapsulates 8 metrics across three real networks used as benchmarks scaling from 17 km2 to 41,850 km2 to encapsulate the complexity of optimising transport networks at different scales, traffic demands and constraint densities. To solve this more comprehensive MO-DNDP, this paper proposes the Physarum-inspired algorithm PANDA that improves upon the classical Physarum Solver algorithm by harnessing the attractant sensing and merging capabilities of the biological Physarum Polycephalum slime mould. PANDA is a first attempt at solving the complex MO-DNDP using the Physarum foraging model. PANDA consistently scored better than the classical Solver in the land use rating by circumventing landforms, built-up areas, and environmentally sensitive regions. Additionally, PANDA constructed networks that were on average 30 % better than the existing benchmark networks and 32 % better than the Physarum Solver networks. PANDA improved upon the benchmarks by constructing lower capacity roads that were optimised for the actual traffic demand between each origin–destination pair instead of shared arterials.

A constraint programming approach for multi-objective tourist trip design problem with mandatory visits: A case study for İzmir Turkey

The Orienteering Problem (OP) is an optimization problem that finds the locations and routes that will return the highest profit/benefit, starting from the initial location of the traveler/vehicle, visiting these locations, and ending with the starting location of the tour within a given time or distance limit. There is no obligation to visit all locations in the problem structure. OP has many real-life applications, such as staff routing and disaster relief routing. In this study, OP with Time Windows (OPTW), an extension of OP, is discussed with hotel selection and mandatory visits. Although the main objective of OPTW is profit maximization, it is also essential to minimize the total travel time to complete the tour efficiently. For this reason, we consider the OPTW as a multi-objective problem. In the problem considered here, it is assumed that the profit/benefit, travel time between locations, service period, and time interval that each location can be visited are determined to be known. Within the scope of the study, first, a Mixed Integer Programming (MIP) model is prepared for the problem. Since the proposed mathematical model does not provide solutions in a reasonable time for large networks, the problem is solved by a Constraint Programming (CP) approach. Attractive tourist points of interest for Izmir, one of Turkey's major tourist cities, are determined, and the proposed method is applied to the real-life problem. The problem is modeled as Multi-Objective OPTW with MIP and CP and solved. Also, sensitivity analysis is performed by considering two different scenarios.

Deep Learning for Size-Agnostic Inverse Design of Random-Network 3D Printed Mechanical Metamaterials.

Practical applications of mechanical metamaterials often involve solving inverse problems aimed at finding microarchitectures that give rise to certain properties. The limited resolution of additive manufacturing techniques often requires solving such inverse problems for specific specimen sizes. Moreover, the candidate microarchitectures should be resistant to fatigue and fracture. Such a multi-objective inverse design problem is formidably difficult to solve but its solution is the key to real-world applications of mechanical metamaterials. Here, a modular approach titled "Deep-DRAM" that combines four decoupled models is proposed, including two deep learning (DL) models, a deep generative model based on conditional variational autoencoders, and direct finite element (FE) simulations. Deep-DRAM integrates these models into a framework capable of finding many solutions to the posed multi-objective inverse design problem based on random-network unit cells. Using an extensive set of simulations as well as experiments performed on 3D printed specimens, it is demonstrate that: 1) the predictions of the DL models are in agreement with FE simulations and experimental observations, 2) an enlarged envelope of achievable elastic properties (e.g., rare combinations of double auxeticity and high stiffness) is realized using the proposed approach, and 3) Deep-DRAM can provide many solutions to the considered multi-objective inverse design problem.

Sustainable road network design considering hydrogen fuel cell vehicles

Environmental pollution and energy shortages have brought about an increased focus on new energy vehicles. Hydrogen fuel cell vehicles (HFCVs) have experienced rapid development due to the potential to alleviate energy pressures and reduce pollution emissions. Near zero-carbon emissions offer a promising avenue for promoting sustainable transportation development. To evaluate the impact of HFCVs on the transportation environment, this paper investigates the problem of sustainable transportation network design including HFCVs. Specifically, the problem is formulated as a bi-level multi-objective programming problem, with the upper level aimed at determining the optimal network design scheme considering multiple objectives, while the lower level addresses the mixed traffic flow that comprises both HFCVs and fuel vehicles. To solve the multi-objective sustainable network design problem, an integrated solution framework that combines the particle swarm optimization (PSO) algorithm with the Frank-Wolfe algorithm (FW) is developed. Specifically, the PSO algorithm is utilized to solve the upper-level model and identify the optimal network design schemes, while FW algorithm is adopted to handle mixed traffic flow assignments. Finally, the proposed model and algorithm are implemented in two numerical experiment to demonstrate their effectiveness and efficiency.

