Unsatisfied Constraints Research Articles

Mixed Integer Programming For Patient Admission Scheduling in Hospital Network

The Patient Admission Scheduling (PAS) process involves efficiently managing the admission of patients to specific beds within relevant departments while addressing all their medical needs over a defined time horizon. This study delves into PAS within hospital network, emphasizing the collaborative nature of their interactions. Collaborative interactions are a common challenge in hospitals, where they need to collaborate and share resources to allocate patients to a limited number of beds within a specified timeframe, ensuring all necessary medical conditions are met. To address this challenge, a mixed-integer mathematical programming model for the PAS problem within hospital network is proposed with the aim of minimizing a weighted sum of unsatisfied constraints.

Reinforcement Quantum Annealing: A Hybrid Quantum Learning Automata

We introduce the notion of reinforcement quantum annealing (RQA) scheme in which an intelligent agent searches in the space of Hamiltonians and interacts with a quantum annealer that plays the stochastic environment role of learning automata. At each iteration of RQA, after analyzing results (samples) from the previous iteration, the agent adjusts the penalty of unsatisfied constraints and re-casts the given problem to a new Ising Hamiltonian. As a proof-of-concept, we propose a novel approach for casting the problem of Boolean satisfiability (SAT) to Ising Hamiltonians and show how to apply the RQA for increasing the probability of finding the global optimum. Our experimental results on two different benchmark SAT problems (namely factoring pseudo-prime numbers and random SAT with phase transitions), using a D-Wave 2000Q quantum processor, demonstrated that RQA finds notably better solutions with fewer samples, compared to the best-known techniques in the realm of quantum annealing.

Force balance controls the relaxation time of the gradient descent algorithm in the satisfiable phase.

We numerically study the relaxation dynamics of the single-layer perceptron with the spherical constraint. This is the simplest model of neural networks and serves a prototypical mean-field model of both convex and nonconvex optimization problems. The relaxation time of the gradient descent algorithm rapidly increases near the SAT-UNSAT (satisfiable-unsatisfiable) transition point. We numerically confirm that the first nonzero eigenvalue of the Hessian controls the relaxation time. This first eigenvalue vanishes much faster upon approaching the SAT-UNSAT transition point than the prediction of the Marchenko-Pastur law in random matrix theory derived under the assumption that the set of unsatisfied constraints are uncorrelated. This leads to a nontrivial critical exponent of the relaxation time in the SAT phase. Using a simple scaling analysis, we show that the isolation of this first eigenvalue from the bulk of spectrum is attributed to the force balance at the SAT-UNSAT transition point. Finally, we show that the estimated critical exponent of the relaxation time in the nonconvex region agrees very well with that of frictionless spherical particles, which have been studied in the context of the jamming transition of granular materials.

A Novel Sliding Mode Control with Low-Pass Filter for Nonlinear Handling Chain System in Container Ports

Nonlinearities in a container port handling chain include mainly nonnegative arrive rate of container cargoes, limited container handling completion rate, and nonnegative unsatisfied freight requirement constraints. The nonlinearity influences the operation resources availability and consequently the planned container port handling strategies. Developments presented in this work are devoted to a novel design of sliding mode control with low-pass filter (SMC-LPF) to nonlinear handling chain system (HCS) in container ports. The SMC-LPF can effectively reduce unsatisfied freight requirement of the HCS and make chattering decrease significantly. To illustrate the effectiveness and accuracy of the proposed SMC-LPF, an application to a real container port in China is outlined. The performances of the SMC-LPF for the nonlinear HCS in container ports outperform those of the traditional method, particle swarm optimization algorithm, and slide mode control under simulations with a unit step signal and a sinusoidal signal with offset as the freight requirements. The contributions herein demonstrate the proposed control strategy in weakening chattering, reducing the unsatisfied freight requirements to 0 as close as possible in the HCS, maximizing the operation resilience and robustness of port and shipping supply chain against parametric perturbation, external disturbances, and fluctuant handling abilities.

