Mechanism Design Problem Research Articles

Performance Comparison of Recent Population-Based Metaheuristic Optimisation Algorithms in Mechanical Design Problems of Machinery Components

The optimisation of complex engineering design problems is highly challenging due to the consideration of various design variables. To obtain acceptable near-optimal solutions within reasonable computation time, metaheuristics can be employed for such problems. However, a plethora of novel metaheuristic algorithms are developed and constantly improved and hence it is important to evaluate the applicability of the novel optimisation strategies and compare their performance using real-world engineering design problems. Therefore, in this paper, eight recent population-based metaheuristic optimisation algorithms—African Vultures Optimisation Algorithm (AVOA), Crystal Structure Algorithm (CryStAl), Human-Behaviour Based Optimisation (HBBO), Gradient-Based Optimiser (GBO), Gorilla Troops Optimiser (GTO), Runge–Kutta optimiser (RUN), Social Network Search (SNS) and Sparrow Search Algorithm (SSA)—are applied to five different mechanical component design problems and their performance on such problems are compared. The results show that the SNS algorithm is consistent, robust and provides better quality solutions at a relatively fast computation time for the considered design problems. GTO and GBO also show comparable performance across the considered problems and AVOA is the most efficient in terms of computation time.

A deep learning augmented genetic algorithm approach to polycrystalline 2D material fracture discovery and design

The gestalt of computational methods including physics-based molecular dynamics simulations, data-driven machine learning (ML) models, and biologically-inspired genetic algorithms affords a powerful toolbox for tackling materials mechanism discovery and design problems. Here, we leverage these methods to investigate the complex multidimensional problem of polycrystalline 2D material fracture. We focus first on graphene and in doing so, demonstrate a practical workflow for exploring the structural dependencies of fracture energy. Despite training our ML model on exclusively single crystal fracture in increments of 10° orientations, we can identify a crack branching mechanism responsible for high bicrystal toughness centered at initial crystal orientation angles of 19° and 41°. These high peaks span only a few degrees in range and are completely overlooked by a search with stride 10°. Furthermore, we can discover qualitative physical phenomena such as collective fracture branch termination and extract quantitative trends relating angular dispersion and mis-orientation angles of crystal grains to fracture energy. None of these complex polycrystalline behaviors were presented in the training data, and the predictive power of the model ultimately allows us to expeditiously generate polycrystalline graphene structures with bespoke fracture paths, a task with great implications in industrial design applications and mechanism discovery. Furthermore, the approach is not limited to graphene specifically, as we demonstrate by retraining the model for another more complex 2D material—MoS2—and achieve polycrystalline fracture predictions of comparable accuracy.

Smart Charging of Electric Vehicles: An Innovative Business Model for Utility Firms

Problem definition: By providing an environmentally friendly alternative to traditional vehicles, electric vehicles will transform urban mobility, particularly in smart cities. In practice, after an electric vehicle is plugged in, the charging station completes charging as soon as possible. Given that the procurement cost of electricity and associated emissions vary significantly during a day, substantial savings can be achieved by smart charging—delaying charging until the cost is lower. In this paper, we study smart charging as an innovative business model for utility firms. Academic/practical relevance: Utility firms are already investing in charging stations, and they can achieve significant cost savings through smart charging. Methodology: We consider a mechanism design problem in which a utility firm first announces pairs of charging price and completion time. Then, each customer selects the pair that maximizes their utility. Given the selected completion times, the utility firm solves the optimal control problem of determining the charging schedule that minimizes the cost of charging under endogenous, time-varying electricity procurement cost. We assume that there are ample parking spots with chargers at the charging station. Results: We devise an intuitive and practically implementable policy for scheduling charging of electric vehicles under given completion times. We prove that this policy is optimal if all customers arrive at the station simultaneously. We also characterize the optimal pairs of charging price and completion time. By using real electricity demand and generation data from the largest electricity market in the United States, we find that cost and emissions savings from smart charging are approximately 20% and 15%, respectively, during a typical summer month. Managerial implications: In contrast to the current practice of charging vehicles without delay, we show that it is economically and environmentally beneficial to delay charging some vehicles and to set charging prices based on customers’ inconvenience cost of delays. We also find that most of the savings from implementing smart charging can be achieved during peak-demand days, highlighting the effectiveness of smart charging.

