Non-deterministic Problem Research Articles

P ≠ np: The Set of Deterministic Problems that are Solvable in Polynomial Time is Unequal to the Set of Non-Deterministic Problems that are Solvable in Polynomial Time

p ≠ np: The Set of Deterministic Problems that are Solvable in Polynomial Time is Unequal to the Set of Non-Deterministic Problems that are Solvable in Polynomial Time

Robust optimization of hypoid gear contact performance considering tooth form error: Design sensitivity and Pareto front

Optimization of hypoid gear contact performance is challenging due to its nonconvex nature and the handling of non-linear constraints involving complex gear contact behavior. In addition, the contact performance in the existing optimization schemes is highly reliant on the manufacturing quality, for example, the uncertain tooth form errors induced by machining tolerances and blade wear are usually ignored. To tackle these problems, a robust optimization methodology is proposed for hypoid gear contact performance. A finite element/contact mechanics model is established, which considers the stochastic tooth form errors following a Gaussian distribution model. The non-linear constraints are incorporated to avoid edge contact under loaded conditions, and tooth surface interference due to error. This methodology guarantees the feasible solution space and reduces the optimization complexity by the independent identification model. The identification model of the optimal solution is flexible in the parameter selection while keeping tooth depth. This non-deterministic problem is optimized based on the pattern search method. The Pareto front and design sensitivity analysis demonstrate the effectiveness and robustness of the proposed optimization methodology.

BRANCHING PROCESS MODELLING: A TOOL FOR DECIPHERING COMPLEX REAL-WORLD PHENOMENA USING R PROGRAMMING

The reproduction of organisms such as human beings, cells or neutrons can be modeled via branching processes.The theory of branching processes offers suitable mathematical models to depict the chance-based progression of systems, where elements like cells, particles, or general individuals replicate and perish over a certain lifespan. These models are employed to illustrate stochastic systems like chain reactions, lineage continuation of surnames, elimination of pests, population growth, and gene spread. This study clearly showcases the likelihood of extinction, its timing, and the odds of complete offspring through vivid examples. The decline of prominent families from history has often been observed and has sparked numerous speculations. The branching process is a very useful tool in many real life problems (non-deterministic problems) and random phenomenon. Research indicates that when the average number of descendants for each entity exceeds 1 (meaning individuals reproduce at a rate slightly higher than self-replacement), the branching process doesn't necessarily cease. On the other hand, if this average number is 1 or lower, the process will inevitably face extinction.

A novel algorithm based on a modified PSO to predict 3D structure for proteins in HP model using Transfer Learning

Most intracellular activities of living organisms are performed by proteins that have unique and complex 3-Dimensional (3D) structures, playing very important roles in their operations. Due to importance and challenges of predicting 3D structures for proteins, laboratory methods with limitations such as time consuming and high cost have been developed. Computational methods use a sequence of amino acids to obtain the 3D structure. They encounter with a nondeterministic problem having polynomial completion time (NP-Complete problem); with a chain of amino acids as input, and a protein, with 3D structure, as output. In this paper, a new population-based algorithm, under Predatory Search Strategy-Particle Swarm Optimization (PSS-PSO) framework, is presented for predicting the 3D structure; using Hydrophobic-Polar (HP) model on Face-Centered Cubic (FCC) lattice. In this approach, name TRL-PSSPSO, two new moves are proposed to direct each solution toward the native structure: Local Move for reaching a dense hydrophobic core and large H-H contacts and Meta Move for reaching optimal structure, by using Transfer learning. Two datasets are considered for evaluating and the results on some set of standard protein benchmarks show outperforming the state-of-the-art approaches. They show that the proposed approach can improve the accuracy of template-free prediction in an acceptable manner.

