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A constraint satisfaction problem (CSP), \(\textsf {Max-CSP}(\mathcal {F})\) , is specified by a finite set of constraints \(\mathcal {F}\subseteq \lbrace [q]^k \rightarrow \lbrace 0,1\rbrace \rbrace\) for positive integers q and k. An instance of the problem on n variables is given by m applications of constraints from \(\mathcal {F}\) to subsequences of the n variables, and the goal is to find an assignment to the variables that satisfies the maximum number of constraints. In the (γ ,β)-approximation version of the problem for parameters 0 ≤ β ≤ γ ≤ 1, the goal is to distinguish instances where at least γ fraction of the constraints can be satisfied from instances where at most β fraction of the constraints can be satisfied. In this work, we consider the approximability of this problem in the context of sketching algorithms and give a dichotomy result. Specifically, for every family \(\mathcal {F}\) and every β < γ, we show that either a linear sketching algorithm solves the problem in polylogarithmic space or the problem is not solvable by any sketching algorithm in \(o(\sqrt {n})\) space. In particular, we give non-trivial approximation algorithms using polylogarithmic space for infinitely many constraint satisfaction problems. We also extend previously known lower bounds for general streaming algorithms to a wide variety of problems, and in particular the case of q=k=2, where we get a dichotomy, and the case when the satisfying assignments of the constraints of \(\mathcal {F}\) support a distribution on \([q]^k\) with uniform marginals. Prior to this work, other than sporadic examples, the only systematic classes of CSPs that were analyzed considered the setting of Boolean variables q = 2, binary constraints k =2, and singleton families \(|\mathcal {F}|=1\) and only considered the setting where constraints are placed on literals rather than variables. Our positive results show wide applicability of bias-based algorithms used previously by [47] and [41], which we extend to include richer norm estimation algorithms, by giving a systematic way to discover biases. Our negative results combine the Fourier analytic methods of [56], which we extend to a wider class of CSPs, with a rich collection of reductions among communication complexity problems that lie at the heart of the negative results. In particular, previous works used Fourier analysis over the Boolean cube to initiate their results and the results seemed particularly tailored to functions on Boolean literals (i.e., with negations). Our techniques surprisingly allow us to get to general q-ary CSPs without negations by appealing to the same Fourier analytic starting point over Boolean hypercubes. [ABSTRACT FROM AUTHOR]

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and non-convex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction problems. Tree search algorithms come with a variety of tunable parameters that are notoriously challenging to tune by hand. A growing body of research has demonstrated the power of using a data-driven approach to automatically optimize the parameters of tree search algorithms. These techniques use a training set of integer programs sampled from an application-specific instance distribution to find a parameter setting that has strong average performance over the training set. However, with too few samples, a parameter setting may have strong average performance on the training set but poor expected performance on future integer programs from the same application. Our main contribution is to provide the first sample complexity guarantees for tree search parameter tuning. These guarantees bound the number of samples sufficient to ensure that the average performance of tree search over the samples nearly matches its future expected performance on the unknown instance distribution. In particular, the parameters we analyze weight scoring rules used for variable selection. Proving these guarantees is challenging because tree size is a volatile function of these parameters: we prove that, for any discretization (uniform or not) of the parameter space, there exists a distribution over integer programs such that every parameter setting in the discretization results in a tree with exponential expected size, yet there exist parameter settings between the discretized points that result in trees of constant size. In addition, we provide data-dependent guarantees that depend on the volatility of these tree-size functions: our guarantees improve if the tree-size functions can be well approximated by simpler functions. Finally, via experiments, we illustrate that learning an optimal weighting of scoring rules reduces tree size. [ABSTRACT FROM AUTHOR]

The efficiency of material supply for workstations using Automatic Guided Vehicles (AGVs) is largely determined by the performance of the AGV dispatching scheme. This paper proposes a new solution approach for the AGV dispatching problem (AGVDP) for material replenishment in a general manufacturing workshop where workstations are in a matrix layout, and where uncertainty in replenishment time of workstations and stochastic unloading efficiencies of AGVs are dynamic contextual factors. We first extend the literature proposing a mixed integer optimisation model with a delivery satisfaction soft constraint of material orders and two objectives: transportation costs and delivery time deviation. We then develop a new knowledge-guided estimation of distribution algorithm with delivery satisfaction evaluation for solving the model. Our algorithm fuses three knowledge-guided strategies to enhance optimisation capabilities at its respective execution stages. Comprehensive numerical experiments with instances built from a real-world scenario validate the proposed model and algorithm. Results demonstrate that the new algorithm outperforms three popular multi-objective evolutionary algorithms, a discrete version of a recent multi-objective particle swarm optimisation, and a multi-objective estimation of distribution algorithm. Findings of this work provide major implications for workshop management and algorithm design. [ABSTRACT FROM AUTHOR]

Conceptual design is a pivotal stage of new product development. The function-behaviour-structure framework is adopted in this stage to help designers search design space and generate conceptual solutions iteratively. Computer-aided methods developed within this framework will yield significant insight into facilitating the cognitive activities of designers. In order to solve the mapping process from behaviours to structures which is a typical constraint satisfaction problem, a cerebellar operant conditioning-inspired constraint satisfaction approach is proposed in this paper. The design constraints-driven operant conditioning and its regulation mechanism by the cerebellum are analysed for the first time. Proposition logic is applied to transfer the constraint satisfaction problem into a propositional satisfiability problem while an undirected graph is utilised to model design space. Inspired by the modularised cerebellar structure, a modularised constraint satisfaction neural network is constructed to determine the satisfiability of design problems. Conceptual solutions can be generated by clustering the embedding of nodes in this network. The proposed approach imitates the design constraint-driven operant conditioning to narrow down design space without assigning specific values to design components. It reduces design iterations and avoids combinatorial explosions during conceptual design. [ABSTRACT FROM AUTHOR]

This paper proposes a novel reliable model predictive control (MPC) method for active vibration control of structure with nonprobabilistic uncertainties. First, the framework of reliable MPC is established by integrating nonprobabilistic reliability constraints into nominal MPC. Based on the first‐order Taylor expansion and first‐passage theory, an efficient nonprobabilistic reliability analysis method that is suitable for online computation is proposed. A nonprobabilistic Kalman filter is further proposed for determine system states and their uncertain region. Unlike most robust MPC approaches, the proposed reliable MPC focuses on the satisfaction of state constraints in terms of structural reliability and is more suitable for structures with stringent safety requirements. Compared to existing reliability‐based vibration control methods, reliable MPC requires no knowledge of disturbance and exhibits greater adaptability to load environments. The effectiveness and superiority of the proposed reliable MPC are validated through a numerical example and an engineering case study. [ABSTRACT FROM AUTHOR]

