Non-deterministic Polynomial-time Hard Problem Research Articles

Solving Vehicle Routing Problem using Machine Learning based clustering and TSP Cluster Redistribution

Vehicle Routing Problem (VRP) is a well-known challenging nondeterministic polynomial-time hard (NP-hard) problem in logistics domain. Time window based VRP is an extension of the problem. The basic problem is to identify optimal set of routes for a fleet of vehicles to traverse to deliver to a given set of customers in a specified time duration. The objective is to minimize the costs of traversed routes. This paper proposes a machine learning and TSP based cluster redistribution approach to solve the time window based VRP. The proposed approach consists of three phases: machine learning based cluster creation, TSP based cluster routes and cluster re-distribution. The results demonstrate the efficacy and optimality of the proposed solution. Keywords: Vehicle Routing Problem (VRP), Time window based VRP, Machine learning

Tensor Rank Regularization with Bias Compensation for Millimeter Wave Channel Estimation

This paper presents a novel method of tensor rank regularization with bias compensation for channel estimation in a hybrid millimeter wave MIMO-OFDM system. Channel estimation is challenging due to the unknown number of multipath components that determines the channel rank. In general, finding the intrinsic rank of a tensor is a non-deterministic polynomial-time (NP) hard problem. However, by leveraging the sparse characteristics of millimeter wave channels, we propose a modified CANDECOMP/PARAFAC (CP) decomposition-based method that jointly estimates the tensor rank and channel component matrices. Our approach differs from most existing works that assume the number of channel paths is known and the proposed method is able to estimate channel parameters accurately without the prior knowledge of number of multipaths. The objective of this work is to estimate the tensor rank by a novel sparsity-promoting prior that is incorporated into a standard alternating least squares (ALS) function. We introduce a weighting parameter to control the impact of the previous estimate and the tensor rank estimation bias compensation in the regularized ALS. The channel information is then extracted from the estimated component matrices. Simulation results show that the proposed scheme outperforms the baseline l1 strategy in terms of accuracy and robustness. It also shows that this method significantly improves rank estimation success at the expense of slightly more iterations.

Gamified incentive sharing mechanism of edge computing among edge service providers

Edge computing is important for the efficiency of an entire system. It makes the Internet of Things technologies more sustainable and improves users' experience and satisfaction. Generally, owing to the heterogeneity of edge servers, computing resources are unbalanced, resulting in energy wastage. Existing studies, however, have only focused on incentive mechanisms for edge collaboration; therefore, the willingness of edge servers to share resources needs further exploration. Furthermore, few studies have considered more than one edge service provider (ESP) in the incentive mechanism, which is unsustainable for selfish ESPs to optimize their computing resource allocation process. To deal with this issue, a gamified process is introduced into edge computing. Then, a system throughput maximization problem is proposed to utilize idle resources through gamification-based edge cooperation. This is proven to be a non-deterministic polynomial-time hard problem. To resolve this problem, a greedy algorithm is proposed. The experimental results demonstrate that the proposed algorithm improves the throughput by ranges of [36.9%, 87.2%] and [10.0%, 13.1%] when compared with that from no gamification and an existing greedy algorithm, respectively, when considering the influential factors. The proposed gamified mechanism helps to improve system efficiency by reducing idle computing resources and motivating ESPs to process share during production, which further enhances the smart utilization of limited global resources.

Reconfigurable Stochastic neurons for Restricted Boltzmann Machine

Neuromorphic implementation of Boltzmann Machine using a network of stochastic neurons can allow non-deterministic polynomial-time (NP) hard combinatorial optimization problems to be efficiently solved. Efficient implementation of such Boltzmann Machine with simulated annealing desires the statistical parameters of the stochastic neurons to be dynamically tunable, however, there has been limited research on stochastic semiconductor devices with controllable statistical distributions. Here, we demonstrate a fully digitized stochastic neurons based on reconfigurable stochastic model that can realize tunable stochastic dynamics in its output sampling characteristics. We emulate the Restricted Boltzmann Machine based on reconfigurable stochastic neurons and leverage the handwritten digits from the MNIST dataset to validate its recognition capabilities and investigate the accuracy of several distinct network parameters.