The patient bed assignment problem solved by autonomous bat algorithm

The patient bed assignment problem consists of managing, in the best possible way, a set of beds with particular features and assigning them to a set of patients with special requirements. This assignment problem can be seen an optimization problem, of which the intended aims are usually to minimize the number of internal movements within a unit and to maximize bed usage according to the levels of criticality of the patients, among others. The usual approaches for solving this problem follow a traditional model based on the constraint programming paradigm, mainly using hard constraints. However, in real-life problems, constraints that should ideally be satisfied are often violated. In this paper, we present a new model for the patient bed assignment problem based on the minimum sum of unsatisfied constraints. This technique enables the consideration of soft constraints in the potential solutions that exhibit the best performance. The aim is to find the assignment that minimizes a weighted sum of the unsatisfied constraints. To this end, we use an autonomous binary version of the bat algorithm, which is an optimization technique inspired by the bio-sonar behaviour of microbats, to find the best set of potential solutions without requiring any expert user knowledge to achieve an efficient solution process. To validate our proposal, we use our model to solve problem instances based on data from several hospitals, and we perform a detailed comparative statistical analysis with a traditional constraint programming solver and several well-known optimization algorithms, including the classic bat algorithm. Promising results show that our approach is capable of efficiently solving 30 instances with decreased solution times.

Parsing as semantically guided constraint solving: the role of ontologies

In the Parsing-as-Constraint-Solving model of language processing, grammar syntax is described modularly through independent constraints among direct constituents of a phrase - constraints such as: “in verb phrases, a verb must precede its complements”, or “in noun phrases, a noun requires a determiner”. Parsing reduces to verifying the constraints relevant to an input phrase, but instead of the typical hierarchical (i.e., parse tree) representations of a successful parse (and also typical complete silence upon unsuccessful parses), the main result is a list of satisfied constraints, and if the input is not totally conforming, also a list of unsatisfied constraints. The latter can serve various purposes beyond plain parsing, such as guiding the correction of any imperfections found in the input- and we can still construct a parse tree if needed, as a side effect. While almost purely syntax-based, the Parsing-as-Constraint-Solving model lends itself well to accommodating interactions with other levels of analysis. These however have been little explored. In this position paper we discuss how to extend this model to incorporate semantic information, in particular from ontologies, and with particular guidance from unsatisfied constraints. This departs from more typical constraint-solving schemes, where failed constraints are simply listed and do not actively contribute to the parse. By giving failed constraints a more active role, we can arrive at more precise analyses and at more appropriate corrections of flawed input. Because even not totally conforming sentences can be more precisely parsed, we gain in expressivity with respect to both the classical, strictly stratified approach to NLP, and the less precise and less reliable statistically-based methods.

QoS-based Web Service Composition Applying an Improved Genetic Algorithm (IGA) Method

In recent years, it has been made possible to compose exiting services when a user's request cannot be satisfied by a single web service. Web service composition is faced with several challenges among which is the rapid growth in the number of available web services leading to increased number of web services offering the same functionalities. The difference between similar services is Quality of Service (QoS) consisting of various non-functional factors such as execution time, availability, security, etc. As a result, multiple choices are possible in making a composition plan. Among numerous plans, selecting a composition plan that fulfills customer's requirements has become an important and time-consuming problem. In this paper, the researchers propose a semi-heuristic genetic algorithm that is a combination of both a heuristic method and the genetic algorithm. This heuristic method changes chromosomes based on unsatisfied constraints. Research findings show that the proposed method can be applied to find a composition plan that satisfies user's requirements more efficiently than other methods.