The N-Queens problem is a fundamental challenge in combinatorial optimization, commonly used as a benchmark for assessing the efficiency of algorithms. Traditional algorithms, such as Backtracking with Forward Checking (BFC), constraint satisfaction problem (CSP) techniques, Lookahead algorithms, and heuristic-based methods, often face challenges with exponential time complexity, making them less practical for large-scale instances. This paper introduces a novel algorithm, non-sequential conflict resolution (NSCR), which improves performance over traditional algorithms through dynamic conflict resolution. The NSCR algorithm iteratively resolves conflicts among queens by adjusting their positions, aiming to optimize both time complexity and memory usage. While NSCR also operates within exponential time bounds, it demonstrates improved scalability and efficiency compared to traditional methods. A significant strength of the NSCR algorithm lies in its space complexity, which is O(n), and a time complexity that, while typically lower than traditional methods, can reach O(n3) in the worst-case scenario. This linear space complexity is highly advantageous, particularly when dealing with large problem sizes, as it ensures efficient use of memory resources. Comparative analysis with the aforementioned algorithms shows that NSCR offers superior resource management, using up to 60% less memory and reducing runtime by approximately 50%, making it an efficient option for large-scale instances of the N-Queens problem. The algorithm's performance, evaluated on problem sizes ranging from 8 to 1000 queens, highlights its ability to manage computational resources effectively, despite the inherent challenges of exponential time complexity. [ABSTRACT FROM AUTHOR]

In the context of constructing new power systems, the intermittency and volatility of high-penetration renewable generation pose new challenges to the stability and secure operation of power systems. Enhancing the ramping capability of power systems has become a crucial measure for addressing these challenges. Therefore, this paper proposes a bi-level peak regulation optimization model for power systems considering ramping capability and demand response, aiming to mitigate the challenges that the uncertainty and volatility of renewable energy generation impose on power system operations. Firstly, the upper-level model focuses on minimizing the ramping demand caused by the uncertainty, taking into account concerned constraints such as the constraint of price-guided demand response, the constraint of satisfaction with electricity usage patterns, and the constraint of cost satisfaction. By solving the upper-level model, the ramping demand of the power system can be reduced. Secondly, the lower-level model aims to minimize the overall cost of the power system, considering constraints such as power balance constraints, power flow constraints, ramping capability constraints of thermal power units, stepwise ramp rate calculation constraints, and constraints of carbon capture units. Based on the ramping demand obtained by solving the upper-level model, the outputs of the generation units are optimized to reduce operation cost of power systems. Finally, the proposed peak regulation optimization model is verified through simulation based on the IEEE 39-bus system. The results indicate that the proposed model, which incorporates ramping capability and demand response, effectively reduces the comprehensive operational cost of the power system. [ABSTRACT FROM AUTHOR]

Mining frequent sequences (FS) with constraints in a sequence database (SDB) are a critical task in Data Mining, as it forms the basis for discovering meaningful patterns within sequential data. However, traditional algorithms tackling the direct mining of constrained FSs from the SDB often exhibit poor performance, especially when dealing with large SDBs and low support thresholds. Moreover, constraint-based sequence mining algorithms face additional challenges, such as increased runtime and memory usage, particularly when constraints change frequently. To address these issues, this paper introduces an efficient method for generating FSs that include a user-defined sub-sequence. Specifically, the discovered FSs must be super-sequences of the given sub-sequence. Rather than directly discovering these sequences from a sequence database (SDB) in the traditional manner, the proposed method quickly generates constrained FSs from frequent closed sequences (FCS) and frequent generator sequences (FGS). This process involves categorizing constrained FSs into equivalence classes; each represented by FCSs and FGSs. An efficient method is then adapted to swiftly generate constrained FSs within each class based on the representative elements, which are FCSs and FGSs. Additionally, a novel technique called Constraint Satisfaction Technique (CST) is introduced to circumvent computationally expensive checks for the inclusion relation among sequences during the generation process. Furthermore, a novel algorithm named MFS-SubSC is developed based on the proposed theoretical results to generate all constrained FSs efficiently. Experimental results demonstrate that the proposed algorithm surpasses state-of-the-art methods in terms of runtime, memory usage, and scalability. [ABSTRACT FROM AUTHOR]

We study logical reduction (factorization) of relations into relations of lower arity by Boolean or relative products that come from applying conjunctions and existential quantifiers to predicates, i.e. by primitive positive formulas of predicate calculus. Our algebraic framework unifies natural joins and data dependencies of database theory and relational algebra of clone theory with the bond algebra of C.S. Peirce. We also offer new constructions of reductions, systematically study irreducible relations and reductions to them and introduce a new characteristic of relations, ternarity, that measures their 'complexity of relating' and allows to refine reduction results. In particular, we refine Peirce's controversial reduction thesis, and show that reducibility behaviour is dramatically different on finite and infinite domains. [ABSTRACT FROM AUTHOR]

Rate of penetration (ROP) is crucial for evaluating drilling efficiency, with accurate prediction essential for enhancing performance and optimizing parameters. In practice, complex and variable downhole environments pose significant challenges for mechanistic ROP equations, resulting in prediction difficulties and low accuracy. Recently, data-driven machine learning models have been widely applied to ROP prediction. However, these models often lack mechanistic constraints, limiting their performance to specific conditions and reducing their real-world applicability. Additionally, geological variability across wells further hinders the transferability of conventional intelligent models. Thus, combining mechanistic knowledge with intelligent models and enhancing model stability and transferability are key challenges in ROP prediction research. To address these challenges, this paper proposes a Mechanism-Data Fusion and Transfer Learning method to construct an intelligent prediction model for ROP, achieving accurate ROP predictions. A multilayer perceptron (MLP) was selected as the base model, and training was performed using data from neighboring wells and partial data from the target well. The Two-stage TrAdaBoost.R2 algorithm was employed to enhance model transferability. Additionally, drilling mechanistic knowledge was incorporated into the model's loss function as a constraint to achieve a fusion of mechanistic knowledge and data-driven approaches. Using MAPE as the measure of accuracy, compared with conventional intelligent models, the proposed ROP prediction model improved prediction accuracy on the target well by 64.51%. The model transfer method proposed in this paper has a field test accuracy of 89.71% in an oilfield in China. These results demonstrate the effectiveness and feasibility of the proposed transfer learning method and mechanistic–data integration approach. [ABSTRACT FROM AUTHOR]

