NP-hard Problem Research Articles

A novel evolutionary strategy optimization algorithm for reliability redundancy allocation problem with heterogeneous components

The reliability-redundancy allocation problem (RRAP) is an optimization problem that maximizes system reliability under some constraints. In most studies on the RRAP, either active redundant components or cold standby components are used in a subsystem. This paper presents a new model for the RRAP of a system with a mixed redundancy strategy, in which all components can be heterogeneous. This formulation leads to a more precise solution for the problem; however, RRAP is an np-hard problem, and the new mixed heterogeneous model will be more complicated to solve. After formulating the issue, a novel design of an evolutionary strategy optimization algorithm is proposed to solve that. The problem consists of discrete and continuous variables, and different mutation strategies are designed for each. The new formulation of the problem and the new method for solving it lead to better results than those reported in other recent papers. We implement the new suggested heterogeneous model with the PSO and SPSO algorithms to better compare the proposed algorithm. Results show improvement in both system reliability and fitness evaluation count.

Implementation of a Cuckoo Search intelligent simulation system for node placement problem in Wireless Mesh Networks: Performance evaluation for tuning hyperparameters [formula omitted] and [formula omitted]

In recent years, Internet of Things (IoT) is the hottest topics in the research and implementation of wireless networks. Most of the research of IoT-based applications is related with the data collecting and processing using sensors and actuators. As the network environment for connecting IoT devices are considered WLAN or Bluetooth. The Wireless Mesh Networks (WMNs) are the most suitable networks for the Internet of Things (IoT) due to their numerous benefits. However, they have several issues related to wireless communications. One solution is the optimization of position and location of mesh routers. But finding the best location of mesh routers is an NP-hard problem. To deal with this issue, we propose and implement an intelligent simulation system based on the Cuckoo Search (CS) algorithm called WMN-CS. In the implemented system, the hyperparameters should be tuned to find better solutions. This paper evaluates the WMN-CS performance for various combination of hyperparameters by tuning host bird discovery rate (pa) and scale parameter (γ). The simulation results show that a better performance is achieved when the scale parameter (γ) is between 0.07 and 0.09 and the host bird recognition rate (pa) is between 0.900 and 0.925.

From Single-Objective to Bi-Objective Maximum Satisfiability Solving

The declarative approach is key to efficiently finding optimal solutions to various types of NP-hard real-world combinatorial optimization problems. Most work on practical declarative solvers—ranging from classical integer programming to finite-domain constraint optimization and maximum satisfiability (MaxSAT)—has focused on optimization under a single objective; fewer advances have been made towards efficient declarative techniques for multi-objective optimization problems. Motivated by significant recent advances in practical solvers for MaxSAT, in this work we develop BiOptSat, an exact declarative approach for finding Pareto-optimal solutions to bi-objective optimization problems, with propositional logic as the underlying constraint language. BiOptSat can be viewed as an instantiation of the lexicographic method. The approach makes use of a single Boolean satisfiability solver that is incrementally employed throughout the entire search procedure, allowing for finding a single Pareto-optimal solution, finding one representative solution for each non-dominated point, and enumerating all Pareto-optimal solutions. We detail several algorithmic instantiations of BiOptSat, each building on recent algorithms proposed for single-objective MaxSAT. We empirically evaluate the instantiations compared to recently-proposed alternative approaches to multi-objective MaxSAT solving on several real-world domains from the literature, showing the practical benefits of our approach.

Research and application of rough set attribute reduction algorithm based on genetic algorithm in pipeline network

Abstract Explosion accidents often occur in urban underground pipeline network systems, which has caused safety issues in public life and industrial production. GIS technology can visually manage pipeline equipment and solve the problem of valve closure analysis in the event of current accidents, avoiding the escalation of the situation, but it cannot make predictions. Attribute reduction is one of the core contents of rough set theory and is an NP-hard problem. This article proposes a custom attribute reduction algorithm based on an algorithm and uses the algorithm in the historical burst pipeline dataset of the water supply pipeline industry. The results have shown that this method combined with a decision tree can make predictions before water pipe leakage. The algorithm provides the best result of attribute reduction for decision tree methods, which will improve the speed and accuracy of decision-making.

Parameter-Insensitive Min Cut Clustering With Flexible Size Constrains.

Clustering is a fundamental topic in machine learning and various methods are proposed, in which K-Means (KM) and min cut clustering are typical ones. However, they may produce empty or skewed clustering results, which are not as expected. In KM, the constrained clustering methods have been fully studied while in min cut clustering, it still needs to be developed. In this paper, we propose a parameter-insensitive min cut clustering with flexible size constraints. Specifically, we add lower limitations on the number of samples for each cluster, which can perfectly avoid the trivial solution in min cut clustering. As far as we are concerned, this is the first attempt of directly incorporating size constraints into min cut. However, it is a NP-hard problem and difficult to solve. Thus, the upper limits is also added in but it is still difficult to solve. Therefore, an additional variable that is equivalent to label matrix is introduced in and the augmented Lagrangian multiplier (ALM) is used to decouple the constraints. In the experiments, we find that the our algorithm is less sensitive to lower bound and is practical in image segmentation. A large number of experiments demonstrate the effectiveness of our proposed algorithm.