Bayesian auctions with efficient queries

Designing dominant-strategy incentive compatible (DSIC) mechanisms for a seller to generate (approximately) optimal revenue by selling items to players is a fundamental problem in Bayesian mechanism design. However, most existing studies assume that the seller knows the entire distribution from which the players' values are drawn. Unfortunately, this assumption may not hold in reality: for example, when the distributions have exponentially large supports or do not have succinct representations. In this work we consider, for the first time, the query complexity of Bayesian mechanisms. The seller only has limited oracle accesses to the players' distributions, via quantile queries and value queries. For single-item auctions, we design mechanisms with logarithmic number of value or quantile queries which achieve almost optimal revenue. We then prove logarithmic lower-bounds, i.e., logarithmic number of queries are necessary for any constant approximation DSIC mechanisms, even when randomized and adaptive queries are allowed. Thus our mechanisms are almost optimal regarding query complexity. Our lower-bounds can be extended to multi-item auctions with monotone subadditive valuations, and we complement this part with constant approximation mechanisms for unit-demand or additive valuation functions. Our results are robust even if the answers to the queries contain noises. Thus, in those settings the seller needs to access much less than the entire distribution to achieve approximately optimal revenue.

Dynamic mechanism design on social networks

This paper studies a mechanism design problem with networked agents and stochastically evolving private information. In contrast to the canonical mechanism design theory focusing only on information asymmetry, we also pay attention to the topology of social network among agents. We find that the standard first-order approach for mechanism design is invalid in dynamic environment. As a remedy, a novel ironing technique is proposed, which produces a perfectly sorting allocation. Based on the optimal dynamic mechanism obtained, we define and compare some important nodes and edges in a network for different ranges of synergy parameter. We further discuss the network intervention problem, in which the principal can intervene to change the ex-ante distribution of individual types.

Encoding and exploring latent design space of optimal material structures via a VAE-LSTM model

Variational autoencoders (VAE) are machine learning models that can extract low dimensional representations of data from datasets of high complexity and volume. Importantly, they can be used for generative purposes to reconstruct complex data, such as images, from a low dimensional encoding of only a few variables. Long short-term memory (LSTM) neural networks are well suited to learning logical trajectory relationships within datasets. Using these two models in concert, we develop a VAE-LSTM approach to learn a classic mechanical materials design problem. Here, we focus on the compliance optimization of cantilever design, using a VAE to encode cantilever structures into a 2D latent space and a LSTM to learn trajectories in that latent space corresponding to the optimization process. Ultimately, we are able to clearly visualize the space of cantilever design, generate new design with extremely low density beyond the original dataset, and obtain optimal cantilever structures inspired by nature. We also demonstrate how the resulting designs can be manufactured using 3D printing, offering a rapid pathway from concept to prototype. The method we developed here can be generalized to other image-based datasets encapsulating changes from multiple factors. The ability offered by our approach to interpret complex behavior, via representations in simplified space, has great potential for application in the intelligent design and manufacturing of materials structure problems.

Funding public projects: A case for the Nash product rule

We study a mechanism design problem where a community of agents wishes to fund public projects via voluntary monetary contributions by the community members. This serves as a model for public expenditure without an exogenously available budget, such as participatory budgeting or voluntary tax programs, as well as donor coordination when interpreting charities as public projects and donations as contributions. Our aim is to identify a mutually beneficial distribution of the individual contributions. In the preference aggregation problem that we study, agents with linear utility functions over projects report the amount of their contribution, and the mechanism determines a socially optimal distribution of the money. We identify a specific mechanism—the Nash product rule—which picks the distribution that maximizes the product of the agents’ utilities. This rule is Pareto efficient and incentivizes agents to contribute their entire budget while spending each agent’s contribution only on projects the agent finds acceptable.