We present a novel data-driven Model Predictive Control (MPC) algorithm for nonlinear systems. The method is based on recent extensions of behavioural theory and Willem's Fundamental Lemma for nonlinear systems by the means of adequate Input–Output (IO) quasi-Linear Parameter-Varying (qLPV) embeddings. Thus, the MPC is formulated to ensure regulation and IO constraints satisfaction, based only on measured datasets of sufficient length (and under persistent excitation). The main innovation is to consider the knowledge of the function that maps the qLPV realisation, and apply an extrapolation procedure in order to generate the corresponding future scheduling trajectories, at each sample. Accordingly, we briefly discuss the issues of closed-loop IO stability and recursive feasibility certificates of the method. The algorithm is tested and discussed with the aid of a numerical application. [ABSTRACT FROM AUTHOR]

The complexity of the promise constraint satisfaction problem \(\operatorname{(PCSP)}(\mathbf{A},\mathbf{B})\) is largely unknown, even for symmetric \(\mathbf{A}\) and \(\mathbf{B}\) , except for the case when \(\mathbf{A}\) and \(\mathbf{B}\) are Boolean. First, we establish a dichotomy for \(\operatorname{PCSP}(\mathbf{A},\mathbf{B})\) where \(\mathbf{A},\mathbf{B}\) are symmetric, \(\mathbf{B}\) is functional (i.e., any \(r-1\) elements of an \(r\) -ary tuple uniquely determines the last one), and \((\mathbf{A},\mathbf{B})\) satisfies technical conditions we introduce called dependency and additivity. This result implies a dichotomy for \(\operatorname{PCSP}(\mathbf{A},\mathbf{B})\) with \(\mathbf{A},\mathbf{B}\) symmetric and \(\mathbf{B}\) functional if (i) \(\mathbf{A}\) is Boolean, or (ii) \(\mathbf{A}\) is a hypergraph of a small uniformity, or (iii) \(\mathbf{A}\) has a relation \(R^{\mathbf{A}}\) of arity at least three such that the hypergraph diameter of \((A,R^{\mathbf{A}})\) is at most one. Second, we show that for \(\operatorname{PCSP}(\mathbf{A},\mathbf{B})\) , where \(\mathbf{A}\) and \(\mathbf{B}\) contain a single relation, \(\mathbf{A}\) satisfies a technical condition called balancedness, and \(\mathbf{B}\) is arbitrary, the combined basic linear programming relaxation and the affine integer programming (AIP) relaxation is no more powerful than the (in general strictly weaker) \({{\rm AIP}}\) relaxation. Balanced \(\mathbf{A}\) include symmetric \(\mathbf{A}\) or, more generally, \(\mathbf{A}\) preserved by a transitive permutation group. [ABSTRACT FROM AUTHOR]

We study the complexity of infinite-domain constraint satisfaction problems (CSPs): our basic setting is that a complexity classification for the CSPs of first-order expansions of a structure 21 can be transferred to a classification of the CSPs of first-order expansions of another structure 53. We exploit a product of structures (the algebraic product) that corresponds to the product of the respective polymorphism clones and present a complete complexity classification of the CSPs for first-order expansions of the n-fold algebraic power of (ℚ;<). This is proved by various algebraic and logical methods in combination with knowledge of the polymorphisms of the tractable first-order expansions of (ℚ;<) and explicit descriptions of the expressible relations in terms of syntactically restricted first-order formulas. By combining our classification result with general classification transfer techniques, we obtain surprisingly strong new classification results for highly relevant formalisms such as Allen's Interval Algebra, the n-dimensional Block Algebra, and the Cardinal Direction Calculus, even if higher-arity relations are allowed. Our results confirm the infinite-domain tractability conjecture for classes of structures that have been difficult to analyze with older methods. For the special case of structures with binary signatures, the results can be substantially strengthened and tightly connected to Ord-Horn formulas; this solves several longstanding open problems from the artificial intelligence (AI) literature. [ABSTRACT FROM AUTHOR]

Constraint Programming (CP) is a successful methodology for solving combinatorial problems from various domains. Efficiently modeling the problem at hand as a Constraint Satisfaction Problem is a crucial, but difficult task in CP. Toward this, a recent approach that is attracting increasing interest is Constraint Acquisition, i.e., the (semi)automatic learning of constraints through examples of solutions and non-solutions. This paper introduces a hybrid methodology that combines passive and active learning strategies to acquire both global and fixed arity constraints. This hybrid approach leverages the strengths of both techniques to address their individual limitations. Passive learning rapidly learns constraints from example solutions, while active learning refines and contextualizes constraints through user interaction. The core of the methodology consists of a passive learning module where subsets of variables are compared against global constraints and are validated using a CP solver. Constraints consistently present across multiple solution sets are identified as global constraints that belong to the model. Then, fixed arity constraints are refined through an active learning module with user input. Experiments across various problem types, from simple to complex, demonstrate the efficiency of the proposed hybrid methodology. [ABSTRACT FROM AUTHOR]

The task of localizing distinct anatomical structures in medical image data is an essential prerequisite for several medical applications, such as treatment planning in orthodontics, bone-age estimation, or initialization of segmentation methods in automated image analysis tools. Currently, Anatomical Landmark Localization (ALL) is mainly solved by deep-learning methods, which cannot guarantee robust ALL predictions; there may always be outlier predictions that are far from their ground truth locations due to out-of-distribution inputs. However, these localization outliers are detrimental to the performance of subsequent medical applications that rely on ALL results. The current ALL literature relies heavily on implicit anatomical constraints built into the loss function and network architecture to reduce the risk of anatomically infeasible predictions. However, we argue that in medical imaging, where images are generally acquired in a controlled environment, we should use stronger explicit anatomical constraints to reduce the number of outliers as much as possible. Therefore, we propose the end-to-end trainable Global Anatomical Feasibility Filter and Analysis (GAFFA) method, which uses prior anatomical knowledge estimated from data to explicitly enforce anatomical constraints. GAFFA refines the initial localization results of a U-Net by approximately solving a Markov Random Field (MRF) with a single iteration of the sum-product algorithm in a differentiable manner. Our experiments demonstrate that GAFFA outperforms all other landmark refinement methods investigated in our framework. Moreover, we show that GAFFA is more robust to large outliers than state-of-the-art methods on the studied X-ray hand dataset. We further motivate this claim by visualizing the anatomical constraints used in GAFFA as spatial energy heatmaps, which allowed us to find an annotation error in the hand dataset not previously discussed in the literature. [ABSTRACT FROM AUTHOR]

