Non-deterministic Polynomial-time Research Articles

Integral-Valued Pythagorean Fuzzy-Set-Based Dyna Q+ Framework for Task Scheduling in Cloud Computing.

Task scheduling is a critical challenge in cloud computing systems, greatly impacting their performance. Task scheduling is a nondeterministic polynomial time hard (NP-Hard) problem that complicates the search for nearly optimal solutions. Five major uncertainty parameters, i.e., security, traffic, workload, availability, and price, influence task scheduling decisions. The primary rationale for selecting these uncertainty parameters lies in the challenge of accurately measuring their values, as empirical estimations often diverge from the actual values. The integral-valued Pythagorean fuzzy set (IVPFS) is a promising mathematical framework to deal with parametric uncertainties. The Dyna Q+ algorithm is the updated form of the Dyna Q agent designed specifically for dynamic computing environments by providing bonus rewards to non-exploited states. In this paper, the Dyna Q+ agent is enriched with the IVPFS mathematical framework to make intelligent task scheduling decisions. The performance of the proposed IVPFS Dyna Q+ task scheduler is tested using the CloudSim 3.3 simulator. The execution time is reduced by 90%, the makespan time is also reduced by 90%, the operation cost is below 50%, and the resource utilization rate is improved by 95%, all of these parameters meeting the desired standards or expectations. The results are also further validated using an expected value analysis methodology that confirms the good performance of the task scheduler. A better balance between exploration and exploitation through rigorous action-based learning is achieved by the Dyna Q+ agent.

Routing problem for reducing significant outages in optical networks and its system analysis

Optical communication networks are operated with great care to avoid outages. In particular, significant outages having a devastating impact on society must be avoided, and several countries specify “significance standards” for network outages. Although the impact of possible outages strongly depends on routing methods for requested connections, there has been no research specifically on these standards. This paper for the first time, to the best of our knowledge, introduces a routing problem to minimize the impact of outages on a given significance standard. We have shown this problem to be non-deterministic polynomial-time hardness, and an efficient heuristic method is proposed. This method searches for a good solution by reducing the problem to a shortest-path search, where the significance of a link failure is regarded as the link weight, and suppresses outage impact compared with other routing methods. In addition, the analysis of the system dependence among a network model, mean time to repair (MTTR) of failure elements, and significance standards suggests that the total system design considering the MTTR, significance standards, and routing method could dramatically reduce the impact of significant outages on optical networks.

A novel optimization framework integrating multiple initialization, automatic topologization and MINLP reduction to accelerate large-scale heat exchanger network synthesis

Ensuring the solution feasibility and achieving an acceptable solution time for the non-deterministic polynomial-time hard (NP-hard) problem of heat exchanger network (HEN) synthesis is still challenging. In this study, we developed a novel optimization framework for efficiently solving large-scale HEN synthesis problems to obtain near global optimal solutions, simultaneously addressing the solution's infeasibility and time. The optimization framework consists of a multiple initial HEN design model (M-INI model), a new distance-based auto structure transformer (A-STR transformer), and a reduced non-linear programming model (R-NLP model). The M-INI model generates various HEN designs based on pinch analysis by varying the minimum approach temperature and the modes of stream splitting and mixing. The A-STR transformer is first proposed to automatically convert various HEN designs into associated superstructure-based topologies as multiple initial starting points for accelerating the solution of the R-NLP model. A strategy for approximating the temperature difference calculation is further applied to reduce the computational loads. Four case studies were conducted using the proposed method to minimize the total annual cost (TAC). The solutions of general cases 1 and 2 are almost equal to the best results in the literature, while the solution time is reduced by 98.7 % and 99.8 %, respectively, which demonstrates the performance of the proposed method. Especially, the method was applied to two practical industrial HEN cases: a large-scale low-grade heat recovery system and a crude distillation unit. The results of large-scale case 3 show that the optimal solution near the global optimal solution only requires 251.7 s. Case 4 includes pre-splitting in scenario A and free splitting in scenario B. Compared to scenario A, the TAC and solution time in scenario B were reduced by 33.9 % and 93.1 %, indicating that the pre-splitting strategy excludes the optimal from the search space. The proposed novel optimization framework demonstrates the efficiency and applicability of handling large-scale HEN synthesis problems. It can also guide engineers in the design of a large-scale HEN with lower costs and effort.