Parametric design, life cycle assessment, and optimization of a discrete product with application to an electric traction motor

Humans are surrounded and even dependent on discrete products for their daily activities. Product design processes have been vastly studied towards a healthy economic prosperity and other technical objectives (e.g., low risk). However, recent studies show that these methods have been lacking in terms of the environmental challenges humanity faces in the present and future. This study proposes a novel design framework that incorporates a parametric life cycle assessment (PLCA) as part of the optimization-based design model of a discrete product at early stage. Electric traction motor design applied to an electric vehicle is used as a case study. The results of performing a multi-objective design problem and an uncertainty analysis using Monte Carlo simulation show the usefulness of incorporating the PLCA in a transparent manner, as required by the International Standards Organization. Future work suggests investigating the expansion of this technique to support a broader range of objective functions.

Designing Together: Exploring Collaborative Dynamics of Multi-Objective Design Problems in Virtual Environments

Abstract The pace of technological advancements has been rapidly increasing in recent years, with the advent of artificial intelligence, virtual/augmented reality, and other emerging technologies fundamentally changing the way human beings work. The adoption and integration of these advanced technologies necessitate teams with diverse disciplinary expertise, to help teams remain agile in an ever-evolving technological landscape. Significant disciplinary diversity amongst teams, however, can be detrimental to team communication and performance. Additionally, accelerated by the COVID-19 pandemic, the adoption and use of technologies that enable design teams to collaborate across significant geographical distances have become the norm in today's work environments, further complicating communication and performance issues. Little is known about the way in which technology-mediated communication affects the collaborative processes of design. As a first step toward filling this gap, the current work explores the fundamental ways experts from distinct disciplinary backgrounds collaborate in virtual design environments. Specifically, we explore the conversational dynamics between experts from two complementary yet distinct fields: non-destructive evaluation (NDE) and design for additive manufacturing (DFAM). Using Markov modeling, the study identified distinct communicative patterns that emerged during collaborative design efforts. Our findings suggest that traditional assumptions regarding communication patterns and design dynamics may not be applicable to expert design teams working in virtual environments.

A Comparison of Power Take-Off Architectures for Wave-Powered Reverse Osmosis Desalination of Seawater with Co-Production of Electricity

Several power take-off (PTO) architectures for wave-powered reverse osmosis (RO) desalination of seawater are introduced and compared based on the annual average freshwater production and the size of the components, which strongly relate to the costs of the system. The set of architectures compared includes a novel series-type PTO architecture not previously considered. These seawater hydraulic PTO architectures are composed of a WEC-driven pump, an RO module, an intake charge pump driven by an electric motor, and a hydraulic motor driving an electric generator for electric power production. This study is performed using an efficient two-way coupled steady-state model for the average performance of the system in a given sea state, including freshwater permeate production, electric power production, and electric power consumption. A multi-objective design problem is formulated for the purposes of this comparative study, with the objectives of maximizing annual freshwater production, minimizing the displacement of the WEC-driven pump, and minimizing the installed RO membrane area. This establishes a framework for comparison in the absence of a mature techno-economic model. The requirement that the system produces enough electric power to meet its consumption is applied as a constraint on the operation of the system. The oscillating wave surge converter Oyster 1 is assumed as the WEC. Weights on performance of the system in a given sea state are based on historical data from Humboldt Bay, CA. This study finds that (1) architectures in a series configuration allow for a reduction in the WEC-driven pump size of 59–92% compared to prior work, (2) varying the displacement of the WEC-driven pump between sea conditions does not provide any significant advantage in performance, and (3) varying the active RO membrane area between sea condition offers improvements between 7% and 41% in each design objective.

