Non-deterministic Polynomial Problem Research Articles

Exploring the Potential of DNA Computing for Complex Big Data Problems: A Case Study on the Traveling Car Renter Problem.

The traveling car renter problem (TCRP) is a variant of the Traveling Salesman Problem (TSP) wherein the salesman utilizes rented cars for travel. The primary objective of this problem is to identify a solution that minimizes the cumulative operating costs. Given its classification as a non-deterministic polynomial (NP) problem, traditional computers are not proficient in effectively resolving it. Conversely, DNA computing exhibits unparalleled advantages when confronted with NP-hard problems. This paper presents a DNA algorithm, based on the Adleman-Lipton model, as a proposed approach to address TCRP. The solution for TCRP can be acquired by following a series of fundamental steps, including coding, interaction, and extraction. The time computing complexity of the proposed DNA algorithm is O(n2m) for TCRP with n cities and m types of cars. By conducting simulation experiments, the solutions for certain instances of TCRP are computed and compared to those obtained by alternative algorithms. The proposed algorithm further illustrates the potential of DNA computing, as a form of parallel computing, to address more intricate large-scale problems.

Dynamic resource allocation for energy-efficient downlink NOMA systems in 5G networks

Non-Orthogonal Multiple Access (NOMA) is a promising energy-efficient technology designed to satisfy the demands of future networks by efficiently sharing radio resources. In NOMA, the same radio resource is simultaneously assigned to two users at different power levels based on the NOMA-power domain. Resource allocation in NOMA presents a non-convex challenge, characterized as a non-deterministic polynomial (NP-hard) problem. This involves user and channel assignment and power allocation, making it an extraordinarily complex task to achieve an optimal solution. In this work, Simulated Annealing (SA) is proposed as an optimization technique for resource allocation in an energy-efficient downlink NOMA system. This resource allocation scheme addresses user and channel assignment, as well as power allocation, using SA as an efficient standalone approach to maximize energy efficiency in NOMA. SA is utilized to execute the assignment of users to channels, distribute the necessary power for each channel, and determine the power ratio among users sharing the same channel. The results obtained demonstrate a significant improvement in energy efficiency, outperforming the existing numerical methods by 22 %. The proposed SA scheme not only achieves a close optimal solution but also in less computational time, offering sufficient reliability in terms of energy efficiency enhancement when compared to the existing numerical method.

Kalman filtering and sine arithmetic optimization algorithm (KSAOA) for wireless sensor network clustering

Hierarchical routing is a crucial approach for enhancing the energy efficiency of Wireless Sensor Networks (WSN). The selection of sensor clusters poses a Non-deterministic Polynomial (NP) problem, typically addressed using meta-heuristic algorithms. However, existing research has not adequately considered the observation error of node energy and the limited convergence performance of their meta-heuristic algorithms. To address these challenges, we proposes a novel approach called KSAOA (Kalman filtering and Sine Arithmetic Optimization Algorithm) for WSN clustering, aimed at prolonging the service lifetime and enhancing the network balance of WSN. The proposed model combines Kalman filtering for estimating node energy and the Sine Arithmetic Optimization Algorithm (SAOA) for clustering nodes. SAOA builds upon the Arithmetic Optimization algorithm (AOA) by introducing a sine factor to extend the exploration boundary and a levy flight strategy to improve local exploration. Additionally, greedy algorithms are employed in the data transfer phase to enhance operational efficiency. The experimental results demonstrate the effectiveness of the proposed method in tabular and graphical form. The results are analyzed through comparative experiments to show that the proposed strategy is effective in improving the balance of network lifetime and network energy consumption.

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.