Although rapid economic growth can produce various positive outcomes, the fast-paced society that inevitably accompanies it often results in longer working hours and higher stress levels, leading to reduced participation in sport activities among employees. To better understand this phenomenon, we aimed to explore the constraints and experiences of adult workers. We collected data from adult workers in Singapore who desired to participate in sport activities but were unable to do so due to various constraints. A total of 10 individuals were purposefully selected for interviews. This study identified four key themes: (a) factors causing the reduction of sport participation opportunities, (b) changes in sport activities and satisfaction, (c) nostalgic feelings associated with sport activities, and (d) the role of nostalgia in enhancing sport involvement. The findings of this study suggest the possibility of adapting the conceptual model of nostalgia to sport activities, as well as identifying four factors that hinder employees from engaging in sport activities. [ABSTRACT FROM AUTHOR]

QUBO (quadratic unconstrained binary optimization) has become the modeling language for quantum annealing and quantum‐inspired annealing solvers. We present different approaches in QUBO for the magic square problem and the quadratic assignment problem (QAP), which can be modeled by linear equations and a permutation constraint over integer variables. Different ways of encoding integers by Booleans in QUBO amount to models, the implementation of which could have very different performance. Experiments performed on the Fixstars Amplify Annealer Engine, a quantum‐inspired annealing solver, show that, compared to the classical one‐hot encoding, using unary encoding for integers performs slightly better for the QAP and much better for magic square. [ABSTRACT FROM AUTHOR]

In the context of digitalized educational research, the rapid advancement of internet technologies and big data has catalyzed the transformation of traditional teaching models. The flipped classroom, recognized for its flexibility and efficiency, has garnered significant attention. However, the challenge of scientifically optimizing teaching decisions in flipped classrooms to maximize educational outcomes remains critical. Previous studies have achieved some progress in optimizing teaching decisions within flipped classrooms, yet they often suffer from a lack of methodological diversity, inadequate consideration of multi-level constraints, and struggle to adapt to dynamic teaching environments. Addressing these deficiencies, this research introduces a hybrid evolutionary algorithm combining differential evolution and greedy backtracking. Defined and classified constraints within flipped classroom teaching decisions, the construction of constraint networks, and the creation of multi-level decision spaces are transformed and solved through this hybrid algorithm, offering a systematic optimization strategy. Case analysis confirms the effectiveness and practicality of the proposed method, aiming to bolster decision-making in flipped classrooms and advance the development of digitalized teaching. [ABSTRACT FROM AUTHOR]

We study the complexity of the Distributed Constraint Satisfaction Problem (DCSP) on a synchronous, anonymous network from a theoretical standpoint. In this setting, variables and constraints are controlled by agents which communicate with each other by sending messages through fixed communication channels. Our results endorse the well-known fact from classical CSPs that the complexity of fixed-template computational problems depends on the template's invariance under certain operations. Specifically, we show that DCSP(Γ) is polynomial-time tractable if and only if Γ is invariant under symmetric polymorphisms of all arities. Otherwise, there are no algorithms that solve DCSP(Γ) in finite time. We also show that the same condition holds for the search variant of DCSP. Collaterally, our results unveil a feature of the processes' neighbourhood in a distributed network, its iterated degree, which plays a major role in the analysis. We explore this notion establishing a tight connection with the basic linear programming relaxation of a CSP. [ABSTRACT FROM AUTHOR]

For a class of full‐states constraints nonlinear system with actuator failure, an adaptive fuzzy disturbance observer tracking design is carried out by using Lyapunov function and the dynamic surface method. The integral explosion problem is avoided by using the dynamic surface design method. Because the disturbance of the system is unknown, a nonlinear fuzzy disturbance observer is designed to estimate the unknown disturbance. And the unknown nonlinear function is approximated fuzzy logic systems. Based on the Lyapunov function method and backstepping approach, the stability of considered systems are analysed. And the proposed method can guarantee that all the signals in the closed‐loop system are bounded and the system output can track the desired signal to the small neighbourhood range. In addition, the fuzzy disturbance observer can estimate the unknown disturbance state well. Finally, several sets of simulation examples are given and compared with other method, and the experimental results are quantitatively analysed. Then, the robustness and superiority of the proposed control scheme are verified and demonstrated. [ABSTRACT FROM AUTHOR]

Surrogate-based optimization (SBO) is a powerful approach for global optimization of high-dimensional expensive black-box functions, commonly consisting of four modules: design of experiment, function evaluation, surrogate construction, and infill sampling criterion. This work develops a robust and efficient SBO framework for aerodynamic shape optimization using discontinuous Galerkin methods as the computational fluid dynamics evaluation. Innovatively, the prior adjoint gradient information of the baseline shape is used to improve the performance of the sampling plan in the preliminary design of the experiment stage and further improve the robustness and efficiency of the construction of surrogate(s). Specifically, the initial sample points along the direction of objective rise have a high probability of being transformed into feasible points in a subspace of objective descending. Numerical experiments verified that the proposed gradient-improved sampling plan is capable of stably exploring the design space of objective descending and constraint satisfaction even with limited sample points, which leads to a stable improvement of the resultant aerodynamic performance of the final optimized shape. [ABSTRACT FROM AUTHOR]

The article proposes a convex distributed robust model predictive control algorithm for collision avoidance in multi‐agent systems with additive disturbances, which utilizes the concept of tube model predictive control to address the disturbances. To tackle the coupled collision avoidance constraints, each agent integrates assumed nominal position and input trajectories from its neighbors, rather than relying on actual ones. Compatibility constraints are then designed using the normal vector of the constructed separating hyperplanes for collision avoidance and the residual collision avoidance margin of the optimal solutions at the last time step to restrict deviations between assumed and actual trajectories and ensure consistency among the agents. The nonconvex collision and obstacle avoidance constraints are convexified using the concept of safe sets, transforming them into time‐varying closed polyhedral constraints while accounting for the impact of disturbances. Particularly, the residual collision avoidance margin is incorporated into the construction of safe sets for the satisfaction of coupled collision avoidance constraints. Consequently, the original collision avoidance optimal control problems can be efficiently and simultaneously solved for all agents using standard quadratic programming techniques. Under the design of local terminal constraint sets for each agent, the proposed algorithm ensures a rigorous analysis of robust constraint satisfaction for collision avoidance constraints, as well as an assessment of recursive feasibility and closed‐loop stability. The effectiveness of the algorithm is demonstrated through an illustrative example, and simulation results validate its ability to successfully achieve collision and obstacle avoidance even in the presence of disturbances. [ABSTRACT FROM AUTHOR]

