Sofiene Lassoued, Laxmikant Shrikant Bahetic, Nathalie Weiß-Borkowskib
et al.
Flexible Manufacturing Systems (FMS) are pivotal in optimizing production processes in today's rapidly evolving manufacturing landscape. This paper advances the traditional job shop scheduling problem by incorporating additional complexities through the simultaneous integration of automated guided vehicles (AGVs) and tool-sharing systems. We propose a novel approach that combines Colored-Timed Petri Nets (CTPNs) with actor-critic model-based reinforcement learning (MBRL), effectively addressing the multifaceted challenges associated with FMS. CTPNs provide a formal modeling structure and dynamic action masking, significantly reducing the action search space, while MBRL ensures adaptability to changing environments through the learned policy. Leveraging the advantages of MBRL, we incorporate a lookahead strategy for optimal positioning of AGVs, improving operational efficiency. Our approach was evaluated on small-sized public benchmarks and a newly developed large-scale benchmark inspired by the Taillard benchmark. The results show that our approach matches traditional methods on smaller instances and outperforms them on larger ones in terms of makespan while achieving a tenfold reduction in computation time. To ensure reproducibility, we propose a gym-compatible environment and an instance generator. Additionally, an ablation study evaluates the contribution of each framework component to its overall performance.
Vikrant Ashvinkumar, Rezaul Chowdhury, Jie Gao
et al.
Motivated by the problem of estimating bottleneck capacities on the Internet, we formulate and study the problem of vantage point selection. We are given a graph $G=(V, E)$ whose edges $E$ have unknown capacity values that are to be discovered. Probes from a vantage point, i.e, a vertex $v \in V$, along shortest paths from $v$ to all other vertices, reveal bottleneck edge capacities along each path. Our goal is to select $k$ vantage points from $V$ that reveal the maximum number of bottleneck edge capacities. We consider both a non-adaptive setting where all $k$ vantage points are selected before any bottleneck capacity is revealed, and an adaptive setting where each vantage point selection instantly reveals bottleneck capacities along all shortest paths starting from that point. In the non-adaptive setting, by considering a relaxed model where edge capacities are drawn from a random permutation (which still leaves the problem of maximizing the expected number of revealed edges NP-hard), we are able to give a $1-1/e$ approximate algorithm. In the adaptive setting we work with the least permissive model where edge capacities are arbitrarily fixed but unknown. We compare with the best solution for the particular input instance (i.e. by enumerating all choices of $k$ tuples), and provide both lower bounds on instance optimal approximation algorithms and upper bounds for trees and planar graphs.
This paper investigates a multiuser millimeter-wave (mmWave) uplink system in which each user is equipped with a multi-antenna fluid antenna system (FAS) while the base station (BS) has multiple fixed-position antennas. Our primary objective is to maximize the system capacity by optimizing the transmit covariance matrices and the antenna position vectors of the users jointly. To gain insights, we start by deriving upper bounds and approximations for the capacity. Then we delve into the capacity maximization problem. Beginning with the simple scenario of a single user equipped with a single-antenna FAS, we demonstrate that a closed-form optimal solution exists when there are only two propagation paths between the user and the BS. In the case where multiple propagation paths are present, a near-optimal solution can also be obtained through a one-dimensional search method. Expanding our focus to multiuser cases, in which users are equipped with either single- or multi-antenna FAS, we show that the original capacity maximization problems can be reformulated into distinct rank-one programmings. Then, we propose alternating optimization algorithms to deal with the transformed problems. Simulation results indicate that FAS can improve the capacity of the multiple access channel (MAC) greatly, and the proposed algorithms outperform all the benchmarks.
