Constraint Satisfaction Research Articles

Adaptive gain design for Zero-Order Hold discrete-time implementation of explicit reference governor

Explicit reference governor (ERG) is an add-on unit that provides constraint handling capability to pre-stabilized systems. The main idea behind ERG is to manipulate the derivative of the applied reference in continuous time such that the satisfaction of state and input constraints is guaranteed at all times. However, ERG should be practically implemented in discrete-time. This paper studies the discrete-time implementation of ERG, and provides conditions under which the feasibility and convergence properties of the ERG framework are maintained when the updates of the applied reference are performed in discrete time. Specifically, using Zero-Order Hold (ZOH) discretization method, we develop an adaptive algorithm to adjust the gain of the discretized term based on actual measurements to maintain all properties of ERG when implemented in discrete-time. The proposed approach is validated via extensive simulation and experimental studies.

Clustering bike sharing stations using Quantum Machine Learning: A case study of Toronto, Canada

Quantum Machine Learning (QML) is a field that combines the principles of Quantum Computing (QC) and Machine Learning (ML). QC works by taking advantage of the properties of quantum physics, such as superposition and entanglement. To fully realize the potential of this technology, more research is necessary, as the field of QML is still in its early stages. Since QC technologies and devices continue to develop quickly, it is important to identify the use cases and applications that benefit the most. This paper investigates the potentials of QC, and more specifically, Quantum Annealing (QA), for clustering real-world data in transportation systems. The Bike Sharing System (BSS) is used as a case study applying a clustering model on QA computers. The main contribution of this research is to introduce a hybrid model to cluster stations in a BSS by solving it as a Constraint Satisfaction Problem (CSP) problem with different methods on a QA computer using a real-time dataset. In addition to the practical contribution, this research also offers theoretical advancements in the field of computational optimization by defining a new topology for the input data that is compatible with QC topology (e.g., Chimera topology). The goal of real-time clustering BSS stations based on dynamic and static datasets is, in fact, to assist decision-makers in better managing and minimizing the risk of bike unavailability at each station and rebalancing bikes shared. Three different methods have been used to determine the number of clusters, and Euclidean, Manhattan, Pearson, and Spearman dissimilarity functions have been applied to cluster the stations. The evaluation is done using the magnitude vs. cardinality approach. The distribution of the stations, magnitude, and cardinality of the results indicate the potential to use QC for clustering for a real-world application, e.g., BSS.

Modular control architecture for safe marine navigation: Reinforcement learning with predictive safety filters

Many autonomous systems are safety-critical, making it essential to have a closed-loop control system that satisfies constraints arising from underlying physical limitations and safety aspects in a robust manner. However, this is often challenging to achieve for real-world systems. For example, autonomous ships at sea have nonlinear and uncertain dynamics and are subject to numerous time-varying environmental disturbances such as waves, currents, and wind. There is increasing interest in using machine learning-based approaches to adapt these systems to more complex scenarios, but there are few standard frameworks that guarantee the safety and stability of such systems. Recently, predictive safety filters (PSF) have emerged as a promising method to ensure constraint satisfaction in learning-based control, bypassing the need for explicit constraint handling in the learning algorithms themselves. The safety filter approach leads to a modular separation of the problem, allowing the use of arbitrary control policies in a task-agnostic way. The filter takes in a potentially unsafe control action from the main controller and solves an optimization problem to compute a minimal perturbation of the proposed action that adheres to both physical and safety constraints. In this work, we combine reinforcement learning (RL) with predictive safety filtering in the context of marine navigation and control. The RL agent is trained on path-following and safety adherence across a wide range of randomly generated environments, while the predictive safety filter continuously monitors the agents' proposed control actions and modifies them if necessary. The combined PSF/RL scheme is implemented on a simulated model of Cybership II, a miniature replica of a typical supply ship. Safety performance and learning rate are evaluated and compared with those of a standard, non-PSF, RL agent. It is demonstrated that the predictive safety filter is able to keep the vessel safe, while not prohibiting the learning rate and performance of the RL agent.

