Mechanism Design Problem Research Articles

Screening Inattentive Buyers

Information plays a crucial role in mechanism design problems. A potential complication is that buyers may be inattentive, and so their information may endogenously and flexibly depend on the offered mechanism. I show that it is without loss of generality to consider contour mechanisms, which comprise triplets of allocation probabilities, prices, and beliefs, and are uniquely determined by a single such point. The mechanism design problem then reduces to Bayesian persuasion along the optimal contour. This reduction has significant implications for both the implementation of the optimal mechanism and the revenues that can be achieved. (JEL C11, D11, D82, D83)

A Tool for Supporting Conceptual Design of Multiple State Mechanical Devices

Research into conceptual design of mechanical systems has evolved as an area of interest since last few decades. Conceptual design plays a significant role as an early stage of design to produce designs with higher quality by economically exploring a larger solution space. Several attempts have been made by researchers to automate the conceptual design synthesis process using computer support. However, most of that work has been focused on single state design problems. This paper deals with multiple state mechanical design problems and proposes a systematic method for synthesizing a larger solution space. A web-based tool is developed to guide designers through the step-by-step synthesis process by providing automated retrieval of initial solution proposals and modification rules.

The combined social engineering particle swarm optimization for real-world engineering problems: A case study of model-based structural health monitoring

Structural health monitoring (SHM) is a substantial research direction in structural engineering being scrutinized in recent years due to its significance in ensuring structural safety and reliability. The SHM using evolutionary computation has gained wide significance thanks to its computational capability and robust performance. By bearing in mind the necessity of efficient search mechanisms, a new algorithm merging the recent social engineering optimizer (SEO) and the particle swarm algorithm (PSO) is proposed in this work. The new algorithm, called the social engineering particle swarm optimization algorithm (SEPSO), combines the PSO population-based elitist-solution mechanism and the SEO two-solution attacker–defender paradigm to establish an effective global–local algorithm for solving complex engineering optimization problems. The SEPSO is developed, benchmarked, and compared with some state-of-the art algorithms using available test functions in the literature. Furthermore, the SEPSO is applied on selected mechanical design problems from the CEC2020 real-world constraint optimization competition in addition to comparison with the best-performed algorithms for benchmarking purpose. The SEPSO algorithm exhibits outstanding results when solving the benchmark functions and the real-world constraint optimization problems. Moreover, aiming to solve the complex problem of the SHM inverse problem, the SEPSO is employed. The SHM framework is presented and applied on the American Society of Civil Engineering (ASCE) frame structure based on an efficient fusion of objective function formulation. Several damage cases are tested using partial and noise-contaminated data. The proposed approach shows notable detectability and severity evaluation regardless the modal data malfunctions. Meanwhile, the proposed SEPSO can serve as an effective global–local search algorithm for solving real-world engineering problems.

A Bayesian learning framework for fast prediction and uncertainty quantification of additively manufactured multi-material components

Multi-material design in additive manufacturing relies on fast and accurate prediction of the physical response of mesostructured parts with arbitrary material distributions, which is extraordinarily challenging owing to the unknown parameters in constitutive modeling, manufacturing uncertainties, and high computational cost. Here, we employ an interdisciplinary framework to address these challenges by integrating experimentation, mechanical modeling, and statistical learning. Using advanced Bayesian learning and inference to optimally combine the simulation and experimental data, this framework enables (1) parameter calibration, (2) fast and accurate prediction of the physical response, and (3) uncertainty quantification of additively manufactured multi-material components. We demonstrate the framework based on a mechanical design problem involving three-point bending of multi-material beams. By training the Bayesian learning model with simulation and experimental data from selected multi-material designs, the beam deflection with an arbitrary mesostructure is shown to be accurately and rapidly predicted. Correlation of data sampling with the emulator uncertainty and discrepancy is demonstrated; this correlation can be used to identify regions with insufficient data sampling. The posterior distribution of each calibrated parameter is determined, revealing physical insights into the relative importance of these parameters in the mechanical design problem. By leveraging the advantages from both physically-based and data-driven approaches, the Bayesian learning framework allows for prediction and calibration using a somewhat small dataset, and therefore has great potential for widespread use in multi-material additive manufacturing applications.