Probability Distributions of Asphalt Pavement Responses and Performance under Random Moving Loads and Pavement Temperature

Asphalt pavements are damaged by traffic load repetitions. Conventionally, the allowed number of load repetitions until pavement failure is calculated based on empirical transfer functions from deterministic pavement mechanical responses to performance. However, the mechanical responses and damage to the pavement are uncertain under a random realistic traffic load and pavement temperature. Therefore, the non-deterministic problem—that is, the probability distributions of asphalt pavement responses and performance under random moving loads and pavement temperatures—was investigated in this study. Random factors include the load pressure, vehicle wandering, speed, and temperature inside the asphalt layer. A combination of the response surface and first-order reliability methodologies was recommended to calculate the probability of mechanical responses at any point within the pavement, for reasons of computational efficiency. The accuracy of this method was verified by a Monte-Carlo simulation. Then, the effects of the mean values and standard deviations of the random factors on the probability distributions of the mechanical responses were discussed. Finally, probability distributions of pavement performance (i.e., probability density distributions of cumulative damage for fatigue failure and rutting after repeated random loads) were calculated using transfer functions and the probability distributions of the mechanical responses; thereby, the failure probability of the pavement after a given number of load repetitions was obtained. The results show that the previous deterministic analysis could not fully reflect the random characteristics of pavement mechanical responses under realistic random moving loads, and the mean values and standard deviations of the random factors have significant effects on the probability distributions of mechanical responses and performance. The failure probability of the pavement after a given number of load repetitions can be used as a guide to reliability-based pavement design. This study on the probability distributions of asphalt pavement responses and performance exhibits the potential to understand pavement behavior and could be beneficial as a complement during reliability-based pavement design.

Choquet integrals of set-valued functions with respect to set-valued fuzzy measures

As powerful tools for modeling nondeterministic problems, Choquet integrals have attracted much attention in recent years. This study generalizes the existing set-valued Choquet integrals and formulates the theory of Choquet integrals with respect to set-valued fuzzy measures. First, a set-valued Choquet integral of a real-valued function is defined using the set of Choquet integrals of real-valued functions with respect to fuzzy measure selections of a set-valued fuzzy measure. The integrand is then extended to set-valued functions, after which various properties, convergence theorems, and set-valued Jensen's inequalities are obtained. Second, following how single-valued Choquet integrals are defined, an alternative set-valued Choquet integral of real-valued function is formulated using Aumann integrals. Through these steps, the existing set-valued Choquet integrals are covered.

Mobile Robot Optimal Path Planning in the Configuration Spacebased on Smoothing A*

—Mobile robots have been widely applied in the industrial world. Mobile robots are proven to help humans work, especially repetitive ones. A robot needs to plan its trajectory to move as desired, a concept that requires path planning. Path planning is a non-deterministic problem that plays a role in finding a path to connect the system to the desired destination. The existing path planning algorithm proposes a path with sharp bends that make it difficult for the robot to maneuver so that it can still be optimized from the sides of the proposed path. One way is to make smoother turns so that the robot is not difficult to turn. Applying the interpolation method using b-spline makes the proposed path smoother. B-spline is a spline feature that provides a specific order and minimal support for domain partitioning. B-spline is applied to the Smoothing A*(SA*) algorithm, one of the breakthrough methods to produce smoother paths. As a result, SA* consistently produces paths shorter than the stateof-the-art by 0.957% and shorter than the baseline by 4.891%.

Flexible FOND HTN Planning: A Complexity Analysis

Hierarchical Task Network (HTN) planning is an expressive planning formalism that has often been advocated to address real-world problems. Yet few extensions exist that can deal with the many challenges encountered in the real world, one being the capability to express uncertainty. Recently, a new HTN formalism for fully observable nondeterministic problems was proposed and studied theoretically. In this paper, we lay out limitations of that formalism and propose an alternative definition, which addresses and resolves such limitations. We also study its complexity for certain problems.