A two-stage stochastic model for a multi-objective blood platelet supply chain network design problem incorporating frozen platelets

Platelet supply chain (PLT SC) management is always a challenging task for healthcare systems due to the nature of platelets (PLTs). PLTs have an extremely short shelf life and their demand is highly uncertain, which may lead to a high percentage of wastage and shortage in the corresponding PLT SC. This paper proposes a two-stage stochastic programming (2SSP) model to investigate the opportunity of incorporating frozen PLTs (FPLTs) into the PLT SC to see how it can improve the performance of the PLT SC in which the PLTs are used only in liquid form with respect to the platelet shortage, wastage and substitution penalties in transfusions. To investigate a more realistic situation when clear targets of blood shortage, wastage and substitution penalties are available, an extended goal programming model is built based on the proposed 2SSP model. Furthermore, we generate scenarios based on the real data provided by healthcare practitioners using the combination of a top-down forecasting approach and a Monte Carlo based scenario generation method. From the experimental results we note that, when comparing the model that incorporates FPLTs with the one that doesn't, the average reduction rates for platelet shortages, wastage, and substitution penalties in transfusions are 0.55, 0.55, and 0.23, respectively, when 40% of the overall demand is from patients who can receive both liquid PLTs and thawed PLTs sourced from FPLTs (Patient Type I). These rates can be further improved to 0.64, 0.55 and 0.23 or 0.65, 0.55 and 0.23 when 50% or 60% of the total demand is from Patient Type I. Furthermore, in contrast to real-world performance, the output of the 2SSP model, when not incorporating FPLTs, results in notable reductions in platelet shortage, wastage, and substitution penalties by 95%, 56% and 18%, respectively.

Modelling a bi-level multi-objective post-disaster humanitarian relief logistics network design problem under uncertainty

Post-disaster humanitarian relief logistics focuses on managing the supply and shipment of relief items. Owing to the complexity arising from the hierarchical decision relationship and the uncertainties of demand and transportation, it is challenging to develop an effective humanitarian relief logistics network (HRLN). A globalized robust bi-level multi-objective HRLN model involving uncertainties in transportation time, transportation cost and demand is developed to address this problem, in which an upper-level decision-maker focuses on the allocation problem and a lower-level decision-maker considers the supply problem. For tractability, the goal programming approach is employed to trade off conflicting timeliness, satisfaction and operational cost objectives. The proposed globalized robust bi-level HRLN model is reformulated as its globalized robust counterpart formulations under two different perturbation structures. The primal–dual approach is adopted to transform the bi-level models into equivalent mixed-integer conic programs. A case study concerning an Iranian earthquake is conducted to prove the performance of the proposed model. Globalized robust models are more flexible and able to immunize against uncertainty by comparison with traditional robust optimization and deterministic solutions. The managerial insights of using the globalized robust bi-level optimization approach are reported for disaster response management. The design of an emergency aviation network to circumvent the effects of COVID-19 could be considered in future research.

A local search-based non-dominated sorting genetic algorithm for solving a multi-objective medical tourism trip design problem considering the attractiveness of trips

Nowadays, the medical tourism industry encourages many healthcare practitioners to provide high-quality and low-cost medical services for patients worldwide. The development of operations research models and algorithms is one important instrument for improving the medical tourism industry based on the economic, political, social, and cultural aspects. In this paper, a medical tourism trip design problem is developed where patients travel from their city of residence to a destination city that may be in another country to receive high-quality and low-cost medical care. The most important part of this problem is to visit a number of tourist cities for each patient individually in the destination. In addition to the total cost, the patients prefer to increase the attractiveness of trips by referring to the quality of medical services and the attractiveness of visiting tourist cities. As far as we know in the area of medical tourist studies, no study has considered the minimization of total cost and maximization of the attractiveness of trips, simultaneously using utility function. The proposed multi-objective optimization model assigns the patients from the origin country to the hospitals in the destination country while making their routing and scheduling decisions to visit the tourist cities. The proposed model is limited by patients’ interests and time restrictions while allocating patients to the hospital and orienteering the patients toward visiting tourist attractions. As a complex optimization problem, another significant novelty of this paper is the proposal of a local search-based non-dominated sorting genetic algorithm (LSNSGA-II) for solving the proposed multi-objective optimization model. The proposed algorithm is compared with the original non-dominated sorting genetic algorithm (NSGA-II) and epsilon constraint (EC) method based on different multi-objective criteria. Finally, one main finding from our analyses is finding a trade-off between the total cost and attractiveness of trips as a challenging decision while proposing high-quality solutions in a reasonable time (i.e., less than one hour).

