Chapter 24. Maximum Satisfiabiliy

2021 ◽  
Author(s):  
Fahiem Bacchus ◽  
Matti Järvisalo ◽  
Ruben Martins
Keyword(s):  
Objective Function ◽  
Real World ◽  
Optimization Problems ◽  
Truth Assignment ◽  
Maximum Satisfiability ◽  
Performance Improvements ◽  
Algorithm Portfolios ◽  
Recent Developments ◽  
Significant Performance ◽  
Objective Value

Maximum satisfiability (MaxSAT) is an optimization version of SAT that is solved by finding an optimal truth assignment instead of just a satisfying one. In MaxSAT the objective function to be optimized is specified by a set of weighted soft clauses: the objective value of a truth assignment is the sum of the weights of the soft clauses it satisfies. In addition, the MaxSAT problem can have hard clauses that the truth assignment must satisfy. Many optimization problems can be naturally encoded into MaxSAT and this, along with significant performance improvements in MaxSAT solvers, has led to MaxSAT being used in a number of different application areas. This chapter provides a detailed overview of the approaches to MaxSAT solving that have in recent years been most successful in solving real-world optimization problems. Further recent developments in MaxSAT research are also overviewed, including encodings, applications, preprocessing, incomplete solving, algorithm portfolios, partitioning-based solving, and parallel solving.

scholarly journals Data Downlink System in the Vast IOT Node Condition Assisted by UAV, Large Intelligent Surface, and Power and Data Beacon

Sensors ◽  
2020 ◽  
Vol 20 (20) ◽  
pp. 5748
Author(s):  
Zhibo Zhang ◽  
Qing Chang ◽  
Na Zhao ◽  
Chen Li ◽  
Tianrun Li
Keyword(s):  
Communication Systems ◽  
Optimization Problems ◽  
Minimum Energy ◽  
Numerical Algorithms ◽  
Flight Trajectory ◽  
Performance Improvements ◽  
Minimum Energy Consumption ◽  
Significant Performance ◽  
Downlink System ◽  
The Internet Of Things

The future development of communication systems will create a great demand for the internet of things (IOT), where the overall control of all IOT nodes will become an important problem. Considering the essential issues of miniaturization and energy conservation, in this study, a new data downlink system is designed in which all IOT nodes harvest energy first and then receive data. To avoid the unsolvable problem of pre-locating all positions of vast IOT nodes, a device called the power and data beacon (PDB) is proposed. This acts as a relay station for energy and data. In addition, we model future scenes in which a communication system is assisted by unmanned aerial vehicles (UAVs), large intelligent surfaces (LISs), and PDBs. In this paper, we propose and solve the problem of determining the optimal flight trajectory to reach the minimum energy consumption or minimum time consumption. Four future feasible scenes are analyzed and then the optimization problems are solved based on numerical algorithms. Simulation results show that there are significant performance improvements in energy/time with the deployment of LISs and reasonable UAV trajectory planning.

Boosting branch-and-bound MaxSAT solvers with clause learning

2021 ◽  
pp. 1-21
Author(s):  
Chu-Min Li ◽  
Zhenxing Xu ◽  
Jordi Coll ◽  
Felip Manyà ◽  
Djamal Habet ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Combinatorial Optimization ◽  
Problem Solving ◽  
Branch And Bound ◽  
Real World ◽  
Optimization Problems ◽  
Satisfiability Problem ◽  
Maximum Satisfiability ◽  
Combinatorial Optimization Problems ◽  
Clause Learning