Agglomerative clustering enhanced GA for optimal seed selection in online social networks

Purpose The social media revolution has brought tremendous change in business strategies for marketing and promoting the products and services. Online social networks have become prime choice to promote the products because of the large size of online communities. Identification of seed nodes or identifying the users who are able to maximize the spread of information over the network is the key challenge faced by organizations. It is proved as non-deterministic polynomial-time hard problem. The purpose of this paper is to design an efficient algorithm for optimal seed selection to cover the online social network as much as possible to maximize the influence. In this approach, agglomerative clustering is used to generate the initial population of seed nodes for GA. Design/methodology/approach In this paper agglomerative clustering based approach is proposed to generate the initial population of seed nodes for GA. This approach helps in creating the initial populations of Genetic algorithm from different parts of the network. Genetic algorithm evolves this population and aids in generating the best seed nodes in the network. Findings The performance of of proposed approach is assessed with respect to existing seed selection approaches like k-medoid, k-means, general greedy, random, discounted degree and high degree. The algorithms are compared over networks data sets with varying out-degree ratio. Experiments reveal that the proposed approach is able to improve the spread of influence by 35% as compared to contemporary techniques. Originality/value This paper is original contribution. The agglomerative clustering-based GA for optimal seed selection is developed to improve the spread of influence in online social networks. This paper is of immense importance for viral marketing and the organizations willing to promote product or services online via influential personalities.

Warm-starting constraint generation for mixed-integer optimization: A Machine Learning approach

Mixed Integer Linear Programs (MILP) are well known to be NP-hard (Non-deterministic Polynomial-time hard) problems in general. Even though pure optimization-based methods, such as constraint generation, are guaranteed to provide an optimal solution if enough time is given, their use in online applications remains a great challenge due to their usual excessive time requirements. To alleviate their computational burden, some machine learning techniques (ML) have been proposed in the literature, using the information provided by previously solved MILP instances. Unfortunately, these techniques report a non-negligible percentage of infeasible or suboptimal instances.By linking mathematical optimization and machine learning, this paper proposes a novel approach that speeds up the traditional constraint generation method, preserving feasibility and optimality guarantees. In particular, we first identify offline the so-called invariant constraint set of past MILP instances. We then train (also offline) a machine learning method to learn an invariant constraint set as a function of the problem parameters of each instance. Next, we predict online an invariant constraint set of the new unseen MILP application and use it to initialize the constraint generation method. This warm-started strategy significantly reduces the number of iterations to reach optimality, and therefore, the computational burden to solve online each MILP problem is significantly reduced. Very importantly, all the feasibility and optimality theoretical guarantees of the traditional constraint generation method are inherited by our proposed methodology. The computational performance of the proposed approach is quantified through synthetic and real-life MILP applications.

Multiple-Drones-Multiple-Trucks Routing Problem for Disruption Assessment

This study proposes a multiple-drones-multiple-trucks (MDMT) routing problem to assess infrastructure in the areas of disruption epicenters using multiple drones that operate in synchronicity with multiple trucks. Incorporating the trucks as moving depots enables drones to move across disrupted areas further from their flight range. The MDMT routing problem is formulated as mixed integer linear programming (MILP). This is an NP-Hard (Non-deterministic Polynomial-time Hardness) problem, which is solved by introducing a greedy heuristic algorithm to cluster the disrupted locations and plan each drone’s schedule within each disrupted cluster and between clusters. Both MILP and the greedy heuristic algorithm are tested for small to large test problems extracted from the Minneapolis–St. Paul freeway system with a grid-like network topology. Results show that disrupted locations’ spatial distribution affects the efficient number of active drones and trucks in the system. When direct travel between two nodes takes longer than other alternative paths, increasing the number of trucks accelerates the assessment procedure. Findings also indicate that the spatial distribution of disruptions clustered by the greedy heuristic algorithm is correlated with the routing time and affects drone scheduling. If clusters are scattered, each drone is typically assigned to one cluster for damage assessments. With a dense pocket of clusters in the network, however, a drone moves back and forth between multiple clusters. The proposed framework for disruption assessment provides insights on the optimal deployment of resources to collect information following a network disruption. Practitioners will also benefit from the findings to augment resource management.