Fair and size-scalable participant selection framework for large-scale mobile crowdsensing

Mobile Crowdsensing (MCS) is a cost-efficient community sensing paradigm. It employs massive mobile computing devices such as smartphones to sense and propagate data collectively. Two main problems in MCS aiming to use these applications efficiently and their generated data are participants selection problem and incentive mechanism design problem. Specifically, the participant selection problem is to select a suitable set of participants for collecting the sensing data, while incentive mechanism design is to allocate the suitable incentives to these participants. Since the incentives allocated to the participants affect their behaviors, the system needs to adopt different participant selection methods under different incentive mechanisms. This paper proposes a dynamic participant selection method to select suitable participants under a flexible incentive mechanisms framework. We first adopt a game theory method to estimate the effect that the incentives bring to the participants’ behavior and then predict their mobility patterns. Based on the predicted mobility patterns of the participants, we design a distributed approximate algorithm to solve the participant selection problem. Finally, comprehensive experiments on a real-life large-scale dataset have demonstrated that our method outperforms other well-recognized baselines in various incentive mechanisms.

Dynamic slot allocations with different patience levels

This study considers a mechanism design problem in which service slots are allocated over time to buyers arriving in different periods. Buyers have a multidimensional type representing their valuation and patience level. Some buyers can accept delayed service, whereas others cannot. The seller fully commits to a deterministic mechanism. We show that a mechanism is periodic ex-post incentive compatible if and only if the allocation rule is monotone in valuation and “price equivalence” holds. The dynamic pivot mechanism with reserve prices maximizes the seller's expected revenue if and only if the virtual valuation function is affine.

Optimal Auctions for Spiteful Bidders

Designing revenue-optimal auctions for various settings is perhaps the most important, yet sometimes most elusive, problem in mechanism design. Spiteful bidders have been intensely studied recently, especially because spite occurs in many applications in multiagent system and electronic commerce. We derive the optimal auction for such bidders (as well as bidders that are altruistic). It is a generalization of Myerson’s (1981) auction. It chooses an allocation that maximizes agents’ virtual valuations, but for a generalized definition of virtual valuation. The payment rule is less intuitive. For one, it takes each bidder’s own report into consideration when determining his payment. Moreover, bidders pay even if the seller keeps the item; a similar phenomenon has been shown in other settings with neg- ative externalities (Jehiel, Moldovanu, and Stacchetti 1996; Deng and Pekec 2011). On the other hand, a novel aspect of our auction is that it sometimes subsidizes losers when the item is sold to some other bidder. We also derive a revenue equivalence theorem for this setting. Using it, we generate a short proof of (a slight generalization of) the previously known result that, in two-bidder settings with independently uniformly drawn valuations, second-price auctions yield greater expected revenue than first-price auctions. Finally, we present a template for comparing the expected revenues of any two auction mechanisms that have the same allocation rule (for the valuations distributions at hand).

Optimizing Payments in Dominant-Strategy Mechanisms for Multi-Parameter Domains

In AI research, mechanism design is typically used to allocate tasks and resources to agents holding private information about their values for possible allocations. In this context, optimizing payments within the Groves class has recently received much attention, mostly under the assumption that agent's private information is single-dimensional. Our work tackles this problem in multi-parameter domains. Specifically, we develop a generic technique to look for a best Groves mechanism for any given mechanism design problem. Our method is based on partitioning the spaces of agent values and payment functions into regions, on each of which we are able to define a feasible linear payment function. Under certain geometric conditions on partitions of the two spaces this function is optimal. We illustrate our method by applying it to the problem of allocating heterogeneous items.