Modified dung beetle optimizer with multi-strategy for uncertain multi-modal transport path problem

Abstract Uncertain multi-modal transport path optimization (UMTPO) is a combined optimization non-deterministic polynomial-time hard problem. Its goal is to determine a path with the lowest total transportation cost and carbon emissions from the starting point to the destination. To effectively address this issue, this article proposes a modified dung beetle optimizer (DBO) to address it. DBO is a swarm-based metaheuristic optimization algorithm that has the features of a fast convergence rate and high solution accuracy. Despite this, the disadvantages of weak global exploration capability and falling easily into local optima exist. In this article, we propose a modified DBO called MSHDBO for function optimization and to solve the UMTPO problem. However, for the vast majority of metaheuristic algorithms, they are designed for continuous problems and cannot directly solve discrete problems. Therefore, this article employs a priority based encoding and decoding method to solve the UMTPO problem. To verify the performance and effectiveness of the MSHDBO algorithm, we compared it with other improved versions of the DBO algorithm used in the literature. We confirmed the excellent performance of MSHDBO using 41 benchmark test functions from the IEEE CEC 2017 test suite and IEEE CEC 2022 test suite. Additionally, we compared the MSHDBO algorithm with 10 other state-of-the-art metaheuristic optimization algorithms through a practical UMTPO problem. The experimental results indicated that the MSHDBO algorithm achieved very good performance when solving the UMTPO problem.

Demand Management for Manufacturing Loads Considering Temperature Control under Dynamic Electricity Prices

Demand response (DR) can provide extra scheduling flexibility for power systems. Different from industrial and residential loads, the production process of manufacturing loads includes multiple production links, and complex material flow and energy flow are closely coupled, which can be seen as a typical nondeterministic polynomial-time (NP) hard problem. In addition, there is a coupling effect between the temperature-controlled loads (TCLs) and the manufacturing loads, which has often been ignored in previous research, resulting in conservative electricity consumption planning. This paper proposes an optimal demand management for the manufacturing industry. Firstly, the power consumption characteristics of manufacturing loads are analyzed in detail. A state task network (STN) is introduced to decouple the relationship between energy and material flow in each production link. Combining STN and production equipment parameters, a general MILP model is constructed to describe the whole production process of the manufacturing industry. Then, a mathematical model of the TCLs considering a comfortable human degree is established. Fully considering the electricity consumption behavior of equipment and TCLs, the model predictive control (MPC) method is adopted to generate the optimal scheduling plan. Finally, an actual seat production enterprise is used to verify the feasibility and effectiveness of the proposed demand management strategy.

Optimizing Mixed-Model Synchronous Assembly Lines with Bipartite Sequence-Dependent Setup Times in Advanced Manufacturing

In advanced manufacturing, optimizing mixed-model synchronous assembly lines (MMALs) is crucial for enhancing productivity and adhering to sustainability principles, particularly in terms of energy consumption and energy-efficient sequencing. This paper introduces a novel approach by categorizing sequence-dependent setup times into bipartite categories: workpiece-independent and workpiece-dependent. This strategic division streamlines assembly processes, reduces idle times, and decreases energy consumption through more efficient machine usage. A new mathematical model is proposed to minimize the intervals at which workpieces are launched on an MMAL, aiming to reduce operational downtime that typically leads to excessive energy use. Given the Non-deterministic Polynomial-time hard (NP-hard) nature of this problem, a genetic algorithm (GA) is developed to efficiently find solutions, with performance compared against the traditional branch and bound technique (B&B). This method enhances the responsiveness of MMALs to variable production demands and contributes to energy conservation by optimizing the sequence of operations to align with energy-saving objectives. Computational experiments conducted on small and large-sized problems demonstrate that the proposed GA outperforms the conventional B&B method regarding solution quality, diversity level, and computational time, leading to energy reductions and enhanced cost-effectiveness in manufacturing settings.

Evaluation of genetic algorithm in network-on-chip based architecture

An increase in the number of cores gives a significant bounce in performance than an improvement in any of the factors or hardware. Many core systems use network-on-chip (NoC) for efficient communications among the cores in the system. However, the problem with NoC-based communication is that it significantly consumes a large amount of power and energy because the number of routers increases with the increase in the number of cores in the system. Power consumed by such components leads to degradation of the performance. The placement of cores in the topology is non-deterministic polynomial-time hardness (NP-Hard) problem. The optimal placement of cores in NoC is essential as it minimizes latency and communication costs. Thus, the NP-Hard problem of placing cores is solved using genetic algorithm (GA) based quadtree topology. The proposed work shows the analysis of GA-based quadtree topology, which outperforms other topologies in most aspects. The performance evaluation of GA-based quadtree topology is based on latency, throughput, power, area, bisection bandwidth, and diameter. Comparing these parameters with other topologies shows the prominence of the quadtree topology. The evaluation is performed in the Booksim simulator, and the experimental results revealed that the proposed GA-based quad tree-based topology is efficient for NoC-based communications.