Generation and deployment of honeytokens in relational databases for cyber deception

Despite considerable investments in database security, global statistics indicate an exponential increase in data breaches. Organizations are often unaware of data breaches for weeks, months, or even years. Sufficient for adversaries to compromise and ex-filtrate business or mission-critical data. Recent research suggests using honeytokens for early detection of data breaches in organizations. Existing honeytoken generation methods rely on regular expressions, rule mining, constraint satisfaction, or representation learning, which are complex and limited to a few attributes. We created a framework for generating and deploying honeytokens in relational databases that actively monitor sensitive records and quickly detect data breaches and their misuse. To generate the honeytoken we have used the hierarchical machine learning algorithm which uses a recursive technique to model the parent–child relationships of multi-table databases. The proposed method enables the organization to take remedial action to reduce the impact of data breaches and complement existing database security solutions.

Dynamic-multi-task-assisted evolutionary algorithm for constrained multi-objective optimization

Compared with common multi-objective optimization problems, constrained multi-objective optimization problems demand additional consideration of the treatment of constraints. Recently, many constrained multi-objective evolutionary algorithms have been presented to reconcile the relationship between constraint satisfaction and objective optimization. Notably, evolutionary multi-task mechanisms have also been exploited in solving constrained multi-objective problems frequently with remarkable outcomes. However, previous methods are not fully applicable to solving problems possessing all types of constraint landscapes and are only superior for a certain type of problem. Thus, in this paper, a novel dynamic-multi-task-assisted constrained multi-objective optimization algorithm, termed DTCMO, is proposed, and three dynamic tasks are involved. The main task approaches the constrained Pareto front by adding new constraints dynamically. Two auxiliary tasks are devoted to exploring the unconstrained Pareto front and the constrained Pareto front with dynamically changing constraint boundaries, respectively. In addition, the first auxiliary task stops the evolution automatically after reaching the unconstrained Pareto front, avoiding the waste of subsequent computational resources. A series of experiments are conducted with eight mainstream algorithms on five benchmark problems, and the results confirm the generality and superiority of DTCMO.

On the Complexity of Symmetric vs. Functional PCSPs

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.

Reinforcement learning-based satellite formation attitude control under multi-constraint

As the complexity of space missions increases, the constraints on satellite attitude control become more stringent, particularly for satellites working in orbit formation. This paper introduces a novel method, based on the categorization and modeling of different constraints, for attitude control of satellite formations under multiple constraints. The method employs the Phased Priority Reinforcement Learning (PPRL) approach, which utilizes Deep Deterministic Policy Gradient (DDPG) technology. Considering the complexity of constraints and the challenge posed by the high control dimensionality due to multi-satellite coordination, the method addresses these challenges through a two-step training strategy. The first step addresses the multi-constraint issue for individual satellites and increases the priority of single-satellite training experience data in the experience replay buffer of the second step to enhance data utilization efficiency. To address the issue of reward sparsity in complex high-dimensional constraint models, a detailed reward mechanism is proposed, incorporating both local and global constraints into the reward function, thereby achieving both efficient and effective attitude control. This approach not only meets dynamic, state, and performance constraints but also demonstrates adaptability and robustness through numerical simulations. Compared to traditional methods, this approach achieves significant improvements in control performance and constraint satisfaction, offering a novel solution pathway for high-dimensional control problems in multi-constraint satellite formations.

Safety-Based Speed Control of a Wheelchair Using Robust Adaptive Model Predictive Control.