Threats and Trade-Offs in Resource Critical Crowdsourcing Tasks Over Networks

In recent times, crowdsourcing over social networks has emerged as an active tool for complex task execution. In this paper, we address the problem faced by a planner to incentivize agents in the network to execute a task and also help in recruiting other agents for this purpose. We study this mechanism design problem under two natural resource optimization settings: (1) cost critical tasks, where the planner's goal is to minimize the total cost, and (2) time critical tasks, where the goal is to minimize the total time elapsed before the task is executed. We define a set of fairness properties that should be ideally satisfied by a crowdsourcing mechanism. We prove that no mechanism can satisfy all these properties simultaneously. We relax some of these properties and define their approximate counterparts. Under appropriate approximate fairness criteria, we obtain a non-trivial family of payment mechanisms. Moreover, we provide precise characterizations of cost critical and time critical mechanisms.

MÜHENDİSLİK TASARIM PROBLEMLERİNİ ÇÖZMEK İÇİN KISIT-YÖNETİMİ MEKANİZMALARININ KARŞILAŞTIRMALI BİR ANALİZİ

Optimization problems have numerous real-life applications in science and engineering. The engineering design problems are usually subject to various constraints. Although many state-of-the-art metaheuristic optimization algorithms have been developed during the last decades, these algorithms require additional constraint-handling mechanisms to cope with constrained optimization problems. Therefore, selecting a suitable constraint-handling mechanism requires extensive trial-and-error experiments, which is time-consuming and demanding. In this study, a comparative analysis of the eight constraint handling mechanisms is carried out, guiding decision-makers in their optimization practices. The constraint-handling techniques are used along with the whale optimization algorithm, and 19 real-life mechanical design problems, which are also part of the CEC2020 benchmark suite, are tested in the experimental analysis. The nonparametric statistical analysis incorporating Nemenyi and Holm post-hoc procedures shows that the inverse tangent constraint-handling and eclectic penalty methods exhibit high performance in real-life mechanical design problems.

Advanced arithmetic optimization algorithm for solving mechanical engineering design problems.

The distributive power of the arithmetic operators: multiplication, division, addition, and subtraction, gives the arithmetic optimization algorithm (AOA) its unique ability to find the global optimum for optimization problems used to test its performance. Several other mathematical operators exist with the same or better distributive properties, which can be exploited to enhance the performance of the newly proposed AOA. In this paper, we propose an improved version of the AOA called nAOA algorithm, which uses the high-density values that the natural logarithm and exponential operators can generate, to enhance the exploratory ability of the AOA. The addition and subtraction operators carry out the exploitation. The candidate solutions are initialized using the beta distribution, and the random variables and adaptations used in the algorithm have beta distribution. We test the performance of the proposed nAOA with 30 benchmark functions (20 classical and 10 composite test functions) and three engineering design benchmarks. The performance of nAOA is compared with the original AOA and nine other state-of-the-art algorithms. The nAOA shows efficient performance for the benchmark functions and was second only to GWO for the welded beam design (WBD), compression spring design (CSD), and pressure vessel design (PVD).

TONR: An exploration for a novel way combining neural network with topology optimization

The rapid development of deep learning has opened a new door to the exploration of topology optimization methods. The combination of deep learning and topology optimization has become one of the hottest research fields at the moment. Different from most existing work, this paper conducts an in-depth study on the method of directly using neural networks (NN) to carry out topology optimization. Inspired by the idea from the field of “Inverting Representation of Image” and “Physics-Informed Neural Network”, a topology optimization via neural reparameterization framework (TONR) that can solve various topology optimization problems is formed. The core idea of TONR is Reparameterization, which means the update of the design variables (pseudo-density) in the conventional topology optimization method is transformed into the update of the NN’s parameters. The sensitivity analysis in the conventional topology optimization method is realized by automatic differentiation technology. With the update of NN’s parameters, the density field is optimized. Some strategies for dealing with design constraints, determining NN’s initial parameters, and accelerating training are proposed in the paper. In addition, the solution of the multi-constrained topology optimization problem is also embedded in the TONR framework. Numerical examples show that TONR can stably obtain optimized structures for different optimization problems, including the stress-constrained problem, structural natural frequency optimization problems, compliant mechanism design problems, heat conduction system design problems, and the optimization problem of hyperelastic structures. Compared with the existing methods that combine deep learning with topology optimization, TONR does not need to construct a dataset in advance and does not suffer from structural disconnection. The structures obtained by TONR can be comparable to the conventional methods.