Oscillator-based optimization: design, emulation, and implementation

The emergence of digital computers has profoundly reshaped our interactions with technology and the processing of information. Despite excelling in data processing and arithmetics, these computers face limitations in tackling complex nondeterministic-polynomial (NP) problems. In response, researchers have started searching for new computational paradigms that possess the natural tendency of solving these problems. Oscillator-based optimizers are one such paradigm, where the idea is to exploit the parallelism of oscillators networks in order to efficiently solve NP problems. This involves a process of mapping a given optimization task to a quadratic unconstrained binary optimization program and then mapping the resulting program onto an inter-oscillator coupling circuit encoding its coefficients. This paper presents a comprehensive approach to constructing oscillator-based optimizers, offering both the rationale for employing oscillator networks and formulas for linking optimization coefficients to inter-oscillator coupling. Here, we cover most aspects of oscillator-based optimization starting from the design of the network up to its technical implementation. Moreover, we provide a platform-independent wave digital algorithm, which allows for emulating our network’s behavior in a highly parallel fashion.Graphical

A Hybrid Many-Objective Optimization Algorithm for Job Scheduling in Cloud Computing Based on Merge-and-Split Theory

Scheduling jobs within a cloud environment is a critical area of research that necessitates meticulous analysis. It entails the challenge of optimally assigning jobs to various cloud servers, each with different capabilities, and is classified as a non-deterministic polynomial (NP) problem. Many conventional methods have been suggested to tackle this difficulty, but they often struggle to find nearly perfect solutions within a reasonable timeframe. As a result, researchers have turned to evolutionary algorithms to tackle this problem. However, relying on a single metaheuristic approach can be problematic as it may become trapped in local optima, resulting in slow convergence. Therefore, combining different metaheuristic strategies to improve the overall system enactment is essential. This paper presents a novel approach that integrates three methods to enhance exploration and exploitation, increasing search process efficiency and optimizing many-objective functions. In the initial phase, we adopt cooperative game theory with merge-and-split techniques to train computing hosts at different utilization load levels, determining the ideal utilization for each server. This approach ensures that servers operate at their highest utilization range, maximizing their profitability. In the second stage, we incorporate the mean variation of the grey wolf optimization algorithm, making significant adjustments to the encircling and hunting phases to enhance the exploitation of the search space. In the final phase, we introduce an innovative pollination operator inspired by the sunflower optimization algorithm to enrich the exploration of the search domain. By skillfully balancing exploration and exploitation, we effectively address many-objective optimization problems. To validate the performance of our proposed method, we conducted experiments using both real-world and synthesized datasets, employing CloudSim software version 5.0. The evaluation involved two sets of experiments to measure different evaluation metrics. In the first experiment, we focused on minimizing factors such as energy costs, completion time, latency, and SLA violations. The second experiment, in contrast, aimed at maximizing metrics such as service quality, bandwidth utilization, asset utilization ratio, and service provider outcomes. The results from these experiments unequivocally demonstrate the outstanding performance of our algorithm, surpassing existing state-of-the-art approaches.

THSI-RP: A two-tier hybrid swarm intelligence based node clustering and multi-hop routing protocol optimization for wireless sensor networks

Wireless sensor networks exploit clustering and routing techniques to improve energy efficiency, but these methods are generally considered as a non-deterministic polynomial (NP-hard) problem. To tackle this problem, we propose a novel two-tier hybrid swarm intelligence-based hierarchical routing protocol (THSI-RP). In the first tier, THIS-RP incorporates a hybrid swarm intelligence algorithm that combines Grey Wolf Optimization (GWO) and Marine Predators Algorithm (MPA) for the clustering algorithm. By incorporating the wolf factors from GWO into MPA as elite predators, we enhance the network search efficiency. This algorithm achieves adaptive optimal clustering with a controllable scale, considering the residual energy of nodes, relative distance between nodes, and node centrality. In the second tier, the routing algorithm uses a hybrid SI algorithm based on GWO and the graph model. First, we integrate distance and energy factors to dynamically select forwarding nodes using GWO. Then, based on the distance and energy balance principle, a weight cost function is established and combined with the minimum spanning tree method to construct a communication routing tree between the forwarding node and the base station to achieve optimized inter-cluster multi-hop routing. Simulation results demonstrate that THSI-RP outperforms several typical routing protocols in various metrics over EEUC, LPSO, LGWO, and LACO. For instance, THSI-RP achieves percentage improvement total packets by 290%, 10.9%, 8.9%, 19.9%, respectively. It also performs better in FND by 88.7%, 10.9%, 8.6%, and 16.3%, in HDN by 86.6%, 8.1%, 6.3%, and 17.1%, and in ADN by 41.7%, 8.2%, 6.4%, 18.3%.