A Scalable CMOS Ising Computer Featuring Sparse and Reconfigurable Spin Interconnects for Solving Combinatorial Optimization Problems

No existing algorithms can find exact solutions to the combinatorial optimization problems (COPs) classified as non-deterministic polynomial-time (NP) hard problems. Alternatively, Ising computer based on the Ising model and annealing process has recently drawn significant attention. The Ising computers can find approximate solutions to the NP-hard COPs by observing the convergence of dynamic spin states. However, they have encountered challenges in mapping the optimization problems to the inflexible Ising computers with fixed spin interconnects. In this article, we propose a scalable CMOS Ising computer with sparse and reconfigurable spin interconnects for arbitrary mapping of spin networks with minimal overhead. Without a mapping algorithm, the proposed Ising computer provides a method for directly mapping COPs to the reconfigurable hardware. A 65-nm CMOS Ising test chip with 252 spins is fabricated and used for solving COPs, including max-cut problems.

Improved Metaheuristics-Based Clustering with Multihop Routing Protocol for Underwater Wireless Sensor Networks.

Underwater wireless sensor networks (UWSNs) comprise numerous underwater wireless sensor nodes dispersed in the marine environment, which find applicability in several areas like data collection, navigation, resource investigation, surveillance, and disaster prediction. Because of the usage of restricted battery capacity and the difficulty in replacing or charging the inbuilt batteries, energy efficiency becomes a challenging issue in the design of UWSN. Earlier studies reported that clustering and routing are considered effective ways of attaining energy efficacy in the UWSN. Clustering and routing processes can be treated as nondeterministic polynomial-time (NP) hard optimization problems, and they can be addressed by the use of metaheuristics. This study introduces an improved metaheuristics-based clustering with multihop routing protocol for underwater wireless sensor networks, named the IMCMR-UWSN technique. The major aim of the IMCMR-UWSN technique is to choose cluster heads (CHs) and optimal routes to a destination. The IMCMR-UWSN technique incorporates two major processes, namely the chaotic krill head algorithm (CKHA)-based clustering and self-adaptive glow worm swarm optimization algorithm (SA-GSO)-based multihop routing. The CKHA technique selects CHs and organizes clusters based on different parameters such as residual energy, intra-cluster distance, and inter-cluster distance. Similarly, the SA-GSO algorithm derives a fitness function involving four parameters, namely residual energy, delay, distance, and trust. Utilization of the IMCMR-UWSN technique helps to significantly boost the energy efficiency and lifetime of the UWSN. To ensure the improved performance of the IMCMR-UWSN technique, a series of simulations were carried out, and the comparative results reported the supremacy of the IMCMR-UWSN technique in terms of different measures.

A multi-stage genetic algorithm for instance selection dedicated to k nearest neighbours classification: application to robot wall following problem

K nearest neighbours algorithm is a classic, well studied yet a promising classification technique with high accuracy and best learning time compared to other classification algorithms. The goal is to overcome its slow classification time using instance selection by eliminating redundant and erroneous data. The instance selection problem has been classified as a non-deterministic polynomial time hard problem. In this article, the aim is to keep up with real time applications such as robotics with limited memory, while maintaining the fast-learning speed and high classification accuracy. We introduce a new multistage genetic algorithm for instance selection consisting of successive genetic instance selection stages with iterative search space reduction. The results witnessed an extreme reduction in classification time, reaching 99% without any significant penalty in the accuracy. It has been tested successfully using real traces of robot wall following navigation datasets and favourably compared to other approaches using various datasets.