Beyond the worst-case analysis of random priority: Smoothed and average-case approximation ratios in mechanism design

A mechanism for the random assignment problem takes agents' private preferences over items as input and outputs an allocation. One of the mainstream mechanisms, Random Priority, is asymptotically the best mechanism for welfare maximization. However, its approximation ratio is Θ(n), which implies that there is a large discrepancy between its performance and the optimal social welfare. We evaluate the performance of Random Priority beyond the worst-case analysis in the hope of addressing the inconsistency between the widespread use of the mechanism in practice and the undesired theoretical performance guarantee. We show that with small random noise applied to the worst-case inputs, Random Priority has a constant smoothed approximation ratio. When agents' preference values are independent random variables, Random Priority is nearly optimal evaluated by the average-case approximation ratio. En route to these results, we develop analytics tools to show the insights that the efficiency loss is small on most instances. To our limited knowledge, this is the first work that introduces smoothed analysis to algorithmic mechanism design problems. These results may pave the way for further studies for approximate mechanism design problems beyond the worst-case analysis.

A new chaotic Lévy flight distribution optimization algorithm for solving constrained engineering problems

AbstractThis work proposed a new metaheuristic dubbed as Chaotic Lévy flight distribution (CLFD) algorithm, to address physical world engineering optimization problems that incorporate the chaotic maps in the elementary Lévy flight distribution (LFD). Hybridization aims to increase the LFD rate of convergence while also providing a problem‐free optimization approach. The proposed methodology is investigated for five case studies of constrained optimization issues followed by shape optimization of structural design. The outcomes from the CFLD algorithm are further contrasted with its fundamental version and other distinguished recently introduced algorithms. The computational analysis illustrates the dominance of CLFD over other considered optimizers. Moreover, the present investigation shows that CLFD is a robust technique that can efficiently find optimal mechanical design problems with a proper chaotic map selection.

On the complexity of dynamic mechanism design

We introduce a simple dynamic mechanism design problem in which the designer offers two items in two consecutive stages to a single buyer. The buyer's joint distribution of valuations for the two items is known, and the buyer knows the valuation for the current item, but not for the one in the future. The designer seeks to maximize expected revenue, and the mechanism must be deterministic, truthful, and ex-post individually rational. We show that finding the optimum deterministic mechanism in this situation — arguably one of the simplest meaningful dynamic mechanism design problems imaginable — is NP-hard. We also prove several positive results, including a polynomial-time linear programming-based algorithm for the revenue optimal randomized mechanism (even for many buyers and many stages). We prove strong separations in revenue between non-adaptive, adaptive, and randomized mechanisms, even when the valuations in the two stages are independent.

Decentralized Edge Intelligence: A Dynamic Resource Allocation Framework for Hierarchical Federated Learning

To enable the large scale and efficient deployment of Artificial Intelligence (AI), the confluence of AI and Edge Computing has given rise to Edge Intelligence, which leverages on the computation and communication capabilities of end devices and edge servers to process data closer to where it is produced. One of the enabling technologies of Edge Intelligence is the privacy preserving machine learning paradigm known as Federated Learning (FL), which enables data owners to conduct model training without having to transmit their raw data to third-party servers. However, the FL network is envisioned to involve thousands of heterogeneous distributed devices. As a result, communication inefficiency remains a key bottleneck. To reduce node failures and device dropouts, the Hierarchical Federated Learning (HFL) framework has been proposed whereby cluster heads are designated to support the data owners through intermediate model aggregation. This decentralized learning approach reduces the reliance on a central controller, e.g., the model owner. However, the issues of resource allocation and incentive design are not well-studied in the HFL framework. In this article, we consider a two-level resource allocation and incentive mechanism design problem. In the lower level, the cluster heads offer rewards in exchange for the data owners' participation, and the data owners are free to choose which cluster to join. Specifically, we apply the evolutionary game theory to model the dynamics of the cluster selection process. In the upper level, each cluster head can choose to serve a model owner, whereas the model owners have to compete amongst each other for the services of the cluster heads. As such, we propose a deep learning based auction mechanism to derive the valuation of each cluster head's services. The performance evaluation shows the uniqueness and stability of our proposed evolutionary game, as well as the revenue maximizing properties of the deep learning based auction.