Task management skills and their deficiencies during care delivery in simulated medical emergency situation: A classification

Our objective was to develop the analysis of task management skills by proposing a framework classifying task management stages and deficiencies. Few studies of non-technical skills have detailed the components of task management skills through behavioural markers, despite their central role in care delivery. A post hoc qualitative behavioural analysis was performed of recordings made of professional training sessions based upon simulated scenarios. Four recorded sessions in a high-fidelity simulation setting were observed and recorded. Two scenarios were used (cardiac arrest and respiratory failure), and there were two training sessions per scenario. Four types of task management deficiencies were identified with regards to task constraints: constraint relaxation, unsatisfied constraints, additional constraints and constraint transgression. Both equipment and space constraints were also identified. The lack of prerequisite actions when preparing the environment, corequisite actions for equipment and protocol monitoring, or postrequisite actions to restore the environment were associated with task management deficiencies. Deficiencies in task management behaviours can be identified in simulated as well as actual medical emergency settings. This framework opens perspectives for both training caregivers and designing ergonomic work situations.

Local search methods based on variable focusing for random K-satisfiability.

We introduce variable focused local search algorithms for satisfiabiliity problems. Usual approaches focus uniformly on unsatisfied clauses. The methods described here work by focusing on random variables in unsatisfied clauses. Variants are considered where variables are selected uniformly and randomly or by introducing a bias towards picking variables participating in several unsatistified clauses. These are studied in the case of the random 3-SAT problem, together with an alternative energy definition, the number of variables in unsatisfied constraints. The variable-based focused Metropolis search (V-FMS) is found to be quite close in performance to the standard clause-based FMS at optimal noise. At infinite noise, instead, the threshold for the linearity of solution times with instance size is improved by picking preferably variables in several UNSAT clauses. Consequences for algorithmic design are discussed.

Overcurrent Relays Coordination Considering the Priority of Constraints

In interconnected networks, it is impossible to satisfy all coordination constraints. Some methods have been proposed in the literature to determine the minimum break point set (MBPS) before the coordination procedure. In this paper, a new method is presented which coordinates overcurrent relays and simultaneously determines minimum unsatisfied constraints as broken constraints (BCs). For the implementation of this method, a new objective function (OF) is defined that also includes constraints with various weightings. These weightings determine the priority of constraints for being satisfied which are obtained by means of some expert rules. The expert rules of previous papers are modified and weighted to determine the priority of constraints. The genetic algorithm is used to optimize the OF that has an internal feedback for determining the minimum BCs considering coordination criterion. The effectiveness of the proposed technique is demonstrated by comparing the results of two sample networks with those obtained by using the recently developed techniques.

Reverse Bridge Theorem under Constraint Partition

Reverse bridge theorem (RBTH) has been proved to be both a necessary and sufficient condition for solving Nonlinear programming problems. In this paper, we first propose three algorithms for finding constraint minimum points of continuous, discrete, and mixed-integer nonlinear programming problems based on the reverse bridge theorem. Moreover, we prove that RBTH under constraint partition is also a necessary and sufficient condition for solving nonlinear programming problems. This property can help us to develop an algorithm using RBTH under constraints. Specifically, the algorithm first partitions mixed-integer nonlinear programming problems (MINLPs) by their constraints into some subproblems in similar forms, then solves each subproblem by using RBTH directly, and finally resolves those unsatisfied global constraints by choosing appropriate penalties. Finally, we prove the soundness and completeness of our algorithm. Experimental results also show that our algorithm is effective and sound.

The PCP theorem by gap amplification

The PCP theorem [Arora and Safra 1998; Arora et. al. 1998] says that every language in NP has a witness format that can be checked probabilistically by reading only a constant number of bits from the proof. The celebrated equivalence of this theorem and inapproximability of certain optimization problems, due to Feige et al. [1996], has placed the PCP theorem at the heart of the area of inapproximability. In this work, we present a new proof of the PCP theorem that draws on this equivalence. We give a combinatorial proof for the NP-hardness of approximating a certain constraint satisfaction problem, which can then be reinterpreted to yield the PCP theorem. Our approach is to consider the unsat value of a constraint system, which is the smallest fraction of unsatisfied constraints, ranging over all possible assignments for the underlying variables. We describe a new combinatorial amplification transformation that doubles the unsat-value of a constraint-system, with only a linear blowup in the size of the system. The amplification step causes an increase in alphabet-size that is corrected by a (standard) PCP composition step. Iterative application of these two steps yields a proof for the PCP theorem. The amplification lemma relies on a new notion of “graph powering” that can be applied to systems of binary constraints. This powering amplifies the unsat-value of a constraint system provided that the underlying graph structure is an expander. We also extend our amplification lemma towards construction of assignment testers (alternatively, PCPs of Proximity) which are slightly stronger objects than PCPs. We then construct PCPs and locally-testable codes whose length is linear up to a polylog factor, and whose correctness can be probabilistically verified by making a constant number of queries. Namely, we prove SAT ∈ PCP 1/2,1 [log 2 ( n ⋅poly log n ), O (1)].