A Corpus-Based and Fuzzy Assessment-Based Study of Labels in Spoken English

Label English is common in spoken English, but for most English learners, it is difficult to use and express labels correctly and appropriately. This is mainly due to their lack of understanding of this expression. Label English is equivalent to Chinese grammar, using different markup components to form a complete sentence. In this paper, five tags commonly used by native English speakers, namely, or something, or something, and so on, and that, and everything, will be studied. Through the method of fuzzy evaluation, it illustrates the use of labels by Chinese English learners and the similarities and differences between Chinese English learners and native English speakers. Corpus is a product of language research and corresponding computer technology. It is a model of the combination of quantitative and qualitative methods in language research. It makes its due contribution to revealing the essence of language and can provide scientific basis for language research. Based on the above background, the purpose of this paper is to study tags in spoken English through corpus and vague evaluation. And the top five tags are retrieved in CLEC and LOB. Then, the frequency of occurrence is counted. Finally, the variance of each label is calculated by using the method of fuzzy evaluation, to determine whether there are significant differences between the two corpuses. The fuzzy evaluation method can make the results clear and systematic, can better solve the vague and difficult to quantify problems, and is suitable for solving various non-deterministic problems. The results show that besides “and so on,” Chinese English learners use labels less frequently than native English speakers. In terms of structure, both of them adopt the prototype of tags, but most Chinese learners misuse some of their own tags. The main reasons for this phenomenon are mother tongue transfer and inadequate pragmatic competence. In contrast, native English speakers use tags more frequently. In terms of usage form, the prototypes of the above five tags are used, but there are also variants, mainly in the form of expansion and lexical variants. The 106 tagged words found in CLEC were searched one by one in COLSEC. It was found that only 19 expressions appeared in the corpus, with a total frequency of only 271 and a standard frequency of 371. The total frequency of this type of expression in LOB is 11072 times, and the standard frequency is 1055 times. In addition, these expressions also have the pragmatic functions of inference, reinforcement, and compliance.

Air quality deterministic and probabilistic forecasting system based on hesitant fuzzy sets and nonlinear robust outlier correction

Performing scientific and accurate forecasting and realizing the quantitative description of uncertainties in air quality remain challenging prospects. Because of the strong volatility and uncertainty of air pollutant concentrations, this problem increases in difficulty when multiple requirements are considered. In this study, a novel air quality deterministic and probabilistic forecasting system based on hesitant fuzzy sets and nonlinear robust outlier correction was proposed to realize air quality early warning. The proposed system solves the non-stochastic non-deterministic problem in air quality forecasting considering a novel hesitant fuzzy time series forecasting model wherein the intervals are partitioned by different approaches with optimal weights determined by the multi-objective JAYA algorithm. The forecasting performance is further enhanced with the introduction of a new nonlinear error correction model based on an outlier robust extreme learning machine and multi-objective JAYA algorithm, and the quality of the solution obtained is verified by sensitivity analysis. However, point forecast information alone is not sufficient to facilitate the rational integration of pollution control measures. Therefore, this study conducts probabilistic forecasting and constructs proper prediction intervals based on the optimal distribution of the forecasting residuals. By comparing the results with typical counterparts and comparison models considering multiple metrics, the experimental results confirmed the improvement scheme proposed in this study on the traditional fuzzy time series forecasting method while the effectiveness of applying the proposed system to air quality early warning was confirmed as well.

Width and Complexity of Belief Tracking in Non-Deterministic Conformant and Contingent Planning

It has been shown recently that the complexity of belief tracking in deterministic conformant and contingent planning is exponential in a width parameter that is often bounded and small. In this work, we introduce a new width notion that applies to non-deterministic conformant and contingent problems as well. We also develop a belief tracking algorithm for non-deterministic problems that is exponential in the problem width, analyze the width of non-deterministic benchmarks, compare the new notion to the previous one over deterministic problems, and present experimental results.

An Approach to Ship Deck Arrangement Optimization Problem Using an Improved Multiobjective Hybrid Genetic Algorithm

Ship deck arrangement design is about determining the positions and dimensions of arranged objects. This paper presents the mathematical model for the ship deck arrangement optimization problem statement and how the individual’s objective and constraint functions are computed. Moreover, an improved multiobjective hybrid genetic algorithm is redesigned to solve this complex nondeterministic problem and generate a set of diverse and rational deck arrangements in the early stage of ship design. An adaptive crossover operator and a novel topological replace operator invoked in this algorithm are described. Finally, the proposed algorithm is tested on a main deck arrangement optimization of an underwater detection ship. In the validation tests, the proposed algorithm is compared to the standard NSGA-II to determine its ability to produce a set of diverse and rational deck arrangements. Subsequently, the performance tests are used to determine the ability of the algorithm to work with the highly constrained arrangement problems and the efficiency of the adaptive crossover and topological replace operators.