Pairwise test case generation with harmony search, one-parameter-at-at-time, seeding, and constraint mechanism integration

Pairwise testing is a method for identifying defects through combinatorial analysis. It involves testing all possible combinations of input parameters in pairs within a system, ensuring that each pair is tested at least once. The field of test case generation is highly active in the realm of combinatorial interaction testing. Research in this area is particularly encouraged, as it falls under the category of non-deterministic polynomial-time hardness. A big challenge in this field is the combinatorial explosion problem. It is about finding the best test suite that covers all possible combinations of interaction strength. In this paper, we present the task of discovering a pairwise test set as a search problem and introduce an innovative testing tool referred to as pairwise test case generation in harmony search algorithm with seeding and constraint mechanism (PHOSC). Experimental results show that PHOSC performs better compared to some existing pairwise strategies in terms of test suite size. Additionally, PHOSC provides a comprehensive framework and serves as a research platform for the generation of pairwise test sets employing the harmony search algorithm. It adopts an approach that focuses on one parameter at a time (OPAT) and incorporates seeding and constraint mechanisms at the same time, thereby enhancing the efficiency and effectiveness of the testing process.

Succinct ordering and aggregation constraints in algebraic array theories

We discuss two extensions to a recently introduced theory of arrays, which are based on considerations coming from the model theory of power structures. First, we discuss how the ordering relation on the index set can be expressed succinctly by referring to arbitrary Venn regions. Second, we show how to add general aggregators to the calculus. The result is a logic that subsumes four previous fragments discussed in the literature and is distinct from array fold logic, in that it can express summations, while its satisfiability problem remains in non-deterministic polynomial time.

A Hybrid Strategy Improved SPEA2 Algorithm for Multi-Objective Web Service Composition

A Hybrid Strategy Improved SPEA2 Algorithm for Multi-Objective Web Service Composition

MEMS Oscillators-Network-Based Ising Machine with Grouping Method.

Combinatorial optimization (CO) has a broad range of applications in various fields, including operations research, computer science, and artificial intelligence. However, many of these problems are classified as nondeterministic polynomial-time (NP)-complete or NP-hard problems, which are known for their computational complexity and cannot be solved in polynomial time on traditional digital computers. To address this challenge, continuous-time Ising machine solvers have been developed, utilizing different physical principles to map CO problems to ground state finding. However, most Ising machine prototypes operate at speeds comparable to digital hardware and rely on binarizing node states, resulting in increased system complexity and further limiting operating speed. To tackle these issues, a novel device-algorithm co-design method is proposed for fast sub-optimal solution finding with low hardware complexity. On the device side, a piezoelectric lithium niobate (LiNbO3) microelectromechanical system (MEMS) oscillator network-based Ising machine without second-harmonic injection locking (SHIL) is devised to solve Max-cut and graph coloring problems. The LiNbO3 oscillator operates at speeds greater than 9 GHz, making it one of the fastest oscillatory Ising machines. System-wise, an innovative grouping method is used that achieves a performance guarantee of 0.878 for Max-cut and 0.658 for graph coloring problems, which is comparable to Ising machines that utilize binarization.

Energy-efficient superparamagnetic Ising machine and its application to traveling salesman problems

The growth of artificial intelligence leads to a computational burden in solving non-deterministic polynomial-time (NP)-hard problems. The Ising computer, which aims to solve NP-hard problems faces challenges such as high power consumption and limited scalability. Here, we experimentally present an Ising annealing computer based on 80 superparamagnetic tunnel junctions (SMTJs) with all-to-all connections, which solves a 70-city traveling salesman problem (TSP, 4761-node Ising problem). By taking advantage of the intrinsic randomness of SMTJs, implementing global annealing scheme, and using efficient algorithm, our SMTJ-based Ising annealer outperforms other Ising schemes in terms of power consumption and energy efficiency. Additionally, our approach provides a promising way to solve complex problems with limited hardware resources. Moreover, we propose a cross-bar array architecture for scalable integration using conventional magnetic random-access memories. Our results demonstrate that the SMTJ-based Ising computer with high energy efficiency, speed, and scalability is a strong candidate for future unconventional computing schemes.