Reducing energy consumption of multiprocessor SoC architectures by exploiting memory bank locality

The next generation embedded architectures are expected to accommodate multiple processors on the same chip. While this makes interprocessor communication less costly as compared to traditional high-end parallel machines, it also makes off-chip requests very costly. In particular, frequent off-chip memory accesses do not only increase execution cycles but also increase overall power consumption. One way of alleviating this power problem is to divide the off-chip memory into multiple banks, each of which can be power-controlled independently using low-power operating modes.In this article, we focus on a multiprocessor-system-on-a-chip (MPSoC) architecture with a banked memory system, and show how code and data optimizations can help us reduce memory energy consumption for embedded applications with regular data access patterns, for example, those from the embedded image and video processing domain. This is achieved by ensuring bank locality, which means that each processor localizes its accesses into a small set of banks in a given time period. We present a mathematical formulation of the bank locality problem. Our formulation is based on constructing a set of matrix equations that capture the mappings between the data, computation, processor, and memory bank spaces. Based on this formulation, we propose a heuristic solution to the bank locality problem under different scenarios. Our solution involves an iterative process through which we try to satisfy as many matrix constraints as possible; the unsatisfied constraints represent the degree of degradation in bank locality. Finally, we report extensive experimental results showing the effectiveness of our strategy in practice. Our results show that the proposed solution improves bank locality significantly, and reduces the overall memory system energy consumption by up to 34% over an approach that makes use of the low-power modes but does not employ our strategy.

PROTEIN THREADING WITH PROFILES AND DISTANCE CONSTRAINTS USING CLIQUE BASED ALGORITHMS

With the advent of experimental technologies like chemical cross-linking, it has become possible to obtain distances between specific residues of a newly sequenced protein. These types of experiments usually are less time consuming than X-ray crystallography or NMR. Consequently, it is highly desired to develop a method that incorporates this distance information to improve the performance of protein threading methods. However, protein threading with profiles in which constraints on distances between residues are given is known to be NP-hard. By using the notion of a maximum edge-weight clique finding algorithm, we introduce a more efficient method called FTHREAD for profile threading with distance constraints that is 18 times faster than its predecessor CLIQUETHREAD. Moreover, we also present a novel practical algorithm NTHREAD for profile threading with Non-strict constraints. The overall performance of FTHREAD on a data set shows that although our algorithm uses a simple threading function, our algorithm performs equally well as some of the existing methods. Particularly, when there are some unsatisfied constraints, NTHREAD (Non-strict constraints threading algorithm) performs better than threading with FTHREAD (Strict constraints threading algorithm). We have also analyzed the effects of using a number of distance constraints. This algorithm helps the enhancement of alignment quality between the query sequence and template structure, once the corresponding template structure is determined for the target sequence.

An Efficient Decoding Algorithm for Low-Density Parity-Check Codes

We present a simple decoding algorithm that modifies soft bit-flipping algorithm for decoding LDPC codes. In our method, a new parameter is explored to distinguish the variables (symbols) belonging to the same number of unsatisfied constraints. A token is also assigned in the method to avoid repeated flipping of the same variable, rather than using a constant taboo length. Our scheme shows a similar computational load as the taboo-based algorithm, while having a similar decoding performance as the belief propagation algorithm.