The Maximum Satisfiability Problem, or MaxSAT, offers a suitable problem solving formalism for combinatorial optimization problems. Nevertheless, MaxSAT solvers implementing the Branch-and-Bound (BnB) scheme have not succeeded in solving challenging real-world optimization problems. It is widely believed that BnB MaxSAT solvers are only superior on random and some specific crafted instances. At the same time, SAT-based MaxSAT solvers perform particularly well on real-world instances. To overcome this shortcoming of BnB MaxSAT solvers, this paper proposes a new BnB MaxSAT solver called MaxCDCL. The main feature of MaxCDCL is the combination of clause learning of soft conflicts and an efficient bounding procedure. Moreover, the paper reports on an experimental investigation showing that MaxCDCL is competitive when compared with the best performing solvers of the 2020 MaxSAT Evaluation. MaxCDCL performs very well on real-world instances, and solves a number of instances that other solvers cannot solve. Furthermore, MaxCDCL, when combined with the best performing MaxSAT solvers, solves the highest number of instances of a collection from all the MaxSAT evaluations held so far.

scholarly journals A stability result for linear Markovian stochastic optimization problems

2020 ◽  
Author(s):  
Adriana Kiszka ◽  
David Wozabal
Keyword(s):  
Stochastic Optimization ◽  
Stochastic Processes ◽  
Objective Function ◽  
Markov Processes ◽  
Optimization Problems ◽  
Stability Result ◽  
Extant Literature ◽  
Numerical Example ◽  
Optimal Values ◽  
Objective Value

Abstract In this paper, we propose a semi-metric for Markov processes that allows to bound optimal values of linear Markovian stochastic optimization problems. Similar to existing notions of distance for general stochastic processes, our distance is based on transportation metrics. As opposed to the extant literature, the proposed distance is problem specific, i.e., dependent on the data of the problem whose objective value we want to bound. As a result, we are able to consider problems with randomness in the constraints as well as in the objective function and therefore relax an assumption in the extant literature. We derive several properties of the proposed semi-metric and demonstrate its use in a stylized numerical example.

scholarly journals Aspect-Based Sentiment Analysis Using Smart Company and Hotel Aspect Review Data

2020 ◽  
pp. 112-118
Author(s):  
C. Selvi ◽  
Niveda. C. P
Keyword(s):  
Knowledge Acquisition ◽  
Sentiment Analysis ◽  
Language Processing ◽  
Real World ◽  
Performance Improvements ◽  
Information Navigation ◽  
Real World Applications ◽  
Significant Performance ◽  
Processing Techniques ◽  
Online Feedback

Digital sources such as smart applications opinions and online feedback statistics are crucial resources to be seeking for customers’ remarks and input. However, the reviews are often disorganized, leading to difficulties in information navigation and knowledge acquisition. The aforementioned problem is overcome by generating aspect-sentiment based embedding for the hotels and companies by looking into reliable reviews of them. The important product aspects are identified based on two observations: 1) the important aspects are usually commented on by a large number of consumers and 2) consumer opinions on the important aspects greatly influence their overall opinions. Aspect frequency and the influence of consumer opinions given to each aspect over their overall opinions are identified for hotel reviews whereas for company reviews approach adopts language processing techniques, policies, and lexicons to address several sentiment evaluation challenges, and convey summarized results. Moreover, aspect ranking achieve significant performance improvements, which demonstrate the capacity of aspect ranking in facilitating real-world applications.

scholarly journals Reduced Cost Fixing for Maximum Satisfiability

2018 ◽  
Author(s):  
Fahiem Bacchus ◽  
Antti Hyttinen ◽  
Matti Järvisalo ◽  
Paul Saikko
Keyword(s):  
Integer Programming ◽  
Real World ◽  
Recent Trend ◽  
Optimization Problems ◽  
State Of The Art ◽  
Boolean Satisfiability ◽  
Maximum Satisfiability ◽  
Hitting Set ◽  
Sat Solvers ◽  
Speed Up

Maximum satisfiability (MaxSAT) offers a competitive approach to solving NP-hard real-world optimization problems. While state-of-the-art MaxSAT solvers rely heavily on Boolean satisfiability (SAT) solvers, a recent trend, brought on by MaxSAT solvers implementing the so-called implicit hitting set (IHS) approach, is to integrate techniques from the realm of integer programming (IP) into the solving process. This allows for making use of additional IP solving techniques to further speed up MaxSAT solving. In this line of work, we investigate the integration of the technique of reduced cost fixing from the IP realm into IHS solvers, and empirically show that reduced cost fixing considerable speeds up a state-of-the-art MaxSAT solver implementing the IHS approach.