Chaotic Harris hawks optimization algorithm

Abstract Harris hawks optimization (HHO) is a population-based metaheuristic algorithm, inspired by the hunting strategy and cooperative behavior of Harris hawks. In this study, HHO is hybridized with 10 different chaotic maps to adjust its critical parameters. Hybridization is performed using four different methods. First, 15 test functions with unimodal and multimodal features are used for the analysis to determine the most successful chaotic map and the hybridization method. The results obtained reveal that chaotic maps increase the performance of HHO and show that the piecewise map method is the most effective one. Moreover, the proposed chaotic HHO is compared to four metaheuristic algorithms in the literature using the CEC2019 set. Next, the proposed chaotic HHO is applied to three mechanical design problems, including pressure vessel, tension/compression spring, and three-bar truss system as benchmarks. The performances and results are compared with other popular algorithms in the literature. They show that the proposed chaotic HHO algorithm can compete with HHO and other algorithms on solving the given engineering problems very successfully.

Meta-heuristic optimization algorithms for solving real-world mechanical engineering design problems: a comprehensive survey, applications, comparative analysis, and results

Meta-heuristic optimization algorithms for solving real-world mechanical engineering design problems: a comprehensive survey, applications, comparative analysis, and results

Event-triggered dissipative control for 2-D switched systems

In this work, the problem of event-triggered mechanism (ETM) and dissipative controller design for discrete-time (DT) two-dimensional (2-D) switched Fornasini-Marchesini (FM) systems is addressed. First of all, the definitions of 2-D (H,L,M,∊)-dissipativity and exponential stability for the considered systems are introduced. Then, the ETM is constructed to determine whether the signal is transmitted or not for the objective of control. Meanwhile, the definition of event-triggered sequence is given based on the line of cross-cut technology. Subsequently, the event-triggered dissipativity analysis and dissipativity-based control problems are solved. And corresponding sufficient conditions are obtained, under which the closed-loop 2-D switched system is exponentially stable and strict dissipative under the ETM. Finally, an illustrative simulation example is employed to verify the availability of the proposed controller design result, and the influence on the dissipativity performance index (DPI) is explored while the triggered parameter is changed.

Mechanism design by observant and informed planners

We study the mechanism design problem where the planner can observe ex-post the first-ranked alternatives or peaks of voter preferences. We contrast this with the design problem where the planner has ex-ante information regarding the peaks of voter preferences.

MAGIKS: Fair Multi-Resource Allocation Game Induced by Kalai-Smorodinsky Bargaining Solution

We study the problem of fair and efficient mechanism design for allocating multiple resources in multiple servers among a set of users with Leontief utilities. This problem is motivated by a mobile edge computing environment where each mobile user cannot establish a wireless connection simultaneously to multiple edge servers. Each user is a selfish utility maximizing agent that chooses a single server for its job execution. When a server is shared by multiple users, a resource allocation rule decides the utility that each user must receive. Our goal is to design a mechanism that always admits a Nash Equilibrium (NE), i.e., a state where no user has incentive to change its server, that (1) can be reached in polynomial time and (2) provides fair and efficient resource allocation. We propose the Multi-resource Allocation Game Induced by Kalai-Smorodinsky bargaining solution (MAGIKS) and prove that under discrete resource demands it finds an NE in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {O}({\textrm {poly}(n)})$ </tex-math></inline-formula> moves for any fixed server configuration, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is the number of users. Furthermore, MAGIKS satisfies envy-freeness, sharing incentive, and Pareto optimality on each server. Regarding fairness among users in different servers, we prove that MAGIKS satisfies 2-approximate envy-freeness and maximin share guarantee. Moreover, we show that 2-approximate envy-freeness is the best that any mechanism that satisfies local Pareto optimality can achieve at its NEs.