Reducing the effect of passengers’ non-compliance with aircraft boarding rules

The quest for efficient aircraft boarding strategies continues to generate lots of business and scientific discussions. Boarding strategies define rules and procedures aimed to reduce boarding time and operational cost. Most of the proposed strategies do not account for passengers’ non-compliance with boarding rules. Non-compliance is one of the major non-deterministic problems that can degrade any performance improvement to be expected from adopting a boarding strategy. To that, it is of paramount interest to shed light on this problem and introduce approaches for mitigating any related performance degradation in the boarding process. Although some recent research investigations considered the effect of non-compliance on the overall boarding time under different strategies, there was a lack of remedial actions. This paper dissects the operational characteristics of the non-compliance activity, proposes two different intervention approaches to deal with non-complying passengers, and analyzes the resulting impact under different categories of boarding strategies using a cellular-automaton-based simulation.

Design of an expert system architecture: An overview

An area of Artificial intelligence (AI) that can claim a large measure of responsibility for the current heightened AI awareness is Knowledge Based Expert System (KBES), computer programs that embody human expertise. KBES specifically enable the computer to assist in solving ill-structured and non-deterministic problems such as design activities including synthesis, evaluation, modeling and decision-making process. The paper explains the role of Backward Chaining method, Forward Chaining method, Rule-Value method as three major methods involved in solving these problems to differentiate the Knowledge Based Expert System programming from normal programming. The development of an expert system requires a tool that will provide for better means of knowledge acquisition, inference mechanism and user interface. This paper brings out an overview of Expert System, a systematic study involving a critical analysis of the Expert System (ES) development, specifying its requirements. Further it highlights the features of Expert System and its implementation.

An optimized crawling technique for maintaining fresh repositories

With the rapid increase in demand of digital information via internet, it becomes imperative for search engines to serve up to date information in response to user query. A web crawler plays a vital role in maintaining local cache of search engine. Today, the biggest challenge for web crawler is how to harness fresh information in its local cache of n constantly changing web pages. These web pages often possess dynamic creation and updation cycle. Moreover, the resources for downloading possible updates are limited. This problem is formulated as non-deterministic optimization problem. Many attempts had been made by researchers in past to solve it. But most of existing techniques work well for small value of n and often intractable for large corpus. The paper presents an optimal solution to deal with this non- deterministic problem for large data. The experimental results show that technique achieves promising results as compared to existing crawler.

Integrated energy system planning research based on big data load prediction method

The planning of integrated energy system is a very complex multi-target, multi-constraint, nonlinear, random uncertainty mixed integrated combination optimization problem, its planning and design process should not only consider the interdependence between the system capacity, energy conversion, energy storage, energy use and other links, but also consider the interaction and integration of cold, hot, electricity and other multi-energy flows, which is essentially a non-deterministic polynomial difficult problem. China’s energy continues to develop rapidly, all kinds of sensors and intelligent equipment data is increasing, the data obtained in the equipment and all kinds of sensors collected energy load prediction related factors such as temperature, weather, wind speed and other data volume increased dramatically, the data dimension is also increasing, the scale of data has also increased from GB to TB or even higher, based on the traditional prediction methods and intelligent prediction methods, has been far below the load forecast desired to achieve accuracy and speed requirements, Therefore, the use of big data technology to predict energy demand is an important future direction.

The Polish Practice of Probabilistic Approach in Power System Development Planning

Power systems can be analyzed using either a deterministic or a probabilistic approach. The deterministic analysis centers on studying the quantities and indicators that characterize the operating states of the power system under strictly defined conditions. However, the long-term horizon of planning analyses, the changes of marketing mechanisms, the development of renewable electricity sources, the leaving from large-scale generation, the growth of smart technology and the increase in consumer awareness make the development of transmission networks a non-deterministic problem. In this article, we propose a planning procedure that takes the probabilistic elements into account. This procedure was developed to take into account the high variability of power flows caused by the generation of renewable sources and international exchange. Such conditions of the power system operation forced a departure from deterministic planning. The new probabilistic approach uses the existing tools and experience gained during subsequent development projects. As part of the probabilistic approach, simulations were carried out using the Latin Hypercube Sampling and Two Point Estimation Method algorithms. These methods effectively reduce the computation time and, at the same time, give satisfactory results. The verification was carried out on a test grid model developed in accordance with the technical standards used in the Polish Power System. Effects were assessed using a deterministic and probabilistic approach. This analysis confirmed the practical possibility of using the probabilistic approach in planning the development of transmission network in Poland. When using a probabilistic approach to predict power flow, the criteria of technical acceptability for a given development variant and the manner in which the strategy is determined are of particular importance.