AI-Assisted optimisation of green concrete mixes incorporating recycled concrete aggregates

Maximising the content of supplementary cementitious materials as a partial replacement for Portland cement and using recycled concrete aggregates as a full or partial replacement for coarse aggregates are among the widely adopted strategies in the design of green concrete. However, the synergetic implications of adopting both approaches on concrete properties add complexity to the design of green concrete mixes. This paper proposes a novel AI-based multi-objective optimisation framework addressing the lack of a systematic method to formulate these concretes and solves the common multi-objective mix design problems. The framework is developed for the mix proportioning of green concrete mixes containing recycled concrete aggregates and commonly used supplementary cementitious materials while considering the desired compressive strength. The proposed optimisation model leverages a dataset of about 2,120 mixes and employs an extreme gradient boosting machine to model the compressive strength requirements as a mechanical constraint throughout the optimsiation process. Moreover, a set of key environmental objectives, including minimising global warming, acidification, fossil fuel depletion potentials, and the cost of production, are targeted. The effectiveness of the framework is validated through case studies across different strength ranges. The results indicate a significant improvement in environmental sustainability indicators, including a 19.6% and 21.6% reduction in global warming and acidification potentials, besides considerable cost savings of up to 23.7% without compromising the mechanical performance of concrete.

Bus Network Design and Frequency Setting in the Post-COVID-19 Pandemic: The Case of London

A transit network design frequency setting model is proposed to cope with the postpandemic passenger demand. The multiobjective transit network design and frequency setting problem (TNDFSP) seeks to find optimal routes and their associated frequencies to operate public transport services in an urban area. The objective is to redesign the public transport network to minimize passenger costs without incurring massive changes to its former composition. The proposed TNDFSP model includes a route generation algorithm (RGA) that generates newlines in addition to the existing lines to serve the most demanding trips, and passenger assignment (PA) and frequency setting (FS) mixed-integer programming models that distribute the demand through the modified bus network and set the optimal number of buses for each line. Computational experiments were conducted on a test network and the network comprising the Royal Borough of Kensington and Chelsea in London.

Bayesian optimization with active learning of design constraints using an entropy-based approach

The design of alloys for use in gas turbine engine blades is a complex task that involves balancing multiple objectives and constraints. Candidate alloys must be ductile at room temperature and retain their yield strength at high temperatures, as well as possess low density, high thermal conductivity, narrow solidification range, high solidus temperature, and a small linear thermal expansion coefficient. Traditional Integrated Computational Materials Engineering (ICME) methods are not sufficient for exploring combinatorially-vast alloy design spaces, optimizing for multiple objectives, nor ensuring that multiple constraints are met. In this work, we propose an approach for solving a constrained multi-objective materials design problem over a large composition space, specifically focusing on the Mo-Nb-Ti-V-W system as a representative Multi-Principal Element Alloy (MPEA) for potential use in next-generation gas turbine blades. Our approach is able to learn and adapt to unknown constraints in the design space, making decisions about the best course of action at each stage of the process. As a result, we identify 21 Pareto-optimal alloys that satisfy all constraints. Our proposed framework is significantly more efficient and faster than a brute force approach.

Nickel-based polycrystalline superalloy composition design framework based on non-dominated sorting genetic algorithm II

Nickel-based superalloy composition design problem has always been a fundamental task for growing demands in intended applications. In this paper, we establish a nickel-based polycrystalline superalloy composition design framework to excavate novel alloys with superior properties efficiently and comprehensively. First, we establish a model of creep resistance with respect to composition proportions with little data knowledge and computational effort based on the Gaussian process regression. Then, we solve the constrained multi-objective nickel-based superalloy composition design problem, aiming at maximizing the creep resistance while minimizing the alloy cost, by meta-heuristic non-dominated sorting genetic algorithm II efficiently, which enables fast searching rather than simply ranking in large-scale solution space. Pareto fronts containing optimal candidate alloys where the trade-off between creep resistance and alloy cost is fully considered are obtained. Finally, we filter the unqualified candidate alloys that dissatisfy the phase fraction of superalloy on several Pareto fronts based on some screening indicators computed by JMatPro software, and a set of well-performed alloys with high creep resistance and low alloy cost is obtained.

Conformal Volumetric Grayscale Metamaterials.

Conformal artificial electromagnetic media that feature tailorable responses as a function of incidence wavelength and angle represent universal components for optical engineering. Conformal grayscale metamaterials are introduced as a new class of volumetric electromagnetic media capable of supporting highly multiplexed responses and arbitrary, curvilinear form factors. Subwavelength-scale voxels based on irregular shapes are designed to accommodate a continuum of dielectric values, enabling the freeform design process to reliably converge to exceptionally high figures of merit (FOMs) for a given multi-objective design problem. Through additive manufacturing of ceramic-polymer composites, microwave metamaterials, designed for the radio-frequency range of 8-12GHz, are experimentally fabricated and devices with extreme dispersion profiles, an airfoil-shaped beam-steering device, and a broadband, broad-angle conformal carpet cloak, are demonstrated. It is anticipated that conformal volumetric metamaterials will lead to new classes of compact and multifunctional imaging, sensing, and communications systems.