Data Disclosure With Non-Zero Leakage and Non-Invertible Leakage Matrix

We study a statistical signal processing privacy problem, where an agent observes useful data <inline-formula> <tex-math notation="LaTeX">$Y$ </tex-math></inline-formula> and wants to reveal the information to a user. Since the useful data is correlated with the private data <inline-formula> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula>, the agent employs a privacy mechanism to generate data <inline-formula> <tex-math notation="LaTeX">$U$ </tex-math></inline-formula> that can be released. We study the privacy mechanism design that maximizes the revealed information about <inline-formula> <tex-math notation="LaTeX">$Y$ </tex-math></inline-formula> while satisfying a strong <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula>-privacy criterion. When a sufficiently small leakage is allowed, we show that the optimizer distributions of the privacy mechanism design problem have a specific geometry, i.e., they are perturbations of fixed vector distributions. This geometrical structure allows us to use a local approximation of the conditional entropy. By using this approximation the original optimization problem can be reduced to a linear program so that an approximate solution for the optimal privacy mechanism can be easily obtained. The main contribution of this work is to consider a non-invertible leakage matrix with non-zero leakage. In our first example, inspired by a watermark application, we first demonstrate the accuracy of the approximation. Then, we employ different measures for utility and privacy leakage to compare the privacy-utility trade-off using our approach with other methods. In particular, we show that by allowing small leakage, significant utility can be achieved using our method compared to the case where no leakage is allowed. In the second and third examples which are based on the MNIST data set and medical applications, we illustrate the suggested design for disclosed data <inline-formula> <tex-math notation="LaTeX">$U$ </tex-math></inline-formula>. It has been shown that the letters of <inline-formula> <tex-math notation="LaTeX">$Y$ </tex-math></inline-formula> which are disclosing more information about <inline-formula> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> are combined (randomized) to produce a new letter of <inline-formula> <tex-math notation="LaTeX">$U$ </tex-math></inline-formula>.

Mapping and Enforcement of Minimally Restrictive Manufacturability Constraints in Mechanical Design

Abstract Traditional design-for-manufacturability (DFM) strategies focus on efficiency and design simplification and tend to be too restrictive for optimization-based design methods; recent advances in manufacturing technologies have opened up many new and exciting design options, but it is necessary to have a wide design space in order to take advantage of these benefits. A simple but effective approach for restricting the design space to designs that are guaranteed to be manufacturable is needed. However, this should leave intact as much of the design space as possible. Work has been done in this area for some specific domains, but a general method for accomplishing this has not yet been refined. This article presents an exploration of this problem and a developed framework for mapping practical manufacturing knowledge into mathematical manufacturability constraints in mechanical design problem formulations. The steps for completing this mapping and the enforcing of the constraints are discussed and demonstrated. Three case studies (a milled heat exchanger fin, a 3-D printed topologically optimized beam, and a pulley requiring a hybrid additive–subtractive process for production) were completed to demonstrate the concepts; these included problem formulation, generation and enforcement of the manufacturability constraints, and fabrication of the resulting designs with and without explicit manufacturability constraints.

Optimal Taxation and R&amp;D Policies

We study the optimal design of corporate taxation and R&amp;D policies as a dynamic mechanism design problem with spillovers. Firms have heterogeneous research productivity, and that research productivity is private information. There are non‐internalized technological spillovers across firms, but the asymmetric information prevents the government from correcting them in the first best way. We highlight that key parameters for the optimal policies are (i) the relative complementarities between observable R&amp;D investments, unobservable R&amp;D inputs, and firm research productivity, (ii) the dispersion and persistence of firms' research productivities, and (iii) the magnitude of technological spillovers across firms. We estimate our model using firm‐level data matched to patent data and quantify the optimal policies. In the data, high research productivity firms get disproportionately higher returns to R&amp;D investments than lower productivity firms. Very simple innovation policies, such as linear corporate taxes combined with a nonlinear R&amp;D subsidy—which provides lower marginal subsidies at higher R&amp;D levels—can do almost as well as the unrestricted optimal policies. Our formulas and theoretical and numerical methods are more broadly applicable to the provision of firm incentives in dynamic settings with asymmetric information and spillovers, and to firm taxation more generally.