Applications of Flower Pollination Algorithm in Electrical Power Systems: A Review

The use of metaheuristic, nature inspired algorithms for solving complex optimization problems with non-linearity and multimodality, has become a popular tool in the field of science and engineering. Presently, there has been much development of such tools, with academics creating new nature-inspired algorithms that could potentially be more efficient and effective. One such algorithm is the Flower Pollination Algorithm (FPA) developed by Xin-She Yang in 2012. This metaheuristic algorithm is modelled after the evolutionary process of flowering plants and has been useful in many fields of science and engineering, particularly in electrical power systems. With the rapid expansion of industries and population growth, engineers are faced with the arduous task of satisfying the growing electrical demand. To improve electrical power systems and reduce running costs, FPA and its variants have been implemented to determine optimal solutions to complex combinatorial optimization problems, with little computational effort, and has proven to be more effective than other popular metaheuristic algorithms, such as Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). Owing to its balanced global and local search capabilities, and better convergence characteristics, numerous studies have been conducted to utilize FPA and its variants in real-world optimization problems. Thus, this paper aims to provide a comprehensive review of FPA and its variants to successfully determine optimal results to non-deterministic polynomial-time hard problems in electrical power systems and other fields of science. To accomplish this, an in- depth description of FPA and its parameters that influence its performance are discussed, including the various modifications and hybridizations of the algorithm. In addition, an in- depth review of applications using FPA and its variants in electrical power systems and other fields of science, is provided.

Resource Allocation in Multicarrier NOMA Systems Based on Optimal Channel Gain Ratios

The application of non-orthogonal multiple access (NOMA) to multicarrier systems can improve the spectrum efficiency and enable massive connectivity in future mobile systems. Resource allocation in multicarrier NOMA systems is a non-deterministic polynomial time-hard problem requiring exhaustive search, which has prohibitive computational complexity. Instead, efficient algorithms that provide a good trade-off between system performance and implementation practicality are needed. In this paper, exact values of the optimal channel gain ratios between a pair of NOMA users are presented for the first time for quadrature amplitude modulation (QAM) schemes. Further, numerical limits are derived for the values of channel gain ratios that fulfill the system constraints. These findings are used to propose a user pairing algorithm with quasi-linear complexity. Further, a novel scheme for data rate and continuous power allocation is proposed. Through numerical simulations, it is proved that the proposed scheme yields an achievable sum-rate close to the performance of exhaustive search, and it outperforms other suboptimal resource allocation schemes.

Reconfigurable Stochastic neurons based on tin oxide/MoS2 hetero-memristors for simulated annealing and the Boltzmann machine

Neuromorphic hardware implementation of Boltzmann Machine using a network of stochastic neurons can allow non-deterministic polynomial-time (NP) hard combinatorial optimization problems to be efficiently solved. Efficient implementation of such Boltzmann Machine with simulated annealing desires the statistical parameters of the stochastic neurons to be dynamically tunable, however, there has been limited research on stochastic semiconductor devices with controllable statistical distributions. Here, we demonstrate a reconfigurable tin oxide (SnOx)/molybdenum disulfide (MoS2) heterogeneous memristive device that can realize tunable stochastic dynamics in its output sampling characteristics. The device can sample exponential-class sigmoidal distributions analogous to the Fermi-Dirac distribution of physical systems with quantitatively defined tunable “temperature” effect. A BM composed of these tunable stochastic neuron devices, which can enable simulated annealing with designed “cooling” strategies, is conducted to solve the MAX-SAT, a representative in NP-hard combinatorial optimization problems. Quantitative insights into the effect of different “cooling” strategies on improving the BM optimization process efficiency are also provided.

An Optimized Nature-Inspired Metaheuristic Algorithm for Application Mapping in 2D-NoC.