Pre-filters design for weighted sum rate maximization in multiuser time reversal downlink systems

In high-speed multiuser Time Reversal (TR) downlink systems, the transmission rate is degraded due to the presence of severe inter-user and inter-symbol interference. Moreover, maximizing the weighted sum rate in such systems is a critical objective, since the weighting factors represent the priority of different users in different applications. However, it faces significant challenges as it is an NP-hard and non-convex problem. In order to suppress these interferences and maximize the weighted sum rate, in this paper we present a novel approach for the joint design of the pre-filters. The proposed method applies successive convex approximation to transform the original problem into a Second-Order Cone Programming (SOCP) problem. Then, a low-complexity iterative algorithm is provided to effectively solve the resulting SOCP problem. According to the simulation results, the proposed method reaches a local optimum within a few iterations and demonstrates superior performance in terms of weighted sum rate compared to the current algorithm.

A better LP rounding for feedback arc set on tournaments

We present a randomized algorithm to approximate the feedback arc set problem on weighted tournaments, a classic well-studied NP-hard problem. Our algorithm is based on rounding its standard linear programming relaxation. It improves the previously best-known LP rounding algorithm by achieving an approximation factor of 2.127 (best known was 2.5). As a result, we have found a better upper bound for the integrality gap of the corresponding LP.

Criteria Convolutions When Combining the Solutions of the Multicriteria Axial Assignment Problem

This paper is devoted to a classical NP-hard problem, known as the three-index axial assignment problem. Within the corresponding framework, the problem of combining feasible solutions is posed as an assignment problem on the set of solutions containing only the components of selected feasible solutions. The issues of combining solutions for the multicriteria problem with different criteria convolutions are studied. In the general case, the combination problem turns out to be NP-hard. Polynomial solvability conditions are obtained for the combination problem.

Distributed service function chaining in NFV-enabled networks: A game-theoretic learning approach

In network function virtualization (NFV), Service Function Chaining (SFC) provides an ordered sequence of virtual network functions (VNFs) and subsequent steering of traffic flows through them to cater to end-to-end services. This paper addresses the NP-hard problem of minimum cost SFC deployment to support customer services that access the carrier network’s NFV infrastructure (NFVI) through some edge routers. To determine the mappings of VNFs to physical servers, a challenging aspect would be the inter-server latencies that may fluctuate over time because of the sharing nature of cloud data centers. To construct the SFC, we come up with three different formulations, each corresponding to a different informational assumption about the link latencies: First, a centralized integer linear programming (ILP) formulation is given under the assumption of the non-causal availability of exact and instantaneous inter-server latencies. The solution to this ILP can serve as a lower bound to benchmark more scalable and realistic schemes. Next, we give a distributed game-theoretic formulation (with service broker agents as players) which only requires the statistical knowledge of link latency fluctuations. The game provably admits a pure Nash equilibrium (NE) and can be solved iteratively through the well-known best response dynamics (BRD) algorithm. Our main novelty lies in the third formulation in which each service broker has neither instantaneous nor statistical knowledge of the latencies. Instead, it relies on a game-theoretic learning algorithm to compose its VNF chain only based on its own history of adopted decisions and experienced delays on each logical link. We prove that the proposed learning algorithm asymptotically converges to NE and evaluate its performance through simulations in terms of convergence and the impact of network parameters.

Multi-objective sustainable flexible job shop scheduling problem: Balancing economic, ecological, and social criteria

Industry 5.0 makes it imperative to reevaluate the manner of using resources in manufacturing systems to ensure sustainability. In this context, scheduling problems are encountering new environmental and human-related challenges, and the concept of sustainable scheduling has gained importance, aiming to balance economic, environmental, and human factors. In this paper, we propose two multi-objective mathematical models to simultaneously address these three factors as objective functions. In the first model, we consider the operator safety while using the Occupational Repetitive Action (OCRA) index to assess ergonomic risks related to task execution. The second model includes workers’ preferences in terms of machines, shifts and task variety. The objective is to improve the general well-being of workers by proposing a schedule that respects as much as possible their preferences. Both models integrate the travel time of workers and products between machines. To solve these NP-hard scheduling problems, we use the Non-dominated Sorting Genetic Algorithms II and III (NSGA-II and NSGA-III), enhanced with a Q-learning strategy for parameter selection and a variable neighborhood search based on reinforcement learning. The obtained results provide a comprehensive analysis of the interactions between these criteria, demonstrating the capability of such approach to achieve a favorable balance between multiple objectives while addressing the new challenges of production scheduling in Industry 5.0 context.