Joint decision-making of virtual module formation and scheduling considering queuing time

Formation and scheduling are the most important decisions in the virtual modular manufacturing system; however, the global performance optimization of the system may be sacrificed via the superposition of two independent decision-making results. The joint decision of formation and scheduling is very important for system design. Complex and discrete manufacturing enterprises such as shipbuilding and aerospace often comprise multiple tasks, processes, and parallel machines, resulting in complex routes. The queuing time of parts in front of machines may account for 90% of the production cycle time. This study established a weighted allocation model of a formation-scheduling joint decision problem considering queuing time in system. To solve this nondeterministic polynomial (NP) problem, an adaptive differential evolution-simulated annealing (ADE-SA) algorithm is proposed. Compared with the standard differential evolution (DE) algorithm, the adaptive mutation factor overcomes the disadvantage that the scale of DE’s differential vector is difficult to control. The selection strategy of the SA algorithm compensates for the deficiency that DE’s greedy strategy may fall into a local optimal solution. The comparison results of four algorithms of a series of random examples demonstrate that the overall performance of ADE-SA is superior to the genetic algorithm, and average iteration, maximum completion time, and move time are 24%, 11%, and 7% lower than the average of other three algorithms, respectively. The method can generate the joint decision-making scheme with better overall performance, and effectively identify production bottlenecks through quantitative analysis of queuing time.

A deep reinforcement learning algorithm for the rectangular strip packing problem.

As a branch of the two-dimensional (2D) optimal blanking problem, rectangular strip packing is a typical non-deterministic polynomial (NP-hard) problem. The classical packing solution method relies on heuristic and metaheuristic algorithms. Usually, it needs to be designed with manual decisions to guide the solution, resulting in a small solution scale, weak generalization, and low solution efficiency. Inspired by deep learning and reinforcement learning, combined with the characteristics of rectangular piece packing, a novel algorithm based on deep reinforcement learning is proposed in this work to solve the rectangular strip packing problem. The pointer network with an encoder and decoder structure is taken as the basic network for the deep reinforcement learning algorithm. A model-free reinforcement learning algorithm is designed to train network parameters to optimize the packing sequence. This design can not only avoid designing heuristic rules separately for different problems but also use the deep networks with self-learning characteristics to solve different instances more widely. At the same time, a piece positioning algorithm based on the maximum rectangles bottom-left (Maxrects-BL) is designed to determine the placement position of pieces on the plate and calculate model rewards and packing parameters. Finally, instances are used to analyze the optimization effect of the algorithm. The experimental results show that the proposed algorithm can produce three better and five comparable results compared with some classical heuristic algorithms. In addition, the calculation time of the proposed algorithm is less than 1 second in all test instances, which shows a good generalization, solution efficiency, and practical application potential.

Microservice combination optimisation based on improved gray wolf algorithm

Microservices architecture is a new paradigm for application development. The problem of optimising the performance of microservice architectures from a non-functional perspective is a typical Nondeterministic Polynomial (NP) problem. Therefore, aiming to quantify the non-functional requirements of computing microservice systems, while solving the problem of latency in computing the best combination of services with the maximum QoS objective function value, this paper proposes a microservice combination approach based on the QoS model and a CGWO algorithm for optimisation computation for this model. The experimental results verify that the error rate of the method is only 0.528% on the non-functional combination optimisation problem, and the computational efficiency of the algorithm increases by 97.29% when the complexity of the problem search space increases, while CGWO improves 65.97% and 81.25% respectively in the accuracy of optimisation compared to the prototype of the algorithm (GWO), and has a stable optimisation performance, aspect. It proves that the research in this paper has a high advantage in automatically searching for the best QoS for the microservice combination problem.