Hosting capacity analysis is essential for effective integration of distributed energy resources into distribution systems. This paper discusses hosting capacity analysis with emphasis on various aspects affecting the process. This paper addresses key research gaps, aiming to improve the accuracy, scalability, and practicality of hosting capacity estimation. Standardized methodologies are highlighted as a need to ensure consistent hosting capacity estimation across distribution systems. Validation and benchmarking frameworks are emphasized for evaluating various estimation approaches. The potential of data-driven techniques, is also discussed for enhancing hosting capacity analysis. Real-time and dynamic estimation techniques which account for changing system conditions are explored, as well as the integration of hosting capacity analysis with distribution planning and operations. Uncertainty quantification and risk assessment in hosting capacity analysis are identified as crucial areas, advocating for probabilistic and stochastic modelling. This study also emphasizes the importance of considering multiple DER interactions and synergies in hosting capacity analysis, enabling a comprehensive understanding of system performance. This survey aims to serve as a valuable resource for researchers, practitioners, and policymakers, providing insights into advancements made and guiding future research efforts to address identified gaps.
In the "Bits Through Queues" paper, it was hypothesized that full feedback always increases the capacity of first-in-first-out queues, except when the service time distribution is memoryless. More recently, a non-explicit sufficient condition under which feedback increases capacity was provided, along with simple examples of service times meeting this condition. While this condition yields examples where feedback is beneficial, it does not offer explicit structural properties of such service times. In this paper, we show that full feedback increases capacity whenever the service time has bounded support. This is achieved by investigating a generalized notion of feedback, with full feedback and weak feedback as particular cases.
We generalize the multiple-play multi-armed bandits (MP-MAB) problem with a shareable arm setting, in which several plays can share the same arm. Furthermore, each shareable arm has a finite reward capacity and a ''per-load'' reward distribution, both of which are unknown to the learner. The reward from a shareable arm is load-dependent, which is the "per-load" reward multiplying either the number of plays pulling the arm, or its reward capacity when the number of plays exceeds the capacity limit. When the "per-load" reward follows a Gaussian distribution, we prove a sample complexity lower bound of learning the capacity from load-dependent rewards and also a regret lower bound of this new MP-MAB problem. We devise a capacity estimator whose sample complexity upper bound matches the lower bound in terms of reward means and capacities. We also propose an online learning algorithm to address the problem and prove its regret upper bound. This regret upper bound's first term is the same as regret lower bound's, and its second and third terms also evidently correspond to lower bound's. Extensive experiments validate our algorithm's performance and also its gain in 5G & 4G base station selection.
Recently, several methods have been proposed for estimating the mutual information from sample data using deep neural networks and without the knowing closed form distribution of the data. This class of estimators is referred to as neural mutual information estimators. Although very promising, such techniques have yet to be rigorously bench-marked so as to establish their efficacy, ease of implementation, and stability for capacity estimation which is joint maximization frame-work. In this paper, we compare the different techniques proposed in the literature for estimating capacity and provide a practitioner perspective on their effectiveness. In particular, we study the performance of mutual information neural estimator (MINE), smoothed mutual information lower-bound estimator (SMILE), and directed information neural estimator (DINE) and provide insights on InfoNCE. We evaluated these algorithms in terms of their ability to learn the input distributions that are capacity approaching for the AWGN channel, the optical intensity channel, and peak power-constrained AWGN channel. For both scenarios, we provide insightful comments on various aspects of the training process, such as stability, sensitivity to initialization.
Francisco McGee, Quentin Novinger, Ronald M. Levy
et al.
Potts models and variational autoencoders (VAEs) have recently gained popularity as generative protein sequence models (GPSMs) to explore fitness landscapes and predict the effect of mutations. Despite encouraging results, quantitative characterization and comparison of GPSM-generated probability distributions is still lacking. It is currently unclear whether GPSMs can faithfully reproduce the complex multi-residue mutation patterns observed in natural sequences arising due to epistasis. We develop a set of sequence statistics to assess the "generative capacity" of three GPSMs of recent interest: the pairwise Potts Hamiltonian, the VAE, and the site-independent model, using natural and synthetic datasets. We show that the generative capacity of the Potts Hamiltonian model is the largest, in that the higher order mutational statistics generated by the model agree with those observed for natural sequences. In contrast, we show that the VAE's generative capacity lies between the pairwise Potts and site-independent models. Importantly, our work measures GPSM generative capacity in terms of higher-order sequence covariation statistics which we have developed, and provides a new framework for evaluating and interpreting GPSM accuracy that emphasizes the role of epistasis.