Some have defended a Fregean view of perceptual content. On this view, the constituents of perceptual contents are Fregean modes of presentation (MOPs). In this paper, I propose that perceptual MOPs are best understood in terms of object files. Object files are episodic representations that store perceptual information about objects. This information is updated when sensory conditions change. On the proposed view, when a subject perceptually represents some object a under two distinct MOPs, then the subject initiates two object files that both refer to a. My defense of this view appeals to its satisfaction of four constraints that I argue theories of perceptual MOPs should satisfy. Furthermore, I show that some existent accounts of perceptual MOPs fail to satisfy them. The defended constraints also indicate what is unique about perceptual, as opposed to linguistic or cognitive, MOPs. [ABSTRACT FROM AUTHOR]

This paper describes several cases of adjunction in the homomorphism preorder of relational structures. We say that two functors Λ and Γ between thin categories of relational structures are adjoint if for all structures A and B, we have that Λ⁢(A) maps homomorphically to B if and only if A maps homomorphically to Γ⁢(𝐁). If this is the case, Λ is called the left adjoint to Γ and Γ the right adjoint to Λ. In 2015, Foniok and Tardif described some functors on the category of digraphs that allow both left and right adjoints. The main contribution of Foniok and Tardif is a construction of right adjoints to some of the functors identified as right adjoints by Pultr in 1970. We generalise results of Foniok and Tardif to arbitrary relational structures, and coincidently, we also provide more right adjoints on digraphs, and since these constructions are connected to finite duality, we also provide a new construction of duals to trees. Our results are inspired by an application in promise constraint satisfaction -- it has been shown that such functors can be used as efficient reductions between these problems. [ABSTRACT FROM AUTHOR]

This paper proposes a trajectory-optimization problem for spacecraft close proximity to a noncooperative target, aiming at the generation of a six-degree-of-freedom (DOF) trajectory with the fuel-optimal objective value and considering multiple constraints on the control magnitude, line-of-sight, and glide-slope. The line-of-sight and glide-slope constraints are coupled between translational and rotational motions. The dual quaternion is an effective method for establishing the translationally and rotationally coupled model, because it can represent the translation and rotation in an integrated manner. Therefore, in this study, the trajectory-optimization problem of spacecraft close proximity coupled with position and attitude is established using dual quaternions. Next, the close-proximity trajectory-optimization problem is converted into a nonlinear programming problem, which can be solved efficiently using well-developed algorithms such as convex optimization. However, the zero-order hold used in the discrete method of convex optimization is an equidistant dispersion, which cannot guarantee the satisfaction of constraints between discrete points. Therefore the pseudospectral convex method is proposed using nonequidistant collocation points to mitigate the problem of constraint violation between discrete points and improve the accuracy and computational efficiency of the algorithm. The proposed algorithm can be applied to tasks such as rendezvous and docking with noncooperative targets and close proximity. Finally, the effectiveness of the proposed method was validated via numerical simulation, and the results were compared with those of the existing approach, GPOPS. The results indicate that the proposed algorithm is superior to GPOPS in computational efficiency and objective values. [ABSTRACT FROM AUTHOR]

The paper presents a new Lyapunov-type predefined-time stabilization control algorithm for stochastic high-order nonlinear systems with asymmetric output constraints. In contrast to stochastic finite-time and fixed-time stabilization, the average value of the settling-time function for stochastic predefined-time stabilization control is independent of both the initial value and the control factors. To mitigate the significant uncertainties arising from the asymmetric output constraint, a tan-type barrier Lyapunov function is formulated. Furthermore, by harnessing the previously mentioned barrier Lyapunov function and integrating the power integrator technique, a controller design strategy is formulated based on the backstepping method. The rigorous analysis in this study proves that the designed controller ensures both the attainment of predefined-time convergence of the system states to the origin in probability and the satisfaction of the output constraint. Finally, an example of a roll angle subsystem for quadrotor UAVs and a numerical illustration are presented to corroborate the theoretical analysis. • A novel Lyapunov-type stochastic predefined-time stable control algorithm is presented in Theorem 1. • Controller design based on the backstepping method is formulated through the power integrator technique. • The tan-type barrier Lyapunov function extends the order range and absorbs the inherent properties of the nonlinear terms. [ABSTRACT FROM AUTHOR]

The key motivation of this paper lies in the development of a high‐level decision‐making framework for autonomous overtaking maneuvers on two‐lane country roads with dynamic oncoming traffic. To generate an optimal and safe decision sequence for such scenario, an innovative high‐level decision‐making framework that combines model predictive control (MPC) and switching control methodologies is introduced. Specifically, the autonomous vehicle is abstracted and modelled as a switched system. This abstraction allows vehicle to operate in different modes corresponding to different high‐level decisions. It establishes a crucial connection between high‐level decision‐making and low‐level behaviour of the autonomous vehicle. Furthermore, barrier functions and predictive models that account for the relationship between the autonomous vehicle and oncoming traffic are incorporated. This technique enables us to guarantee the satisfaction of constraints, while also assessing performance within a prediction horizon. By repeatedly solving the online constrained optimization problems, we not only generate an optimal decision sequence for overtaking safely and efficiently but also enhance the adaptability and robustness. This adaptability allows the system to respond effectively to potential changes and unexpected events. Finally, the performance of the proposed MPC framework is demonstrated via simulations of four driving scenarios, which shows that it can handle multiple behaviours. [ABSTRACT FROM AUTHOR]

Chance constraints are a valuable tool for the design of safe decisions in uncertain environments; they are used to model satisfaction of a constraint with a target probability. However, because of possible non-convexity and non-smoothness, optimizing over a chance constrained set is challenging. In this paper, we consider chance constrained programs where the objective function and the constraints are convex with respect to the decision parameter. We establish an exact reformulation of such a problem as a bilevel problem with a convex lower-level. Then we leverage this bilevel formulation to propose a tractable penalty approach, in the setting of finitely supported random variables. The penalized objective is a difference-of-convex function that we minimize with a suitable bundle algorithm. We release an easy-to-use open-source python toolbox implementing the approach, with a special emphasis on fast computational subroutines. [ABSTRACT FROM AUTHOR]