Mapping application task graphs on intellectual property (IP) cores into network-on-chip (NoC) is a non-deterministic polynomial-time hard problem. The evolution of network performance mainly depends on an effective and efficient mapping technique and the optimization of performance and cost metrics. These metrics mainly include power, reliability, area, thermal distribution and delay. A state-of-the-art mapping technique for NoC is introduced with the name of sailfish optimization algorithm (SFOA). The proposed algorithm minimizes the power dissipation of NoC via an empirical base applying a shared k-nearest neighbor clustering approach, and it gives quicker mapping over six considered standard benchmarks. The experimental results indicate that the proposed techniques outperform other existing nature-inspired metaheuristic approaches, especially in large application task graphs.

RNA Secondary Structure Prediction with Pseudoknots Using Chemical Reaction Optimization Algorithm

RNA molecules play a significant role in cell function especially including pseudoknots. In past decades, several methods have been developed to predict RNA secondary structure with pseudoknots and the most popular one uses minimum free energy. It is a nondeterministic polynomial-time hard (NP-hard) problem. We have proposed an approach based on a metaheuristic algorithm named Chemical Reaction Optimization (CRO) to solve the RNA pseudoknotted structure prediction problem. The reaction operators of CRO algorithm have been redesigned and used on the generated population to find the structure with the minimum free energy. Besides, we have developed an additional operator called Repair operator which has a great influence on our algorithm in increasing accuracy. It helps to increase the true positive base pairs while decreasing the false positive and false negative base pairs. Four energy models have been applied to calculate the energy. To evaluate the performance, we have used four datasets containing RNA pseudoknotted sequences taken from the RNA STRAND and Pseudobase++ database. We have compared the proposed approach with some existing algorithms and shown that our CRO based model is a better prediction method in terms of accuracy and speed.

Collaborative mission optimization for ship rapid search by multiple heterogeneous remote sensing satellites

<p style='text-indent:20px;'>Multiple heterogeneous satellites mission optimization is a typical kind of non-deterministic polynomial-time hard (NP-hard) problem, and some complicated scenarios bring new challenges. A novel method of missing ship rapid search using multiple grouped heterogeneous satellites is introduced in this paper. The focus is on optimization of collaborative mission optimization for various satellites including low-earth orbit (LEO) satellite and geostationary orbit (GEO) satellites. A fast coverage of the wide sea area using imaging satellites with narrow coverage range has become the most important part to tackle this problem. However, due to different imaging mechanisms of heterogeneous satellites and other constraints, it brings a great challenge to construct the optimization model. A constrained optimization problem model considering the cooperation between LEO and GEO satellites is constructed. A solution strategy based on bi-level metaheuristic algorithm is designed. The time optimal solution of the collaborative task planning between LEO and GEO satellites can be obtained based on the optimal attitude maneuver path of GEO satellites. Thus, wide-area search for missing ships can be conducted in an effective way. The effectiveness of the proposed method is verified by an example.</p>

A scatter search algorithm with a novel solution representation for flexible open shop scheduling: a multi-objective optimization

The flexible open shop scheduling problem is the combination of two classical open shop and a parallel machine scheduling problems. Due to the computational complexity of solving the open shop scheduling problem, so far, limited research has considered the assumption of flexibility in this problem. In this study, a bi-objective flexible open shop scheduling with independent setup time is considered. The considered objective functions are to minimize the maximum completion time of jobs and total tardiness. Using the first objective function, an attempt is made to balance the amount of workloads on the machines so that the completion time of the last job is minimized, while using the second one, from the customers' point of view, an attempt is made to reduce the amount of tardiness in delivery of jobs to the customers. Here, firstly, a mixed-integer nonlinear programming model is proposed. Then, to deal with the multi-objective problem, the weighted Lp-metric method is used. Since, this problem is a non-deterministic polynomial-time hard problem (NP-hard), a scatter search algorithm is developed to obtain near-optimal solutions in a reasonable time. In this regard, for the first time, a novel solution representation method is also presented. To ensure the efficiency of the proposed algorithm, the results were compared with NSGA-II using several instances. After analyzing the results using four evaluation metrics, it is observed that the scatter search algorithm performs better than the NSGA-II.