Configuration design of compliant mechanism by infill structure generation method

Part of the authors have proposed an infill structure generation method to obtain several suitable structural configurations, that is different from the structural optimization method that obtains a single optimal configuration. The method arranges the structural components fitted to the principal stress distributions for the grayscale optimum configuration obtained by SIMP method. This study applies the infill structure generation method to a compliant mechanism design problem. Through numerical examples, validity of the proposed method is demonstrated. Then, properties of several obtained structural configurations are compared.

The Design of Optimal Pay-as-Bid Procurement Mechanisms

Problem definition: We consider the mechanism design problem of finding an optimal pay-as-bid mechanism in which the platform chooses an assortment of suppliers that balances the tradeoff between two objectives: providing enough variety to accommodate heterogeneous buyers, yet at low prices. Academic/practical Relevance: Modern buying channels, including e-commerce and public and private procurement, often consist of a single platform that intermediates transactions. Frequently, these platforms implement simple and transparent mechanisms to induce suppliers' direct participation, which typically result in pay-as-bid (or first-price) mechanisms where suppliers set their prices. Methodology: We introduce a novel class of assortment mechanisms that we call k-soft-reserves (k-SRs): if at least k suppliers choose a price below the soft-reserve price, then only those suppliers are added to the assortment; otherwise, all the suppliers are added. Results: For a broad class of symmetric models, we show the optimality of k-SRs. Additionally, we provide evidence of the robustness of k-SRs and of their extensions in more general settings. Managerial implications: Our results give intuitive and simple-to-use prescriptions on how to optimize pay-as-bid assortment mechanisms in practice, with an emphasis on procurement settings.

A Hierarchical Incentive Design Toward Motivating Participation in Coded Federated Learning

Federated Learning (FL) is a privacy-preserving collaborative learning approach that trains artificial intelligence (AI) models without revealing local datasets of the FL workers. While FL ensures the privacy of the FL workers, its performance is limited by several bottlenecks, which become significant given the increasing amounts of data generated and the size of the FL network. One of the main challenges is the straggler effects where the significant computation delays are caused by the slow FL workers. As such, Coded Federated Learning (CFL), which leverages coding techniques to introduce redundant computations to the FL server, has been proposed to reduce the computation latency. In CFL, the FL server helps to compute a subset of the partial gradients based on the composite parity data and aggregates the computed partial gradients with those received from the FL workers. In order to implement the coding schemes over the FL network, incentive mechanisms are important to allocate the resources of the FL workers and data owners efficiently in order to complete the CFL training tasks. In this paper, we consider a two-level incentive mechanism design problem. In the lower level, the data owners are allowed to support the FL training tasks of the FL workers by contributing their data. To model the dynamics of the selection of FL workers by the data owners, an evolutionary game is adopted to achieve an equilibrium solution. In the upper level, a deep learning based auction is proposed to model the competition among the model owners.

SOLVING INTEGER PROGRAMMING PROBLEMS BY USING POPULATION-BASED BEETLE ANTENNAE SEARCH ALGORITHM

Beetle antennae search (BAS) algorithm is a newly proposed single-solution based metaheuristic technique inspired by the beetle preying process. Although BAS algorithm has shown good search abilities, it can be easily trapped into local optimum when it is used to solve hard optimization problems. With the intention to overcome this drawback, this paper presents a population-based beetle antennae search (PBAS) algorithm for solving integer programming problems. This method employs the population's capability to search diverse regions of the search space to provide better guarantee for finding the optimal solution. The PBAS method was tested on nine integer programming problems and one mechanical design problem. The proposed algorithm was compared to other state-of-the-art metaheuristic techniques. The comparisons show that the proposed PBAS algorithm produces better results for majority of tested problems.