Diversity-driven automated web API recommendation based on implicit requirements

With the rapid growth of the web API sharing community, Mashup development has become a popular way for software developers to quickly create Mashup applications. Mashup development allows developers to quickly implement the functionality they want by combining a chosen set of web APIs, which greatly improves development efficiency. However, the existence of numerous web API candidates make it difficult to select the appropriate API quickly. Most existing automated web API recommendation approaches focus on the developer’s description of requirements but typically overestimate the developer’s ability to fully describe their application’s requirements, thus ignoring their implicit and diversified functional requirements. In this paper, we propose a novel automated approach called DI-RAR to retrieve and recommend web API groups for Mashup creation. Specifically, we formulate an automated web API recommendation task as a nondeterministic polynomial problem. First, a self-attention model assigns weights to query to distinguish the core and non-core requirements. then Dynamic planning retrieval generates steiner trees to retrieve API groups and uncovers strongly related implicit requirements to enrich the mashup’s functions. Finally we apply simhash technique to filter similar results and finally provide diverse API groups. experiments based on a real-world dataset are performed to demonstrate the feasibility and efficiency of DI-RAR.

Multi-objective optimization of simultaneous buffer and service rate allocation in manufacturing systems based on a data-driven hybrid approach

The challenge presented by simultaneous buffer and service rate allocation in manufacturing systems represents a difficult non-deterministic polynomial problem. Previous studies solved this problem by iteratively utilizing a generative method and an evaluative method. However, it typically takes a long computation time for the evaluative method to achieve high evaluation accuracy, while the satisfactory solution quality realized by the generative method requires a certain number of iterations. In this study, a data-driven hybrid approach is developed by integrating a tabu search–non-dominated sorting genetic algorithm II with a whale optimization algorithm–gradient boosting regression tree to maximize the throughput and minimize the average buffer level of a manufacturing system subject to a total buffer capacity and total service rate. The former algorithm effectively searches for candidate simultaneous allocation solutions by integrating global and local search strategies. The prediction models built by the latter algorithm efficiently evaluate the candidate solutions. Numerical examples demonstrate the efficacy of the proposed approach. The proposed approach improves the solution efficiency of simultaneous allocation, contributing to dynamic production resource reconfiguration of manufacturing systems.

A Self-Adjusting Search Domain Method-Based Genetic Algorithm for Solving Flexible Job Shop Scheduling Problem.

As a nondeterministic polynomial (NP) problem, the flexible job shop scheduling problem (FJSP) is a difficult problem to be solved in terms of finding an acceptable solution. In last decades, genetic algorithm (GA) displays very promising performance in the field. In this article, a hybrid algorithm combining global and local search with reinitialization (GLRe)-based GA is proposed to minimize makespan for FJSP. The solution of FJSP is conveniently represented by a double-layer chromosome representation method, which is convenient for subsequent genetic operations, that is, sorting of operations and selection of machines. Two strategies of choosing the job with the most remaining operations (CRO) and 6-dimensional variable determined search position (6D-VSP) are proposed as two components for GA, which are applied to generate a population with superior quality and reduce the global search space during the initialization stage. At the same time, in order to prevent the loss of diversity during evolution, a reinitialization strategy is introduced in the later stage of evolution to adaptively adjust the search domain of the problem. Finally, two sets of benchmark data are tested. The experimental results demonstrate the accuracy and effectiveness of the GLRe proposed in this article for solving FJSP.