Electric-powered wheelchairs play a vital role in ensuring accessibility for individuals with mobility impairments. The design of controllers for tracking tasks must prioritize the safety of wheelchair operation across various scenarios and for a diverse range of users. In this study, we propose a safety-oriented speed tracking control algorithm for wheelchair systems that accounts for external disturbances and uncertain parameters at the dynamic level. We employ a set-membership approach to estimate uncertain parameters online in deterministic sets. Additionally, we present a model predictive control scheme with real-time adaptation of the system model and controller parameters to ensure safety-related constraint satisfaction during the tracking process. This proposed controller effectively guides the wheelchair speed toward the desired reference while maintaining safety constraints. In cases where the reference is inadmissible and violates constraints, the controller can navigate the system to the vicinity of the nearest admissible reference. The efficiency of the proposed control scheme is demonstrated through high-fidelity speed tracking results from two tasks involving both admissible and inadmissible references.

Entry guidance for spatial no-fly zones avoidance via model-based reinforcement learning

This paper proposes a novel guidance law for hypersonic entry vehicles, considering no-fly zones with height limits. Traditional planar assumptions restrict the flexibility of trajectory design for scenarios like radar avoidance. Besides, the numerical integration proves inefficient for long-term prediction and avoidance. Therefore, a model-based reinforcement learning policy is designed. It offline learns entry dynamics in advance and onboard plans a feasible trajectory. The planner's state includes flight status and no-fly zones; action presents waypoints; and reward ensures constraint while maximizing terminal precision. Then, analytical prediction converts spatial no-fly zone constraints to flight-path angle constraints, improving precision compared to traditional one-step estimates. Finally, the two parts are assembled into the predictor-corrector framework, which gives the augmented guidance commands. While retaining its robustness to bias, our method reduces online optimization calculations and outperforms constraint satisfaction. Experiments show that the model-based method reduces 60% training in offline training compared with proximal policy optimization. Besides, our method is 80% faster than conventional predictor-corrector guidance regarding online computation speed.

Polynomial Time Linear Programs for Hard Constraint Satisfaction Problems

Polynomial Time Linear Programs for Hard Constraint Satisfaction Problems

Real-time Physically Guided Hair Interpolation

Strand-based hair simulations have recently become increasingly popular for a range of real-time applications. However, accurately simulating the full number of hair strands remains challenging. A commonly employed technique involves simulating a subset of guide hairs to capture the overall behavior of the hairstyle. Details are then enriched by interpolation using linear skinning. Hair interpolation enables fast real-time simulations but frequently leads to various artifacts during runtime. As the skinning weights are often pre-computed, substantial variations between the initial and deformed shapes of the hair can cause severe deviations in fine hair geometry. Straight hairs may become kinked, and curly hairs may become zigzags. This work introduces a novel physical-driven hair interpolation scheme that utilizes existing simulated guide hair data. Instead of directly operating on positions, we interpolate the internal forces from the guide hairs before efficiently reconstructing the rendered hairs based on their material model. We formulate our problem as a constraint satisfaction problem for which we present an efficient solution. Further practical considerations are addressed using regularization terms that regulate penetration avoidance and drift correction. We have tested various hairstyles to illustrate that our approach can generate visually plausible rendered hairs with only a few guide hairs and minimal computational overhead, amounting to only about 20% of conventional linear hair interpolation. This efficiency underscores the practical viability of our method for real-time applications.

Two-stage differential evolution with dynamic population assignment for constrained multi-objective optimization

Using infeasible information to balance objective optimization and constraint satisfaction is a very promising research direction to address constrained multi-objective problems (CMOPs) via evolutionary algorithms (EAs). The existing constrained multi-objective evolutionary algorithms (CMOEAs) still face the issue of striking a good balance when solving CMOPs with diverse characteristics. To alleviate this issue, in this paper we develop a two-stage different evolution with a dynamic population assignment strategy for CMOPs. In this approach, two cooperative populations are used to provide feasible driving forces and infeasible guiding knowledge. To adequately utilize the infeasibility information, a dynamic population assignment model is employed to determine the primary population, which is used as the parents to generate offspring. The entire search process is divided into two stages, in which the two populations work in weak and strong cooperative ways, respectively. Furthermore, multistrategy-based differential evolution operators are adopted to create aggressive offspring. The superior exploration and exploitation ability of the proposed algorithm is validated via some state-of-the-art CMOEAs over artificial benchmarks and real-world problems. The experimental results show that our proposed algorithm gained a better, or more competitive, performance than the other competitors, and it is an effective approach to balancing objective optimization and constraint satisfaction.