Multimedia Authoring with Hierarchical Timed Stream Petri Nets and Java

The expected benefits of modeling documents using a formal technique are twofold. First, the document's model can be checked against logical errors and unsatisfied timing constraints. Second, the same model can serve as reference for implementation purposes. In this context, the paper discusses a methodology for multimedia document design and implementation on heterogeneous and distributed platforms. The design trajectory starts with document modeling in Hierarchical Timed Stream Petri Nets, goes on with model checking against design errors, and continues with automatic translation of HTSPN models into a Java application. A tool prototype supports the methodology with a document editor, a simulator and a HTSPN to Java generator. Its use is exemplified on a guided tour of Florianopolis City, Brazil.

An Improved Tabu Search Method For The Weighted Constraint Satisfaction Problem

Aiming at developing a general problem solver for combinatorial optimization problems, we consider in this paper the weighted constraint satisfaction problem (WCSP), which, given a number of constraints and their weights of importance, asks to minimize the total weight of unsatisfied constraints. We propose a tabu search algorithm for WCSP with the features that it uses an evaluation function, defined in terms of the modified weights of constraints, for guiding the search, and that it incorporates an automatic control mechanism of the weights in the evaluation function. Using this code, we solved a number of problems including those from real applications such as generalized assignment, set covering, parallel shop scheduling, timetabling and nurse scheduling. Many problems that arise in cellular manufacturing can also be formulated as WCSP, including the problems of cell formation and tool selection. Our computational results indicate that the control mechanism of weights makes our tabu search more powerful, and our algorithm is practically usable.

The Approximability of Constraint Satisfaction Problems

We study optimization problems that may be expressed as constraint satisfaction problems. An instance of a Boolean constraint satisfaction problem is given by m constraints applied to n Boolean variables. Different computational problems arise from constraint satisfaction problems depending on the nature of the underlying constraints as well as on the goal of the optimization task. Here we consider four possible goals: Max CSP (Min CSP) is the class of problems where the goal is to find an assignment maximizing the number of satisfied constraints (minimizing the number of unsatisfied constraints). Max Ones (Min Ones) is the class of optimization problems where the goal is to find an assignment satisfying all constraints with maximum (minimum) number of variables set to 1. Each class consists of infinitely many problems and a problem within a class is specified by a finite collection of finite Boolean functions that describe the possible constraints that may be used. Tight bounds on the of every problem in Max CSP were obtained by Creignou [ J. Comput. System Sci., 51 (1995), pp. 511--522]. In this work we determine tight bounds on the approximability (i.e., the ratio to within which each problem may be approximated in polynomial time) of every problem in Max Ones, Min CSP, and Min Ones. Combined with the result of Creignou, this completely classifies all optimization problems derived from Boolean constraint satisfaction. Our results capture a diverse collection of optimization problems such as MAX 3-SAT, Max Cut, Max Clique, Min Cut, Nearest Codeword, etc. Our results unify recent results on the (in-)approximability of these optimization problems and yield a compact presentation of most known results. Moreover, these results provide a formal basis to many statements on the behavior of natural optimization problems that have so far been observed only empirically.

Improving the performance of weighted Lagrange-multiplier methods for nonlinear constrained optimization

Nonlinear constrained optimization problems in discrete and continuous spaces are an important class of problems studied extensively in artificial intelligence and operations research. These problems can be solved by a Lagrange-multiplier method in continuous space and by an extended discrete Lagrange-multiplier method in discrete space. When constraints are satisfied, these methods rely on gradient descents in the objective space to find high-quality solutions. On the other hand, when constraints are violated, these methods rely on gradient ascents in the Lagrange-multiplier space in order to increase the penalties on unsatisfied constraints and to force the constraints into satisfaction. The balance between gradient descents and gradient ascents depends on the relative weights between the objective function and the constraints, which indirectly control the convergence speed and solution quality of the Lagrangian method. To improve convergence speed without degrading solution quality, we propose an algorithm to dynamically control the relative weights between the objective and the constraints. Starting from an initial weight, the algorithm automatically adjusts the weights based on the behavior of the search progress. With this strategy, we are able to eliminate divergence, reduce oscillation, and speed up convergence. We show improved convergence behavior of our proposed algorithm on both nonlinear continuous and discrete problems.