Simplified swarm optimization for bi-objection active reliability redundancy allocation problems

The reliability redundancy allocation problem (RRAP) is a well-known tool in system design, development, and management. The RRAP is always modeled as a nonlinear mixed-integer non-deterministic polynomial-time hardness (NP-hard) problem. To maximize the system reliability, the integer (component active redundancy level) and real variables (component reliability) must be determined to ensure that the cost limit and some nonlinear constraints are satisfied. In this study, a bi-objective RRAP is formulated by changing the cost constraint as a new goal, because it is necessary to balance the reliability and cost impact for the entire system in practical applications. To solve the proposed problem, a new simplified swarm optimization (SSO) with a penalty function, a real one-type solution structure, a number-based self-adaptive new update mechanism, a constrained nondominated-solution selection, and a new pBest replacement policy is developed in terms of these structures selected from full-factorial design to find the Pareto solutions efficiently and effectively. The proposed SSO outperforms several metaheuristic state-of-the-art algorithms, e.g., nondominated sorting genetic algorithm II (NSGA-II) and multi-objective particle swarm optimization (MOPSO), according to experimental results for four benchmark problems involving the bi-objective active RRAP.

Application of incremental satisfiability problem solvers for non-deterministic polynomial-time hard problems as illustrated by minimal Boolean formula synthesis problem

Subject of Research. The paper considers a method for solution of the nondeterministic polynomial hard problem (NP-hard problem) of a minimal Boolean formula synthesis from a given truth table. The solution of this problem is proposed based on its reduction to the Boolean satisfiability problem (SAT). The issues of efficient and convenient software implementation are discussed for reducing nondeterministic polynomial hard problems to the satisfiability problem. Method. For a minimal Boolean formula synthesis, the constraint programming approach was used: a SATformula was created for a given truth table, satisfiable if and only if, there exists a Boolean formula of a given size that satisfies the given truth table. The developed method accent is the application of incremental satisfiability problem solvers. Main Results. A method is proposed for synthesis of a Boolean formula, minimal with respect to the number of operators and terminals, for a given truth table. The method is based on reducing to satisfiability problem and provides the usage of incremental satisfiability problem solvers. The kotlin-satlib framework is developed with the possibility to use the Kotlin and Java languages effectively and conveniently for the software implementation of reducing various nondeterministic polynomial-time hard problems to satisfiability problem. Native interaction with satisfiability problem solvers by Java Native Interface (JNI) technology is used. The proposed method for the minimal Boolean formula synthesis is implemented in the Kotlin programming language using the developed kotlin-satlib framework. Practical Relevance. An experimental study on the example of minimal Boolean formula synthesis has shown that the usage of incremental satisfiability problem solvers for nondeterministic polynomial hard problems is reasonable, since it reduces the total solving time in comparison with the non-incremental approach application.

Community Detection under Stochastic Block Model Likelihood Optimization via Tabu Search –Fuzzy C-Mean Method for Social Network Data

Structure of network, which is known as community detection in networks, has received a great attention in diverse topics, including social sciences, biological studies, politics, etc. There are a large number of studies and practical approaches that were designed to solve the problem of finding the structure of the network. The definition of complex network model based on clustering is a non-deterministic polynomial-time hardness (NP-hard) problem. There are no ideal techniques to define the clustering. Here, we present a statistical approach based on using the likelihood function of a Stochastic Block Model (SBM). The objective is to define the general model and select the best model with high quality. Therefore, integrating the Tabu Search method with Fuzzy c-Mean (FCM) is implemented in different settings. The experiments are designed to find the best structure for different types of networks by maximizing the objective functions. SBM selections are computed by applying two types of criteria, namely Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC). The results show the ability of the proposed method to find the best community of the given networks.