Adaptive variable neighborhood search algorithm with Metropolis rule and tabu list for satellite range scheduling problem

Efficient scheduling of measurement and control resources plays a critical role in successful satellite operations. The tremendous growth in the number of satellites in orbit exacerbates resource scarcity, further enhancing the significance of the satellite range scheduling problem (SRSP). In order to maximize the benefits of measurement and control tasks, we propose an innovative algorithm to solve the SRSP with numerous constraints. Firstly, the SRSP operation flow is analyzed to establish a constraint satisfaction model. A task-resource matching algorithm based on fitness is then designed to generate an initial feasible solution with superior quality by heuristic criteria. Subsequently, an adaptive variable neighborhood search algorithm with Metropolis rule and tabu list (AVNS-MT) is proposed to solve the mathematical model. Three swap neighborhood structures are constructed to explore the solution space efficiently during the variable neighborhood descent search process. Meanwhile, three migration neighborhood structures are devised to enable the shaking of solutions and evasion from the local optimum. Moreover, the incorporation of the Metropolis rule and tabu search strategy will contribute to enhancing the algorithm convergence. Finally, we have conducted extensive simulations to verify the effectiveness and efficiency of the proposed AVNS-MT. Comparison experiments with several state-of-the-art methods validate the superiority of the proposed algorithm.

An improved system design method for cell-based energy storage systems: A combination of a constraint satisfaction problem with an extended Ragone plot

Over the past three decades, advancements in electrical energy storage technologies have substantially enhanced performance and reduced costs, rendering them viable for diverse applications. Cell-based energy storage systems, such as batteries and supercapacitors, are particularly notable for their adaptability and scalable interconnection capabilities. However, the design process for such systems lacks uniform standards, presenting a gap in research for the conceptual system design. This paper introduces an improved system design method (SDM), addressing critical limitations of existing approaches: (a) Shifting from current-based to power-based requirements; (b) Enabling flexible adaptation of operational design points beyond fixed datasheet specifications; (c) Ensuring harmonization of energy storage design with other system components, notably power electronics. Central to our SDM is the novel “extended Ragone plot” (ERP), which maps cell-specific energy–power relations and allows for flexible adjustment of operational limits. Since it can be determined experimentally, the subsequent design method is model-free and can efficiently be executed for different cell types. In the SDM, this ERP is coupled with a constraint satisfaction problem (CSP) to compute a comprehensive design solution space that accommodates all application-specific requirements and component interrelations. It is implemented in a holistic, interactive tool, facilitating mathematical optimization and enabling visual analysis of energy storage system designs. As a proof-of-concept, two case studies on the design of lithium-ion battery systems for stationary grid supply demonstrate the method’s superiority over conventional approaches. While in the first case, an optimal design can be determined immediately, in the second case, there are no valid design solutions based on the cell’s initial operating point. Utilizing the ERP, a practical design solution is achieved by reducing the maximum cell power by approximately 9%, thereby modifying the cell’s available voltage and current limits. This approach provides a possible solution for scenarios where a system design based on data sheets alone is not feasible. A comparative analysis and graphical synthesis of both case studies validate this hypothesis, illustrating the novel system design method’s ability to precalculate and evaluate diverse design scenarios in advance. The source code and data used in this study are openly accessible, offering the SDM as an interactive tool for analyzing and designing energy storage systems.