Investigating the streamability of XProc pipelines

2009 ◽  
Author(s):  
Norman Walsh
Keyword(s):  
Real World ◽  
Performance Improvements ◽  
Significant Performance ◽  
Using Data ◽  
Open Question

XProc: An XML Pipeline Language is a specification being developed by the W3C for describing a sequence of XML operations performed over a set of input documents. Not all of the steps in XProc are known to streamable and consequently, the XProc specification does not require implementations to support streaming. It's an open question whether or not a streaming implementation would be likely to achieve significant performance improvements over a similar non-streaming implementation. Using data collected from real-world pipelines, this paper examines that question.

scholarly journals Managing caching strategies for stream reasoning with reinforcement learning

2020 ◽  
Vol 20 (5) ◽  
pp. 625-640
Author(s):  
CARMINE DODARO ◽  
THOMAS EITER ◽  
PAUL OGRIS ◽  
KONSTANTIN SCHEKOTIHIN
Keyword(s):  
Reinforcement Learning ◽  
Real World ◽  
Performance Improvements ◽  
Novel Approach ◽  
Stream Reasoning ◽  
Significant Performance ◽  
Intelligent Management ◽  
Truth Maintenance ◽  
Constraint Learning ◽  
Real World Problems

AbstractEfficient decision-making over continuously changing data is essential for many application domains such as cyber-physical systems, industry digitalization, etc. Modern stream reasoning frameworks allow one to model and solve various real-world problems using incremental and continuous evaluation of programs as new data arrives in the stream. Applied techniques use, e.g., Datalog-like materialization or truth maintenance algorithms to avoid costly re-computations, thus ensuring low latency and high throughput of a stream reasoner. However, the expressiveness of existing approaches is quite limited and, e.g., they cannot be used to encode problems with constraints, which often appear in practice. In this paper, we suggest a novel approach that uses the Conflict-Driven Constraint Learning (CDCL) to efficiently update legacy solutions by using intelligent management of learned constraints. In particular, we study the applicability of reinforcement learning to continuously assess the utility of learned constraints computed in previous invocations of the solving algorithm for the current one. Evaluations conducted on real-world reconfiguration problems show that providing a CDCL algorithm with relevant learned constraints from previous iterations results in significant performance improvements of the algorithm in stream reasoning scenarios.

Scalable Computing Architecture for Time-Dependent Transportation Optimization Problems Based on High-Performance Computing Techniques

2019 ◽  
Vol 2673 (4) ◽  
pp. 205-216 ◽  
Author(s):  
Pengfei (Taylor) Li ◽  
Peirong (Slade) Wang ◽  
Farzana Chowdhury ◽  
Li Zhang
Keyword(s):  
Objective Function ◽  
High Performance Computing ◽  
High Performance ◽  
Optimization Problems ◽  
Dynamic Network ◽  
Alternative Formulation ◽  
High Fidelity ◽  
Objective Functions ◽  
Performance Computing ◽  
Transportation Optimization