IDENTIFICATION OF PROBLEM SITUATIONS IN FUNCTIONAL DIAGNOSTICS OF INTELLIGENT BUSINESS SYSTEMS

The paper discusses the issues of increasing the efficiency of production activities of an intelligent business system operating in a dynamic environment by reducing its losses by creating a subject technology for reliable identification of problem situations in the process of functional diagnostics of a business system. The object of the research is an intelligent business system of the IT industry, which produces intelligent products, the results of which depend on the mental abilities of its personnel, who own effective intelligent information technologies. The problem-containing environment was chosen as the basis for analyzing the problem situation, in the depths of which the problem situation arises, develops and manifests itself. A problem-containing environment is characterized by structure and behavior. The behavior of the problem-containing environment is determined by the multidimensionality of the ongoing business processes, their interaction and dynamics. To identify deterministic and non-deterministic problem situations, it is proposed to set them by bipartite graphs and use the technology of inference based on precedents, which has serious advantages over the method of inference based on knowledge. In this work, a cognitive method is used to analyze problem situations of an intelligent business system. The basis of cognitive analysis is formed by the problem-containing environment, in the depths of which the problem situation arises. To study the problem-containing environment, the method of analysis of hierarchies is used, the basis of which is a hierarchy which is a system of levels, each of which consists of elements, factors of the problem-containing environment and an intelligent business system. A complex of models has been developed to construct a bipartite graph of a problem situation and to analyze its problem-containing environment. On the basis of a complex of models, a subject technology for identifying problem situations arising in the process of functional diagnostics of intelligent business systems has been created. The results obtained can be used as a theoretical platform for creating an information technology for functional diagnostics of intelligent business systems operating in a dynamic environment.

Pseudo-integral and generalized Choquet integral

Due to many applications, the Choquet integral as a powerful tool for modeling non-deterministic problems needs to be further extended. Therefore the paper is devoted to a generalization of the Choquet integral. As a basis, the pseudo-integral for bounded integrand is extended to the case for nonnegative integrands at first, and then the generalized Choquet integral is defined. As special cases, pseudo-Choquet Stieltjes integrals, pseudo-fuzzy Stieltjes integrals, g-Choquet integrals, pseudo-(N)fuzzy integrals and pseudo-(S)fuzzy integrals are obtained, and various kinds of properties and convergence theorems are shown, meanwhile Markov, Jensen, Minkowski and Hölder inequalities are proved. In the end, the generalized discrete Choquet integral is discussed. The obtained results for the generalized Choquet integral cover some previous results on different types of nonadditive integrals.

Qualitative Numeric Planning: Reductions and Complexity


 
 
 Qualitative numerical planning is classical planning extended with non-negative real variables that can be increased or decreased "qualitatively", i.e., by positive indeterminate amounts. While deterministic planning with numerical variables is undecidable in general, qualitative numerical planning is decidable and provides a convenient abstract model for generalized planning. The solutions to qualitative numerical problems (QNPs) were shown to correspond to the strong cyclic solutions of an associated fully observable non-deterministic (FOND) problem that terminate. This leads to a generate-and-test algorithm for solving QNPs where solutions to a FOND problem are generated one by one and tested for termination. The computational shortcomings of this approach for solving QNPs, however, are that it is not simple to amend FOND planners to generate all solutions, and that the number of solutions to check can be doubly exponential in the number of variables. In this work we address these limitations while providing additional insights on QNPs. More precisely, we introduce two polynomial-time reductions, one from QNPs to FOND problems and the other from FOND problems to QNPs both of which do not involve termination tests. A result of these reductions is that QNPs are shown to have the same expressive power and the same complexity as FOND problems.