A CMOS-compatible oscillation-based VO2 Ising machine solver

Phase-encoded oscillating neural networks offer compelling advantages over metal-oxide-semiconductor-based technology for tackling complex optimization problems, with promising potential for ultralow power consumption and exceptionally rapid computational performance. In this work, we investigate the ability of these networks to solve optimization problems belonging to the nondeterministic polynomial time complexity class using nanoscale vanadium-dioxide-based oscillators integrated onto a Silicon platform. Specifically, we demonstrate how the dynamic behavior of coupled vanadium dioxide devices can effectively solve combinatorial optimization problems, including Graph Coloring, Max-cut, and Max-3SAT problems. The electrical mappings of these problems are derived from the equivalent Ising Hamiltonian formulation to design circuits with up to nine crossbar vanadium dioxide oscillators. Using sub-harmonic injection locking techniques, we binarize the solution space provided by the oscillators and demonstrate that graphs with high connection density (η > 0.4) converge more easily towards the optimal solution due to the small spectral radius of the problem’s equivalent adjacency matrix. Our findings indicate that these systems achieve stability within 25 oscillation cycles and exhibit power efficiency and potential for scaling that surpasses available commercial options and other technologies under study. These results pave the way for accelerated parallel computing enabled by large-scale networks of interconnected oscillators.

Enhancing Transportation Efficiency with Optimal Container Placement Using the Bat Algorithm

Abstract The objective of this article is to provide an in-depth exploration of the complex task of container storage at seaports, a problem characterized as one of the challenging NP (Non-Deterministic Polynomial time) problems. Seaports are faced with the dilemma of accommodating a finite number of containers due to the constrained surface area available, making the management of container storage operations a formidable task. To address this challenge, the present study leverages a meta-heuristic approach aimed at identifying an optimal storage plan for containers within a storage area. This approach is informed by insights drawn from bat swarm intelligence, commonly known as the Bat Algorithm. By integrating principles from this nature-inspired algorithm, the authors seek to develop a robust solution for optimizing container storage strategies in seaports. This approach takes into account several critical constraints, including container travel distances and considerations related to container type and departure dates.

Oscillatory Neural Network-Based Ising Machine Using 2D Memristors.

Neural networks are increasingly used to solve optimization problems in various fields, including operations research, design automation, and gene sequencing. However, these networks face challenges due to the nondeterministic polynomial time (NP)-hard issue, which results in exponentially increasing computational complexity as the problem size grows. Conventional digital hardware struggles with the von Neumann bottleneck, the slowdown of Moore's law, and the complexity arising from heterogeneous system design. Two-dimensional (2D) memristors offer a potential solution to these hardware challenges, with their in-memory computing, decent scalability, and rich dynamic behaviors. In this study, we explore the use of nonvolatile 2D memristors to emulate synapses in a discrete-time Hopfield neural network, enabling the network to solve continuous optimization problems, like finding the minimum value of a quadratic polynomial, and tackle combinatorial optimization problems like Max-Cut. Additionally, we coupled volatile memristor-based oscillators with nonvolatile memristor synapses to create an oscillatory neural network-based Ising machine, a continuous-time analog dynamic system capable of solving combinatorial optimization problems including Max-Cut and map coloring through phase synchronization. Our findings demonstrate that 2D memristors have the potential to significantly enhance the efficiency, compactness, and homogeneity of integrated Ising machines, which is useful for future advances in neural networks for optimization problems.

Efficient Dynamic Distributed Resource Slicing in 6G Multi-Access Edge Computing Networks With Online ADMM and Message Passing Graph Neural Networks

We consider the problem of resource slicing in the 6 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> generation multi-access edge computing (6G-MEC) network. The network includes many non-stationary space-air-ground-sea nodes with dynamic, unstable connections and resources, where any node can be in one of two hidden states: i) reliable – when the node generates/propagates no data errors; ii) unreliable – when the node can generate/propagate random errors. We show that solving this problem is challenging, since it represents a non-deterministic polynomial-time (NP) hard dynamic combinatorial optimization problem depending on the unknown distribution of hidden nodes' states and time-varying parameters (connections and resources of nodes) which can only be observed locally. To tackle these challenges, we develop a new deep learning (DL) model based on the message passing graph neural network (MPNN) to estimate hidden nodes' states in dynamic network environments. We then propose a novel algorithm based on the integration of MPNN-based DL and online alternating direction method of multipliers (ADMM) – extension of the well-known classical “static” ADMM to dynamic settings, where the slicing problem is solved distributedly, in real time, based on local information. We prove that our algorithm converges to a global optimum of our problem with a superior performance even in the highly-dynamic, unreliable scenarios.