Energy efficient MIMO–NOMA aided IoT network in B5G communications

To accelerate future intelligent wireless systems , we designed an energy-efficient Massive multiple-input-multiple-output (MIMO)- non-orthogonal multiple access (NOMA) aided internet of things (IoT) network in this paper to support the massive number of distributed users and IoT devices with seamless data transfer and maintain connectivity between them. Massive MIMO has been identified as a suitable technology to implement the energy efficient IoT network in beyond 5G (B5G) communications due to its distinct characteristics with large number of antennas. However, to provide fast data transfer and maintain hyper connectivity between the IoT devices in B5G communications will bring the challenge of energy deficiency. Hence, we considered a massive MIMO–NOMA aided IoT network considering imperfect channel state information and practical power consumption at the transmitter. The far users of the base stations are selected to investigate the power consumption and quality of service. Then, calculate the power consumption which is non-convex function and non-deterministic polynomial problem. To solve the above problem, fractional programming properties are applied which converted polynomial problem into the difference of convex function . And then we employed the successive convex approximation technique to represent the non-convex to convex function. Effective iterative based branch and the reduced bound process are utilized to solve the problem. Numerical results observe that our implemented approach surpasses previous standard algorithms on the basis of convergence, energy-efficiency and user fairness.

An Urban Bus Network Generation Algorithm Based on Particle Swarm Optimization and Force Field Properties

Due to continuous urban sprawl, large-scale bus network design has become a major challenge in urban transport planning. The continuous increase in urban population and scale makes the factors considered in the urban route network design increasingly complex. Contemporary public transportation network design problems are based more on efficiency goals such as the accessibility and comfort of the transportation network, which increases the difficulty of analyzing the problem. Bus network design is not only an NP-hard (nondeterministic polynomial) problem but also a multivariable and multiobjective problem. This paper focuses on the bivariate and multiobjective bus network design problem of route generation and station selection. This paper proposes an algorithm called the Pseudo Force Field. By combining the idea of Particle Swarm Optimization (PSO) and the properties of the force field, a feasible route generation scheme is provided for the design of the bus network. The algorithm does not need to determine the end station and has a high degree of completion of the demand. This solves the problem of the selection of terminal stations in large-scale road network design. On this basis, the article combines Genetic Algorithm (GA) and Pareto frontier to provide a new route optimization algorithm and proves the effectiveness of the algorithm. The model has achieved theoretical results in the design of the bus route network in the megacity of Shenzhen, China.

Machine Learning Guides the Solution of Blocks Relocation Problem in Container Terminals

The blocks relocation problem (BRP) is a well known and important combinatorial optimization problem, in which the initial storage state and retrieval priority of containers are known, and the containers should be picked up in the retrieval order with the goal of minimizing container relocations. This paper studied how machine-learning techniques guide the solution of this Non-deterministic Polynomial problem(NP-hard problem) NP-hard problem. Through our self-developed data generator, we generated initial state stacking matrices and extracted 22 influencing factors for container relocation operations. The supervised learning method and attribution technique were used to verify the relationship between significant container relocated influence features and the number of container relocations using the unrestricted BRP and restricted BRP models. We characterize the potential patterns in the data based on 22 container relocated influence features using four supervised learning models: random forest (RF), extra trees (ET), support vector machine (SVM), and logistic regression (LR). The experimental results demonstrate that RF has a classification accuracy rate of up to 94% on the restricted BRP model. The attribution technique identifies the most sensitive features to the number of container relocations. We organically integrate machine learning into the BRP problem and propose an interactive iterative framework that may provide a novel method for studying the BRP problem.

Attribute Reduction Algorithm Based on Discrete Particle Swarm Optimization and Variable Precision Rough Set

Attribute reduction is proved to be a non-deterministic polynomial problem (NP). Minimal attribute reduction is the main research content in rough set theory. We find that in the traditional rough set attribute reduction algorithm, the rough set attribute reduction based on discrete particle swarm optimization (DPSO) performs well. However, the fitness function of this method has some limitations. When the minimum attribute reduction result is the conditional attribute set itself, the correct result cannot be obtained. For enhancing the accuracy and efficiency of attribute reduction, we propose an attribute reduction algorithm based on DPSO and variable precision rough set (VPRS). The proposed algorithm uses VPRS to process data more accurately. The new fitness function is constructed, and the attribute dependence is used as the function judgment basis. It can be adjusted automatically as the discrete binary particle swarm evolves, ensuring the convergence speed and evolution direction. Experimental results show that compared with traditional method, the proposed algorithm has stronger effectiveness and higher application value.