Sampling with flows, diffusion, and autoregressive neural networks from a spin-glass perspective

Recent years witnessed the development of powerful generative models based on flows, diffusion, or autoregressive neural networks, achieving remarkable success in generating data from examples with applications in a broad range of areas. A theoretical analysis of the performance and understanding of the limitations of these methods remain, however, challenging. In this paper, we undertake a step in this direction by analyzing the efficiency of sampling by these methods on a class of problems with a known probability distribution and comparing it with the sampling performance of more traditional methods such as the Monte Carlo Markov chain and Langevin dynamics. We focus on a class of probability distribution widely studied in the statistical physics of disordered systems that relate to spin glasses, statistical inference, and constraint satisfaction problems. We leverage the fact that sampling via flow-based, diffusion-based, or autoregressive networks methods can be equivalently mapped to the analysis of a Bayes optimal denoising of a modified probability measure. Our findings demonstrate that these methods encounter difficulties in sampling stemming from the presence of a first-order phase transition along the algorithm's denoising path. Our conclusions go both ways: We identify regions of parameters where these methods are unable to sample efficiently, while that is possible using standard Monte Carlo or Langevin approaches. We also identify regions where the opposite happens: standard approaches are inefficient while the discussed generative methods work well.

Constrained Maximization of the Economic Production Model of Lithium Ore Exploration in Nasarawa

Over 20,000 years ago, mining was discovered as one of the oldest production industries generating over US$700 billions’ of revenue in the world by a few mining companies. For some time, mining work has resulted in a very demanding affair as a result of greater depth, low-grade, limited resources, and complex geo-mining conditions. Therefore, optimization of the mining system plays a vital role in profit maximization with the satisfaction of many constraints. However, today’s mining industry uses complex and sophisticated systems whose reliability has become a critical issue. This work adopted the financial market theory of development to propose a maximized constrained optimization economic production model for lithium ore exploration in Nasarawa, Nigeria using three methods such as: the break-even principle method of cut-off grade between revenue earned and cost incurred; the mortimer’s method principle to determine ore based in two cut-off criteria (original and average good) and the lane method for net profit value thereby maximizing processing capacity. Data obtained from the field and the Ministry of Mines and Solid Minerals were analyzed using energy dispersive x-ray fluorescence (EDXRF) showing the presence of lithium. The froth flotation technique used showed the beneficiation thereby achieving improved lithium concentrates and the inductively coupled atomic emission revealed a high presence of lithium of over 1859 parts per million (ppm) and other minerals.

A Complexity Dichotomy in Spatial Reasoning via Ramsey Theory

Constraint satisfaction problems (CSPs) for first-order reducts of finitely bounded homogeneous structures form a large class of computational problems that might exhibit a complexity dichotomy, P versus NP-complete. A powerful method to obtain polynomial-time tractability results for such CSPs is a certain reduction to polynomial-time tractable finite-domain CSPs defined over k -types, for a sufficiently large k . We give sufficient conditions when this method can be applied and apply these conditions to obtain a new complexity dichotomy for CSPs of first-order expansions of the basic relations of the well-studied spatial reasoning formalism RCC5. We also classify which of these CSPs can be expressed in Datalog. Our method relies on Ramsey theory; we prove that RCC5 has a Ramsey order expansion.

A Hybrid Genetic Algorithm for Ground Station Scheduling Problems

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.

Ant-Inspired Scheduling: Integrating Constraint Satisfaction Problem with Ant Colony Optimization

Ant-Inspired Scheduling: Integrating Constraint Satisfaction Problem with Ant Colony Optimization

Optimization of the production planning process in a nuts and dried fruits industry

A resource-constrained machine scheduling problem is addressed in this paper. The problem arises in an industry located in the Canary Islands (Spain) and is characterized by a set of jobs to be completed on multiple processing lines, where each job has a specific processing time and a sequence-dependent setup time. The objective is to maximize the productivity of the processing lines, subject to constraints such as availability of personnel and processing lines, due dates, precedence order, and setup times, among others.In order to solve this problem, an optimization model that represents the problem as a mixed-integer program is proposed. The paper also introduces a constraint satisfaction heuristic to find near-optimal solutions of the problem. The effectiveness of the proposal is demonstrated through computational experiments on a set of real and synthetic instances, showing that the proposed technique is able to find solutions that are close to the optimal ones within a reasonable amount of time.