Reinforcement Learning for Efficient Design Space Exploration With Variable Fidelity Analysis Models

Abstract Reinforcement learning algorithms can autonomously learn to search a design space for high-performance solutions. However, modern engineering often entails the use of computationally intensive simulation, which can lead to slower design timelines with highly iterative approaches such as reinforcement learning. This work provides a reinforcement learning framework that leverages models of varying fidelity to enable an effective solution search while reducing overall computational needs. Specifically, it utilizes models of varying fidelity while training the agent, iteratively progressing from low- to high fidelity. To demonstrate the effectiveness of the proposed framework, we apply it to two multimodal multi-objective constrained mixed integer nonlinear design problems involving the components of a ground and aerial vehicle. Specifically, for each problem, we utilize a high-fidelity and a low-fidelity deep neural network surrogate model, trained on performance data generated from underlying ground truth models. A tradeoff between solution quality and the proportion of low-fidelity surrogate model usage is observed. Specifically, high-quality solutions are achieved with substantial reductions in computational expense, showcasing the effectiveness of the framework for design problems where the use of just a high-fidelity model is infeasible. This solution quality-computational efficiency tradeoff is contextualized by visualizing the exploration behavior of the design agents.

Multi-objective collaborative assembly line design problem with the optimisation of ergonomics and economics

Manufacturing systems are socio-technical systems, with explicit interactions between humans and technologies in shared workspaces. These shared workspaces could also be called hybrid collaborative manufacturing systems, which involve workers as well as technological equipment and combine the benefits of human workers and new Industry 4.0 technologies, such systems are particularly useful in a context requiring flexibility and adaptability. Furthermore, the new Industry 5.0 approach has the objective to shift toward more human-centric and resilient manufacturing systems. The key problems to solve in the design of collaborative manufacturing systems are the combinatorial assembly line balancing problem and the equipment selection problem. An efficient and sustainable line requires a cost-effective choice of equipment while improving the ergonomics and the safety of workers. Both decisions of balancing workload and the assignment of equipment impact the ergonomics of a collaborative system and present conflicting criteria. To this end, we propose a multi-objective approach, the objectives are the optimisation of the investment costs and the ergonomics with a fatigue and recovery criterion. We propose to linearise the fatigue and recovery to formulate a new Mixed Integer Linear Programming formulation. We developed an exact multi-objective solving algorithm based on the ϵ-constraint to obtain the trade-off between these objectives. We conducted numerical experiments with different instances from the literature with promising results for instances with up to 45 operations. Finally, we discuss insightful managerial conclusions and future research perspectives.

Driver Assisted Lane Keeping with Conflict Management Using Robust Sliding Mode Controller

Lane-keeping assistance design for road vehicles is a multi-objective design problem that needs to simultaneously maintain lane tracking, ensure driver comfort, provide vehicle stability, and minimize conflict between the driver and the autonomous controller. In this work, a cooperative control strategy is proposed for lane-keeping keeping by integrating driving monitoring, variable level of assistance allocation, and human-in-the-loop control. In the first stage, a time-varying physical driver loading pattern is identified based on a relationship between lateral acceleration, road curvature, and the measured maximum driver torque. Together with the monitored driver state that indicates driver mental loading, an adaptive driver activity function is then formulated that replicates the levels of assistance required for the driver in the next stage. To smoothly transition authority between various modes (from manual to autonomous and vice versa) based on the generated levels of assistance, a novel higher-order sliding mode controller is proposed and closed-loop stability is established. Further, a novel sharing parameter (which is proportional to the torques coming from the driver and from the autonomous controller) is used to minimize the conflict. Experimental results on the SHERPA high-fidelity vehicle simulator show the real-time implementation feasibility. Extensive experimental results provided on the Satory test track show improvement in cooperative driving quality by 9.4%, reduction in steering workload by 86.13%, and reduced conflict by 65.38% when compared with the existing design (no sharing parameter). These results on the cooperative performance highlight the significance of the proposed controller for various road transportation challenges.