Traditional formulations for transportation optimization problems mostly build complicating attributes into constraints while keeping the succinctness of objective functions. A popular solution is the Lagrangian decomposition by relaxing complicating constraints and then solving iteratively. Although this approach is effective for many problems, it generates intractability in other problems. To address this issue, this paper presents an alternative formulation for transportation optimization problems in which the complicating attributes of target problems are partially or entirely built into the objective function instead of into the constraints. Many mathematical complicating constraints in transportation problems can be efficiently modeled in dynamic network loading (DNL) models based on the demand–supply equilibrium, such as the various road or vehicle capacity constraints or “IF–THEN” type constraints. After “pre-building” complicating constraints into the objective functions, the objective function can be approximated well with customized high-fidelity DNL models. Three types of computing benefits can be achieved in the alternative formulation: ( a) the original problem will be kept the same; ( b) computing complexity of the new formulation may be significantly reduced because of the disappearance of hard constraints; ( c) efficiency loss on the objective function side can be mitigated via multiple high-performance computing techniques. Under this new framework, high-fidelity and problem-specific DNL models will be critical to maintain the attributes of original problems. Therefore, the authors’ recent efforts in enhancing the DNL’s fidelity and computing efficiency are also described in the second part of this paper. Finally, a demonstration case study is conducted to validate the new approach.

scholarly journals An Attention-Based Multilayer GRU Model for Multistep-Ahead Short-Term Load Forecasting

Sensors ◽  
2021 ◽  
Vol 21 (5) ◽  
pp. 1639
Author(s):  
Seungmin Jung ◽  
Jihoon Moon ◽  
Sungwoo Park ◽  
Eenjun Hwang
Keyword(s):  
Power Consumption ◽  
Prediction Models ◽  
Short Term Memory ◽  
Load Forecasting ◽  
Input Sequence ◽  
Short Term ◽  
Performance Improvements ◽  
Short Term Load Forecasting ◽  
Significant Performance ◽  
Input Variables

Recently, multistep-ahead prediction has attracted much attention in electric load forecasting because it can deal with sudden changes in power consumption caused by various events such as fire and heat wave for a day from the present time. On the other hand, recurrent neural networks (RNNs), including long short-term memory and gated recurrent unit (GRU) networks, can reflect the previous point well to predict the current point. Due to this property, they have been widely used for multistep-ahead prediction. The GRU model is simple and easy to implement; however, its prediction performance is limited because it considers all input variables equally. In this paper, we propose a short-term load forecasting model using an attention based GRU to focus more on the crucial variables and demonstrate that this can achieve significant performance improvements, especially when the input sequence of RNN is long. Through extensive experiments, we show that the proposed model outperforms other recent multistep-ahead prediction models in the building-level power consumption forecasting.

scholarly journals Global optimization based on active preference learning with radial basis functions

2020 ◽  
Author(s):  
Alberto Bemporad ◽  
Dario Piga
Keyword(s):  
Global Optimization ◽  
Objective Function ◽  
Decision Maker ◽  
Optimization Problems ◽  
Global Optimum ◽  
Bayesian Optimization ◽  
Preference Learning ◽  
Global Optimizer ◽  
Radial Basis ◽  
Decision Vector

AbstractThis paper proposes a method for solving optimization problems in which the decision-maker cannot evaluate the objective function, but rather can only express a preference such as “this is better than that” between two candidate decision vectors. The algorithm described in this paper aims at reaching the global optimizer by iteratively proposing the decision maker a new comparison to make, based on actively learning a surrogate of the latent (unknown and perhaps unquantifiable) objective function from past sampled decision vectors and pairwise preferences. A radial-basis function surrogate is fit via linear or quadratic programming, satisfying if possible the preferences expressed by the decision maker on existing samples. The surrogate is used to propose a new sample of the decision vector for comparison with the current best candidate based on two possible criteria: minimize a combination of the surrogate and an inverse weighting distance function to balance between exploitation of the surrogate and exploration of the decision space, or maximize a function related to the probability that the new candidate will be preferred. Compared to active preference learning based on Bayesian optimization, we show that our approach is competitive in that, within the same number of comparisons, it usually approaches the global optimum more closely and is computationally lighter. Applications of the proposed algorithm to solve a set of benchmark global optimization problems, for multi-objective optimization, and for optimal tuning of a cost-sensitive neural network classifier for object recognition from images are described in the paper. MATLAB and a Python implementations of the algorithms described in the paper are available at http://cse.lab.imtlucca.it/~bemporad/glis.

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