Non-convex isotonic regression via the Myersonian approach

Isotonic regression refers to a class of regression models with order constraints. It is widely used in maximum likelihood estimation of ordered parameter, testing of distributions with ordered means, multistage production systems, and machine learning. A vast majority of the literature considers the isotonic regression problems with convex or piece-wise convex objective functions (or those that can be converted to such functions). We connect a class of isotonic regression problems with the so-called ironing problem in mechanism design, by establishing a discrete version of the Myerson’s ironing method. We use such a connection to solve an isotonic regression problem with non-convex objective functions. We also prove the optimality of pool adjacent violator (PAV) algorithm in such a case.

Chaos and intensification enhanced flower pollination algorithm to solve mechanical design and unconstrained function optimization problems

Nature-inspired computation has enjoyed a visible position among the soft computational techniques. Flower Pollination Algorithm (FPA), which is known as one of the outstanding algorithms in this domain, has been shown to be promising in numerous publications. FPA is comprised of two main phases, which are referred to as abiotic and biotic pollination that correspond to local and global search, respectively. It makes use of a user-supplied parameter to switch between them. This parameter is referred to as the switching probability. Thus, it can be put forward that switching probability defines the search characteristic of FPA. The present work introduces several FPA modifications that adopt chaotic maps. Moreover, the developed modifications are further enhanced by using intensifying step sizing procedure that allows a more intensified search towards the end of search. With the help of the introduced chaos in switching probability and incrementally intensifying search, developed FPA modifications are expected to find the hard-to-detect promising regions. Next, such capabilities of chaotic maps are utilized in various building blocks of FPA. Performances of all developed FPA modifications are analysed on the well-known unconstrained real-valued function minimization and mechanical design problems. Finally, appropriate non-parametric statistical analysis is carried out to observe possible statistically significant improvements over the standard FPA. As shown by the experimental study, obtained results induce success of the developed procedures, which clearly add to the capability of the canonical FPA.

Optimization of constrained mechanical design problems using the equilibrium optimization algorithm

Abstract In this work, the optimization of structural and mechanical problems is carried out using the equilibrium optimizer (EO), which is a recent physical-based algorithm.The the ten-bar planar truss structure, planetary gearbox, hydrostatic thrust bearing, and robot gripper mechanism problems are solved using the EO algorithm. The results achieved using the EO in solving these problems are compared with those of recent algorithms. The computational results show that EO yields better outcomes and competitive results that can also be applied for the other problems studied.

Comparison of metaheuristic optimization algorithms for solving constrained mechanical design optimization problems

Determining the solution for real mechanical design problems is a challenging task when using the newly developed and efficient swarm intelligence algorithms. There are so many difficulties to be addressed, including but not limited to mixed decision variables, diverse constraints, inherent errors, conflicting objectives, and numerous locally optimal solutions. This work analyzes the behavior of nine metaheuristic algorithms, namely, salp swarm algorithm (SSA), multi-verse optimizer (MVO), moth-flame optimizer (MFO), atom search optimization (ASO), ecogeography-based optimization (EBO), queuing search algorithm (QSA), equilibrium optimizer (EO), evolutionary strategy (ES) and hybrid self-adaptive orthogonal genetic algorithm (HSOGA). The efficiency of these algorithms is evaluated on eight mechanical design problems using the solution quality and convergence analysis, which verifies the wide applicability of these algorithms to real-world application problems.

Business cycle fluctuations in Mirrlees economies: The case of i.i.d. shocks

I consider a real business cycle model in which agents have private information about the i.i.d. realizations of their value of leisure. For the case of logarithmic preferences I provide an analytical characterization of the solution to the associated mechanism design problem. Moreover, I show a striking irrelevance result: that the stationary behavior of all aggregate variables are exactly the same in the private information economy as in the full information case. Numerical simulations indicate that the irrelevance result approximately holds for more general preferences.