In recent years, the substantial growth in satellite data transmission tasks and volume, coupled with the limited availability of ground station hardware resources, has exacerbated conflicts among missions and rendered traditional scheduling algorithms inadequate. To address this challenge, this paper introduces an improved tabu genetic hybrid algorithm (ITGA) integrated with heuristic rules for the first time. Firstly, a constraint satisfaction model for satellite data transmission tasks is established, considering multiple factors such as task execution windows, satellite–ground visibility, and ground station capabilities. Leveraging heuristic rules, an initial population of high-fitness chromosomes is selected for iterative refinement. Secondly, the proposed hybrid algorithm iteratively evolves this population towards optimal solutions. Finally, the scheduling plan with the highest fitness value is selected as the best strategy. Comparative simulation experimental results demonstrate that, across four distinct scenarios, our algorithm achieves improvements in the average task success rate ranging from 1.5% to 19.8% compared to alternative methods. Moreover, it reduces the average algorithm execution time by 0.5 s to 28.46 s and enhances algorithm stability by 0.8% to 27.7%. This research contributes a novel approach to the efficient scheduling of satellite data transmission tasks. [ABSTRACT FROM AUTHOR]

Constraint satisfaction theories were prominent in the late 20th century and emphasized continuous, rich interaction between many sources of information in a linguistic signal unfolding over time. A major challenge was rigorously capturing these highly interactive comprehension processes and yielding explicit predictions, because the important constraints were numerous and changed in prominence from one context to the next. Connectionist models were conceptually well-suited to this, but researchers had insufficient computing power and lacked sufficiently large corpora to bring these models to bear. These limitations no longer hold, and large language models (LLMs) offer an opportunity to test constraint satisfaction ideas about human language comprehension. We consider how LLMs can be applied to study interactive processes with lexical ambiguity resolution as a test case. We argue that further study of LLMs can advance theories of constraint satisfaction, though gaps remain in our understanding of how people and LLMs combine linguistic information. [ABSTRACT FROM AUTHOR]

Homogeneous polynomial functions have the potential to provide a general modeling framework for yield surfaces in metal plasticity. They incorporate as particular cases many of the previously proposed yield functions and their fitting capabilities allow for capturing a wide range of yield surface shapes. And yet, there are still two unsolved problems which turn into major obstacles when it comes to actual implementations in both academic and industrial environments: The lack of a general optimization algorithm for the calibration of their parameters and the lack of an efficient computational scheme for their value, gradient and hessian. The difficulty of the first problem is two-fold, necessitating an adequate specification of the experimental input data set and satisfaction of the convexity constraint. The second problem is specific to all high degree polynomials and is comprised of issues such as numerical stability, precision and implementation efficiency. We present practical solutions to both problems: An optimization algorithm that reduces to solving a sequence of quadratic problems and a double Horner evaluation scheme that is optimal (featuring the least number of multiplications). The resulting modeling framework can account for arbitrary input data, experimental or from crystal plasticity predictions. As illustration we show new results regarding the relationship between generalized r-values and the earing profile of deep-drawn cylindrical cups. Practicality is demonstrated by the high level of automation of the entire workflow, from material parameters calibration to finite element simulations, and supporting code (Python scripts and constitutive subroutine) made available at https://github.com/stefanSCS/PolyN. [ABSTRACT FROM AUTHOR]

This paper proposes an innovative approach for constrained rendezvous trajectory optimization (CRTO) using stochastic optimal feedback control and unscented transform (UT) uncertainty quantification. The method overcomes limitations of traditional deterministic CRTO solutions that suffer from uncontrolled terminal state error growth and severely deteriorated path constraint satisfaction when initial state uncertainty, dynamics uncertainty, and navigation uncertainty are considered. The approach involves constructing a stochastic optimal feedback control (SOFC) problem with chance constraints and introducing linear feedback control to regulate both the mean and variance of terminal state errors. UT is employed to approximately quantify the state errors and their propagation, transforming the SOFC problem into an unconstrained deterministic optimization (UDO) problem. Differential dynamic programming (DDP) is then used to solve the UDO problem. The obtained stochastic optimal solution provides a robust rendezvous trajectory and a corresponding explicit closed-loop guidance law, improving terminal accuracy and path constraint satisfaction in the presence of various considered uncertainties. The influence of different term weights in the objective function on terminal accuracy and path constraint satisfaction is also studied. The effectiveness of the proposed approach is verified through Monte Carlo simulation, demonstrating the robustness of the closed-loop control strategy. The results highlight the potential of the method in enhancing terminal accuracy and path constraint satisfaction in uncertain rendezvous scenarios. • The uncertainty-resilient rendezvous trajectory optimization algorithm provides not only a nominal trajectory but an explicit optimal state-feedback control policy. • Rendezvous trajectory uncertainty caused by initial state errors, dynamics errors, and navigation errors is propagated using an unscented transformation method. • The proposed method considers common input constraints and path constraints in space rendezvous missions. [ABSTRACT FROM AUTHOR]

During the architectural design phase, the decisions made have a crucial impact on developing complex systems. These decisions often limit the performance bounds and steer subsequent research directions. However, the multitude of architectural components and intricate interrelationships cause component combination explosion. Additionally, the diverse requirements of different stakeholders add complexity to determining the weight of indicators, posing challenges to complex system architecture generation and trade-off. This paper proposes a method for exploring the architectural design space in complex systems realisation, which aims to resolve issues related to the formal representation of architectures, selection within the architectural design space, and trade-offs. Firstly, the architectural design space is represented by formulating and mathematically describing a morphological matrix. Then, the construction of the Constraint Satisfaction Problem model aims to achieve a reduction in the scale of the design space. Moreover, through the evolutionary algorithm, the Pareto front is identified. Weight sensitivity analysis and the improved Technique for Order Preference by Similarity to the Ideal Solution method are combined to assist designers in finding a satisfactory architecture from the design space with many combinations. Finally, the proposed method is verified by the design of the launch vehicle's primary and secondary separation system. [ABSTRACT FROM AUTHOR]