Manufacturing industry is heading towards socialization, interconnection, and platformization. Motivated by the infiltration of sharing economy usage in manufacturing, this paper addresses a new factory model -- shared factory -- and provides a theoretical architecture and some actual cases for manufacturing sharing. Concepts related to three kinds of shared factories which deal respectively with sharing production-orders, manufacturing-resources and manufacturing-capabilities, are defined accordingly. These three kinds of shared factory modes can be used for building correspondent sharing manufacturing ecosystems. On the basis of sharing economic analysis, we identify feasible key enabled technologies for configuring and running a shared factory. At the same time, opportunities and challenges of enabling the shared factory are also analyzed in detail. In fact, shared factory, as a new production node, enhances the sharing nature of social manufacturing paradigm, fits the needs of light assets and gives us a new chance to use socialized manufacturing resources. It can be drawn that implementing a shared factory would reach a win-win way through production value-added transformation and social innovation.
The private search problem is introduced, where a dataset comprised of $L$ i.i.d. records is replicated across $N$ non-colluding servers, each record takes values uniformly from an alphabet of size $K$, and a user wishes to search for all records that match a privately chosen value, without revealing any information about the chosen value to any individual server. The capacity of private search is the maximum number of bits of desired information that can be retrieved per bit of download. The asymptotic (large $K$) capacity of private search is shown to be $1-1/N$, even as the scope of private search is further generalized to allow approximate (OR) search over a number of realizations that grows with $K$. The results are based on the asymptotic behavior of a new converse bound for private information retrieval with arbitrarily dependent messages.
We study natural examples of binary channels with synchronization errors. These include the duplication channel, which independently outputs a given bit once or twice, and geometric channels that repeat a given bit according to a geometric rule, with or without the possibility of bit deletion. We apply the general framework of Cheraghchi (STOC 2018) to obtain sharp analytical upper bounds on the capacity of these channels. Previously, upper bounds were known via numerical computations involving the computation of finite approximations of the channels by a computer and then using the obtained numerical results to upper bound the actual capacity. While leading to sharp numerical results, further progress on the full understanding of the channel capacity inherently remains elusive using such methods. Our results can be regarded as a major step towards a complete understanding of the capacity curves. Quantitatively, our upper bounds sharply approach, and in some cases surpass, the bounds that were previously only known by purely numerical methods. Among our results, we notably give a completely analytical proof that, when the number of repetitions per bit is geometric (supported on $\{0,1,2,\dots\}$) with mean growing to infinity, the channel capacity remains substantially bounded away from $1$.
A class of burst noise-erasure channels which incorporate both errors and erasures during transmission is studied. The channel, whose output is explicitly expressed in terms of its input and a stationary ergodic noise-erasure process, is shown to have a so-called "quasi-symmetry" property under certain invertibility conditions. As a result, it is proved that a uniformly distributed input process maximizes the channel's block mutual information, resulting in a closed-form formula for its non-feedback capacity in terms of the noise-erasure entropy rate and the entropy rate of an auxiliary erasure process. The feedback channel capacity is also characterized, showing that feedback does not increase capacity and generalizing prior related results. The capacity-cost function of the channel with and without feedback is also investigated. A sequence of finite-letter upper bounds for the capacity-cost function without feedback is derived. Finite-letter lower bonds for the capacity-cost function with feedback are obtained using a specific encoding rule. Based on these bounds, it is demonstrated both numerically and analytically that feedback can increase the capacity-cost function for a class of channels with Markov noise-erasure processes.