Integration of Risk-Based Self-Maintenance Activities: Study Case for Crane Distributed System

In today's practice, the coordination of maintenance activities is steadily improved with the use of models. Among them, simulation-based models are attractive because they offer flexibility and can absorb system complexity with ease. Although we avoid state enumeration by using simulation-based models, they can sometimes become computationally demanding. To obtain efficient results, simulation-based models are often implemented on a digital platform. However, there is always concern about whether the implemented model performs adequately and delivers the expected results. In this paper, to address this concern, we propose to perform model calibration. The subject of the paper is calibration through comparison of a risk-based self-maintenance layer, which was created to be executed online without human intervention. The layer is intended for self-assessment of a critical system of overhead cranes operating in hazardous conditions. The case study of the paper is a critical system of overhead cranes operating at a continuous rate, which are part of a hot rolling mill system in a steel plant. The online self-maintenance layer is a nonlinear stochastic optimization model with bounded constraints that aims to evaluate a system-level risk indicator. The estimation of the risk indicator is based on Monte Carlo simulations. Given the features of the model, to evaluate the accuracy and robustness of the layer, only free derivative algorithms, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Nelder-Mead Modified (NMm) in our case, are used in the comparison. The presented work shows in practice common challenges when facing complex nondeterministic polynomial (NP) problems with stochastic functions.

Implementation of bi-directional searching Chemical Reaction Optimization (CRO) algorithm towards achieving cutting tool indexing time minimization in Automatic Tool Changer(ATC)

Determining the optimum cutting tool positions in a tool magazine is a challenging task which involves a huge searching space. Reduction of manufacturing time even by nanoseconds will highly be beneficial for all process industries. The prime focus of this research work is to reduce the total turret or tool indexing time in Automatic Tool Changer (ATC) which in turn curtails the idle non-cutting time of the bi-directional turret or tool magazine in a CNC machine. This variant of optimization problem falls under the category of non-deterministic hard polynomial (NP-hard) problem. Chemical Reaction Optimization (CRO) algorithm is proposed to determine the near optimal/global optimal solution with lesser computational cost. Five benchmark case studies are considered in this work to assess the robustness of the proposed algorithm. From the results, it is evident that the proposed algorithm yields solutions which matches or exceeds with the solution quality.

Meerkat Clan Algorithm for Solving N-Queen Problems

The swarm intelligence and evolutionary methods are commonly utilized by researchers in solving the difficult combinatorial and Non-Deterministic Polynomial (NP) problems. The N-Queen problem can be defined as a combinatorial problem that became intractable for the large ‘n’ values and, thereby, it is placed in the NP class of problems. In the present study, a solution is suggested for the N-Queen problem, on the basis of the Meerkat Clan Algorithm (MCA). The problem of n-Queen can be mainly defined as one of the generalized 8-Queen problem forms, for which the aim is placing 8 queens in a way that none of the queens has the ability of killing the others with the use of the standard moves of the chess queen. The Meerkat Clan environment is a directed graph, called the search space, produced for the efficient search of valid n-queens’ placement, in a way that they do not cause harm to one another. This paper also presents the development of an intelligent heuristic function which is helpful to find the solution with high speed and effectiveness. This study includes a detailed discussion of the problem background, problem complexity, Meerkat Clan Algorithm, and comparisons of the problem solution with the Practical Swarm Optimization (PSO) and Genetic Algorithm (GA. It is an entirely review-based work which implemented the suggested designs and architectures of the methods and a fair amount of experimental results.