In the Determinant Maximization problem, given an n × n positive semi-definite matrix A in Q n × n and an integer k, we are required to find a k × k principal submatrix of A having the maximum determinant. This problem is known to be NP-hard and further proven to be W[1]-hard with respect to k by Koutis (Inf Process Lett 100:8–13, 2006); i.e., a f (k) n O (1) -time algorithm is unlikely to exist for any computable function f. However, there is still room to explore its parameterized complexity in the restricted case, in the hope of overcoming the general-case parameterized intractability. In this study, we rule out the fixed-parameter tractability of Determinant Maximization even if an input matrix is extremely sparse or low rank, or an approximate solution is acceptable. We first prove that Determinant Maximization is NP-hard and W[1]-hard even if an input matrix is an arrowhead matrix; i.e., the underlying graph formed by nonzero entries is a star, implying that the structural sparsity is not helpful. By contrast, Determinant Maximization is known to be solvable in polynomial time on tridiagonal matrices (Al-Thani and Lee, in: LAGOS, 2021). Thereafter, we demonstrate the W[1]-hardness with respect to the rankr of an input matrix. Our result is stronger than Koutis' result in the sense that any k × k principal submatrix is singular whenever k > r . We finally give evidence that it is W[1]-hard to approximate Determinant Maximization parameterized by k within a factor of 2 - c k for some universal constant c > 0 . Our hardness result is conditional on the Parameterized Inapproximability Hypothesis posed by Lokshtanov et al. (in: SODA, 2020), which asserts that a gap version of Binary Constraint Satisfaction Problem is W[1]-hard. To complement this result, we develop an ε -additive approximation algorithm that runs in ε - r 2 · r O (r 3) · n O (1) time for the rank r of an input matrix, provided that the diagonal entries are bounded. [ABSTRACT FROM AUTHOR]

The effective exploitation of infeasible solutions plays a crucial role in addressing constrained multiobjective optimization problems (CMOPs). However, existing constrained multiobjective optimization evolutionary algorithms (CMOEAs) encounter challenges in effectively balancing objective optimization and constraint satisfaction, particularly when tackling problems with complex infeasible regions. Subsequent to the prior exploration, this paper proposes a novel tri-stage with reward-switching mechanism framework (TSRSM), including the push, pull, and repush stages. Each stage consists of two coevolutionary populations, namely Pop 1 and Pop 2 . Throughout the three stages, Pop 1 is tasked with converging to the constrained Pareto front (CPF). However, Pop 2 is assigned with distinct tasks: (i) converging to the unconstrained Pareto front (UPF) in the push stage; (ii) utilizing constraint relaxation technique to discover the CPF in the pull stage; and (iii) revisiting the search for the UPF through knowledge transfer in the repush stage. Additionally, a novel reward-switching mechanism (RSM) is employed to transition between different stages, considering the extent of changes in the convergence and diversity of populations. Finally, the experimental results on three benchmark test sets and 30 real-world CMOPs demonstrate that TSRSM achieves competitive performance when compared with nine state-of-the-art CMOEAs. The source code is available at https://github.com/Qu-jq/TSRSM. [ABSTRACT FROM AUTHOR]

The constraint satisfaction problem (CSP) on a finite relational structure B is to decide, given a set of constraints on variables where the relations come from B, whether or not there is an assignment to the variables satisfying all of the constraints; the surjective CSP is the variant where one decides the existence of a surjective satisfying assignment onto the universe of B. We present an algebraic framework for proving hardness results on surjective CSPs; essentially, this framework computes global gadgetry that permits one to present a reduction from a classical CSP to a surjective CSP. We show how to derive a number of hardness results for surjective CSP in this framework, including the hardness of the disconnected cut problem, of the no-rainbow three-coloring problem, and of the surjective CSP on all two-element structures known to be intractable (in this setting). Our framework thus allows us to unify these hardness results and reveal common structure among them; we believe that our hardness proof for the disconnected cut problem is more succinct than the original. In our view, the framework also makes very transparent a way in which classical CSPs can be reduced to surjective CSPs. [ABSTRACT FROM AUTHOR]

Solving constraint satisfaction problems often involves a large amount of redundant exploration stemming from the existence of subproblems whose information can be reused for other subproblems. Subproblem dominance is a general notion of reusability that arises when one subproblem imposes more constraints on the remaining part of the search than another subproblem and allows the search to reuse the solutions of the dominating subproblem for the dominated subproblem. The search can exploit subproblem dominance by storing the subproblems that have been explored in a cache and abandoning the current subproblem whenever the cache contains a subproblem that dominates it. While using caching makes it possible to solve problems where subproblem dominance arises orders of magnitude faster, storing all of these subproblems can require a substantial amount of memory, making it impractical in many cases. This paper analyses the dominance between different subproblems for various constraint problems, revealing that only a relatively small number of subproblems dominate other subproblems. Based on these findings, two types of strategies are proposed for reducing the number of subproblems stored in the cache: limiting the number of subproblems that can be stored in the cache and periodically cleaning up the cache. An experimental evaluation demonstrates that these strategies provide an effective instrument for reducing the memory consumption of caching, allowing it to be used on a larger scale. However, there is a trade-off between saving memory and reducing redundant exploration, as removing subproblems from the cache may prevent dominance from being detected for certain subproblems. [ABSTRACT FROM AUTHOR]

Finite-domain constraint satisfaction problems are either solvable by Datalog or not even expressible in fixedpoint logic with counting. The border between the two regimes can be described by a universal-algebraic minor condition. For infinite-domain constraint satisfaction problems (CSPs), the situation is more complicated even if the template structure of the CSP is model-theoretically tame.We prove that there is no Maltsev condition that characterizes Datalog already for the CSPs of first-order reducts of (Q; <); such CSPs are called temporal CSPs and are of fundamental importance in infinite-domain constraint satisfaction. Our main result is a complete classification of temporal CSPs that can be expressed in one of the following logical formalisms: Datalog, fixed-point logic (with or without counting), or fixed-point logic with the mod-2 rank operator. The classification shows that many of the equivalent conditions in the finite fail to capture expressibility in Datalog or fixed-point logic already for temporal CSPs. [ABSTRACT FROM AUTHOR]

We give a surprising classification for the computational complexity of the Quantified Constraint Satisfaction Problem over a constraint language Γ, QCSP(ΓG), where G is a finite language over three elements that contains all constants. In particular, such problems are in P, NP-complete, co-NP-complete, or PSpace-complete. Our classification refutes the hitherto widely believed Chen Conjecture. Additionally, we show that already on a 4-element domain there exists a constraint language Γ such that QCSP(Γ) is DP-complete (from Boolean Hierarchy), and on a 10-element domain there exists a constraint language giving the complexity class Θ2P. Meanwhile, we prove the Chen Conjecture for finite conservative languages Γ. If the polymorphism clone of such Γ has the polynomially generated powers property, then QCSP(Γ) is in NP. Otherwise, the polymorphism clone of Γ has the exponentially generated powers property and QCSP(Γ) is PSpace-complete. [ABSTRACT FROM AUTHOR]

The article discusses a study on quantum computing conducted by researchers at Quantinuum and published in the journal Science. It mentions that demonstrated the use of advanced quantum simulation to compute molecular arrangements, indicating a shift from theoretical promise to practical application, particularly in chemistry, with potential implications for drug development and materials science.