Capacity of vehicular networks with infrastructure support is both an interesting and challenging problem as the capacity is determined by the inter-play of multiple factors including vehicle-to-infrastructure (V2I) communications, vehicle-to-vehicle (V2V) communications, density and mobility of vehicles, and cooperation among vehicles and infrastructure. In this paper, we consider a typical delay-tolerant application scenario with a subset of vehicles, termed Vehicles of Interest (VoIs), having download requests. Each VoI downloads a distinct large-size file from the Internet and other vehicles without download requests assist the delivery of the files to the VoIs. A cooperative communication strategy is proposed that explores the combined use of V2I communications, V2V communications, mobility of vehicles and cooperation among vehicles and infrastructure to improve the capacity of vehicular networks. An analytical framework is developed to model the data dissemination process using this strategy, and a closed form expression of the achievable capacity is obtained, which reveals the relationship between the capacity and its major performance-impacting parameters such as inter-infrastructure distance, radio ranges of infrastructure and vehicles, sensing range of vehicles, transmission rates of V2I and V2V communications, vehicular density and proportion of VoIs. Numerical result shows that the proposed cooperative communication strategy significantly boosts the capacity of vehicular networks, especially when the proportion of VoIs is low. Our results provide guidance on the optimum deployment of vehicular network infrastructure and the design of cooperative communication strategy to maximize the capacity.
Francesco Caravelli, Lorenzo Sindoni, Fabio Caccioli
et al.
We consider the problem of finding optimal strategies that maximize the average growth-rate of multiplicative stochastic processes. For a geometric Brownian motion the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a non-linear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases compute optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.
This paper focuses on the capacity of point-to-point relay communications wherein the transmitter is assisted by an intermediate relay. We detail the mathematical model of cutset and amplify and forward (AF) relaying strategy. We present the upper bound capacity of each relaying strategy from information theory viewpoint and also in networks with Gaussian channels. We exemplify various outer region capacities of the addressed strategies with two different case studies. The results exhibit that in low signal-to-noise ratio (SNR) environments the cutset performance is better than amplify and forward strategy.
Thermal properties of few-fermion (n < 5) systems are investigated. The dependence of the heat capacity on the topology and shape of the cavity containing the particles is analyzed. It is found that the maximum of the heat capacity, occuring at low T, discussed recently by Toutounji for a system with n = 1 fermions, is even more visible for n = 2, but fades away for n = 3 and 4. For large T, the classical behavior is obtained; however, when T -> 0, the heat capacity tends to zero exponentially, not linearly, as in macroscopic and even mesoscopic systems. The physical relevance of these results is discussed.
We introduce the concept of the point of minimal capacity of the domain, and observe a connection between this point and the lowest eigenfunction of a Laplacian on this domain, in one special case.
We present an algorithm for calculation of the Gaussian classical capacity of a quantum bosonic memory channel with additive Gaussian noise. The algorithm, restricted to Gaussian input states, is applicable to all channels with noise correlations obeying certain conditions and works in the full input energy domain, beyond previous treatments of this problem. As an illustration, we study the optimal input states and capacity of a quantum memory channel with Gauss-Markov noise [J. Schäfer, Phys. Rev. A 80, 062313 (2009)]. We evaluate the enhancement of the transmission rate when using these optimal entangled input states by comparison with a product coherent-state encoding and find out that such a simple coherent-state encoding achieves not less than 90% of the capacity.
We study the classical problem of noisy constrained capacity in the case of the binary symmetric channel (BSC), namely, the capacity of a BSC whose inputs are sequences chosen from a constrained set. Motivated by a result of Ordentlich and Weissman [In Proceedings of IEEE Information Theory Workshop (2004) 117--122], we derive an asymptotic formula (when the noise parameter is small) for the entropy rate of a hidden Markov chain, observed when a Markov chain passes through a BSC. Using this result, we establish an asymptotic formula for the capacity of a BSC with input process supported on an irreducible finite type constraint, as the noise parameter tends to zero.