Combining vector and raster data in regionalization: A unified framework for delineating spatial unit boundaries for socio-environmental systems analyses

Regionalization has emerged as a crucial research area for the past 50 years, including aggregating smaller areas into larger, contiguous, and/or homogeneous regions. Spatial optimization techniques are advantageous for solving regionalization problems, yet their nondeterministic polynomial-time (NP) hard nature leads to computational complexity and time consumption, especially with extensive datasets. Although regionalization studies play a pivotal role in defining boundaries for multi-scalar analysis and modeling complex socio-environmental systems (SES), current approaches lack integrated consideration of raster and vector data. We introduce a unified, structured framework integrating Geographic Information Systems (GIS), image segmentation, and regionalization to identify and characterize socio-environmental units accounting for various data models and types. We use a public geodatabase of the Rio Grande/Bravo basin, an SES covering diverse cultures, ecosystems, and economies, to demonstrate the functionality of our newly developed method, which effectively identifies spatial units for subsequent SES analysis and modeling. The delineation process accounts for various factors, including administrative boundaries, estimated total quantities, compactness, spatial contiguity, and similarity in socio-environmental characteristics. To make this work reproducible, replicable, and expandable, we developed the approach entirely based on open-source Python packages. Our method is easily transferable to other research using various data formats and spatial scales to delineate spatial unit boundaries effectively and efficiently.

An MPI-based parallel genetic algorithm for multiple geographical feature label placement based on the hybrid of fixed-sliding models

ABSTRACT Multiple Geographical Feature Label Placement (MGFLP) has been a fundamental problem in geographic information visualization for decades. Moreover, the nature of label positioning has proven to be an Nondeterministic polynomial-time hard (NP-hard) problem. Although advances in computer technology and robust approaches have addressed the problem of label positioning, the lengthy running time of MGFLP has not been a major focus of recent studies. Based on a hybrid of the fixed-position and sliding models, a Message Passing Interface (MPI) parallel genetic algorithm is proposed in the present study for MGFLP to label mixed types of geographical features. To evaluate the quality of label placement, a quality function is defined based on four quality metrics: label-feature conflict; label-label conflict; label association with the corresponding feature; label position priority for all three types of features. The experimental results show that the proposed algorithm outperforms the DDEGA, DDEGA-NM, and Parallel-MS in both label placement quality and computation time efficiency. Across three datasets, compared to Parallel-MS, running times decreased from 118.45 to 8.34, 45.98 to 3.51, and 20.01 to 0.43 min, with further reductions in label-label and label-feature conflicts.

Efficient Approaches to Solving Quadratic Diophantine Equations and their Time Complexity

In this paper, we present an efficient approach to solving quadratic Diophantine equations and analyze their time complexity. We propose a deterministic polynomial-time algorithm that provides an upper bound on the elementary operations required to solve such equations. We also present a non-deterministic polynomial-time algorithm for the construction of quadratic non-resiude modulo d, which is a more efficient alternative to the deterministic approach.

An enhanced multilevel secure data dissemination approximate solution for future networks.

Sensitive data, such as financial, personal, or classified governmental information, must be protected throughout its cycle. This paper studies the problem of safeguarding transmitted data based on data categorization techniques. This research aims to use a novel routine as a new meta-heuristic to enhance a novel data categorization based-traffic classification technique where private data is classified into multiple confidential levels. As a result, two packets belonging to the same confidentiality level cannot be transmitted through two routers simultaneously, ensuring a high data protection level. Such a problem is determined by a non-deterministic polynomial-time hardness (NP-hard) problem; therefore, a scheduling algorithm is applied to minimize the total transmission time over the two considered routers. To measure the proposed scheme's performance, two types of distribution, uniform and binomial distributions used to generate packets transmission time datasets. The experimental result shows that the most efficient algorithm is the Best-Random Algorithm ([Formula: see text]), recording 0.028 s with an average gap of less than 0.001 in 95.1% of cases compared to all proposed algorithms. In addition, [Formula: see text] is compared to the best-proposed algorithm in the literature which is the Modified decreasing Estimated-Transmission Time algorithm (MDETA). The results show that [Formula: see text] is the best one in 100% of cases where MDETA reaches the best results in only 48%.