The potential emergence of artificial general intelligence (AGI) systems has sparked intense debate among researchers, policymakers, and the public due to their potential to surpass human intelligence in all domains. This note argues that for an AI to be considered "general", it should achieve superhuman performance not only in zero-sum games but also in general-sum games, where winning or losing is not clearly defined. In this note, I propose a game-theoretic framework that captures the strategic interactions between a representative human agent and a potential superhuman machine agent. Four assumptions underpin this framework: Superhuman Machine, Machine Strategy, Rationality, and Strategic Unpredictability. The main result is an impossibility theorem, establishing that these assumptions are inconsistent when taken together, but relaxing any one of them results in a consistent set of assumptions. This note contributes to a better understanding of the theoretical context that can shape the development of superhuman AI. • A game between a human vs an Artificial General Intelligence system is introduced. • An AI system is general if it is successful in both zero-sum and general-sum games. • Assumptions are Superhuman AI, Machine Strategy, Rationality, and Unpredictability. • An impossibility theorem shows that these assumptions lead to inconsistency. • The result is tight; relaxing any of the assumptions resolves the inconsistency. [ABSTRACT FROM AUTHOR]

Distributed switched large-scale systems are composed by dynamically coupled subsystems, in which interactions among subsystems vary over time according a switching signal. This paper presents a distributed robust switched model-based predictive control (DSwMPC) to control such systems. The proposed method guarantees stabilising the origin of the whole closed-loop system and ensures the constraints satisfaction in the presence of an unknown switching signal. In the distributed model-based predictive control (DMPC) used in this work, by considering the interactions among subsystems as an additive disturbance, the effect of the switch is reflected on the dynamic equation, local, and consistency constraint sets of the nominal subsystems. To compensate the effect of switching signal which creates a time-varying network topology, a robust tube-based switched model-based predictive control (RSwMPC) with switch–robust control invariant set as the target set robust to unknown mode switching is used as local controller. The scheme performance is assessed using three typical examples. The simulation results show that the input and state constraints are satisfied by the proposed DSwMPC at all times. They also validate that the closed-loop system converges to the origin. Also, a comparison of the DSwMPC with a centralised SwMPC (CSwMPC) and a decentralised SwMPC (DeSwMPC) are performed. [ABSTRACT FROM AUTHOR]

The Media Use Model (MUM) presents a metatheoretical framework that aims to unify several existing theories of media processes and effects. It uses a constraint satisfaction approach to coherence to explain the dynamic relationship between a media consumer's motivations, expectations, individual differences, and, primarily, their cognitive processing during media use. The MUM includes six propositions, which represent stages during which a media consumer's existing processing constraints are taken into consideration during their selection, interpretation, and comprehension of media content. It allows for both spontaneous and deliberate processing that can result in coherence or incommensurability, which then predicts continued media use or a change in media selection, respectively. Within this metatheoretical framework, (in)coherence is presented as a continuum where media consumers may have different interpretations of the same media content, which can then be used to understand their responses to it. [ABSTRACT FROM AUTHOR]

Since the open-pit precedence-constrained production scheduling problem is an NP-hard problem, solving it is always a challenging task, especially from a long-term perspective because a mineral deposit containing millions of blocks would require several million precedence arcs as constraints, making the solution time grow exponentially and making a direct approach unfeasible. Therefore, different strategies have been employed since the 1960s to reduce the size of this problem, such as determining the ultimate pit limit, subdividing it into phases, segmenting the production scheduling problem into long-, mid-, and short-term plans, as well as aggregating blocks into clusters, thus significantly reducing the number of precedence arcs. Different modeling and clustering strategies have already been employed in an attempt to reduce the size of the mine sequencing problem, such as layer modeling, re-blocking, bench-phase clustering, or polygon (mining cut) clustering based on a similarity function. The mining cut clustering problem has been solved lately by machine learning and heuristics techniques, and this approach can also introduce operational constraints to the mine sequencing problem, such as equipment size, minimum pit width, and preferential mining direction. In this study, we propose a mining cut clustering model based on Mixed Integer Linear Programming (MILP). Then we solve it by an exact approach and by Constraint Programming (CP), analyzing the strengths and weaknesses of the Constraint Optimization Problem (COP) and Constraint Satisfaction Problem (CSP) techniques. Numerical experiments were carried out on the Bench 15 of the Newman1 dataset, demonstrating the superiority of the COP approach. [ABSTRACT FROM AUTHOR]

Continuous constraint satisfaction is prevalent in many science and engineering fields. When solving continuous constraint satisfaction problems, it is more advantageous for practitioners to derive all feasible regions (i.e., the solution space) rather than a limited number of solution points, since these feasible regions facilitate design concept generation and design tradeoff evaluation. Several central processing unit (CPU)-based branch-and-prune methods and geometric approximation methods have been proposed in prior research to derive feasible regions for continuous constraint satisfaction problems. However, these methods have not been extensively adopted in practice, mainly because of their high computational expense. To overcome the computational bottleneck of extant CPU-based methods, this paper introduces a GPU-based parallel region classification method to derive feasible regions for continuous constraint satisfaction problems in a reasonable computational time. Using interval arithmetic, coupled with the computational power of GPU, this method iteratively partitions the design space into many subregions and classifies these subregions as feasible, infeasible, and indeterminate regions. To visualize these classified regions in the design space, a planar visualization approach that projects all classified regions into one figure is also proposed. The GPU-based parallel region classification method and the planar visualization approach are validated through two case studies about the bird function and the welded beam design. These case studies show that the method and the approach can solve the continuous constraint satisfaction problems and visualize the results effectively and efficiently. A four-step procedure for implementing the method and the approach in practice is also outlined. [ABSTRACT FROM AUTHOR]

Model predictive control is a popular choice for systems that must satisfy prescribed constraints on states and control inputs. Although much progress has been made in distributed model predictive control, existing algorithms tend to be computationally expensive. This limits their use in systems with fast dynamics. In this paper, we propose a new distributed model predictive control algorithm that we term as instant distributed model predictive control (iDMPC). The proposed algorithm employs a realisation of the primal-dual algorithm in the controller dynamics for fast computation. We show that the closed-loop system trajectories with the proposed iDMPC algorithm converge asymptotically to a desired reference. To ensure the satisfaction of the state constraints during the transient, we also include an explicit reference governor in the feedback loop. [ABSTRACT FROM AUTHOR]