Rolling optimal scheduling for urban parcel crowdsourced delivery with new order insertion

The rapid development of mobile information technology has introduced numerous new solutions for delivery companies to enhance profits. One such solution employed by some companies is crowdsourced delivery. In this paper, we focus on rolling optimal scheduling for urban parcel crowdsourced delivery by utilizing private cars that will be in passing with the incorporation of new order insertion. The bonus incentive strategy is introduced to enhance the delivery probability of private car drivers. A static model and a rolling optimization model to maximize profits and the number of parcels delivered by private cars are established. To address the NP-hard problem, a hybrid genetic algorithm and insertion algorithm are designed. Numerical experiments are carried out to verify the proposed method in different scenarios, including the scattered network, clustered network, Dalian network, and Foursquare network. The computational results demonstrate that the method enhances the matching ratio and increases profits. Utilizing private cars that will be in passing for urban parcel delivery reduces the need for dedicated vehicles, mitigating traffic growth and alleviating traffic congestion. Increasing the private car-parcel ratio improves profits and the matching ratio while reducing traffic growth. Raising the incentive coefficient for bonuses increases the matching ratio and detour distance, but profits first increase and then decrease, and delivery distance by dedicated vehicles decreases. Our research findings offer a more rational basis for green urban parcel delivery decision-making by companies.

A universal framework for entanglement detection under group symmetry

One of the fundamental questions in quantum information theory is determining entanglement of quantum states, which is generally an NP-hard problem. In this paper, we prove that all PPT (π―A⊗πB) -invariant quantum states are separable if and only if all extremal unital positive (πB,πA) -covariant maps are decomposable where πA,πB are unitary representations of a compact group and π A is irreducible. Moreover, an extremal unital positive (πB,πA) -covariant map L is decomposable if and only if L is completely positive or completely copositive. We then apply these results to prove that all PPT quantum channels of the form Φ(ρ)=aTr(ρ)dIdd+bρ+cρT+(1−a−b−c)diag(ρ) are entanglement-breaking, and that there is no A-BC PPT-entangled (U⊗U―⊗U) -invariant tripartite quantum state. The former strengthens some conclusions in (Vollbrecht and Werner 2001 Phys. Rev. A 64 062307; Kopszak et al 2020 J. Phys. A: Math. Theor. 53 395306), and the latter resolves some open questions raised in (Collins et al 2018 Linear Algebra Appl. 555 398–411).

VESBELT: An energy-efficient and low-latency aware task offloading in Maritime Internet-of-Things networks using ensemble neural networks

Due to increasing maritime activities, the number of Maritime Internet-of-things (MIoT) devices requiring real-time marine data processing is growing exponentially. To offload maritime tasks and address the limited computational capabilities of heterogeneous MIoT devices, edge and cloud computing networks are employed. However, these networks introduce several challenges, including increased energy consumption and service latency within the complex marine network environment. Current state-of-the-art solutions address these issues by focusing exclusively on real-time offloading data, neglecting the relationship with past offloading tasks. In this work, we develop an optimization framework, named VESBELT, for offloading tasks from Vessel users to nearby Edge Servers or the cloud server, aiming to reduce Energy consumption and service Latency Trade-off through a multi-objective linear programming problem. However, finding optimal solutions from this formulation is considered an NP-hard problem. To address this, we introduce VESBELT-ECNN, VESBELT-EANN, and VESBELT-ELSTM systems that leverage ensemble convolutional, artificial neural networks and Long-short-term memory, respectively, to achieve solutions in polynomial time. The developed ensemble models integrate multiple combinations of deep learning models and exploit the pre-trained models to provide real-time solutions with better prediction accuracy. The experimental findings, obtained using Python programming version 3.10.2, indicate that the proposed VESBELT-ECNN, VESBELT-EANN, and VESBELT-ELSTM systems outperform existing approaches in terms of user Quality of Experience (QoE) in the timeliness domain and energy savings.

Dynamic Cluster Head Selection in WSN

A Wireless Sensor Network (WSN) comprises an ad-hoc network of nodes laden with sensors that are used to monitor a region mostly in the outdoors and often not easily accessible. Despite exceptions, several deployments of WSN continue to grapple with the limitation of finite energy derived through batteries. Thus, it is imperative that the energy of a WSN be conserved and its life prolonged. An important direction of work to this end is towards the transmission of data between nodes in a manner that minimum energy is expended. One approach to doing this is cluster-based routing, wherein nodes in a WSN are organised into clusters, and transmission of data from the node is through a representative node called a cluster-head. Forming optimal clusters and choosing an optimal cluster-head is an NP-Hard problem. Significant work is done towards devising mechanisms to form clusters and choosing cluster heads to reduce the transmission overhead to a minimum. In this article, an approach is proposed to create clusters and identify cluster heads that are near optimal. The approach involves two-stage clustering, with the clustering algorithm for each stage chosen through an exhaustive search. Furthermore, unlike existing approaches that choose a cluster-head on the basis of the residual energy of nodes, the proposed approach utilises three factors in addition to the residual energy, namely the distance of a node from the cluster centroid, the distance of a node from the final destination (base-station), and the connectivity of the node. The approach is shown to be effective and economical through extensive validation via simulations and through a real-world prototypical implementation.

Generating information-dense promoter sequences with optimal string packing.

Dense arrangements of binding sites within nucleotide sequences can collectively influence downstream transcription rates or initiate biomolecular interactions. For example, natural promoter regions can harbor many overlapping transcription factor binding sites that influence the rate of transcription initiation. Despite the prevalence of overlapping binding sites in nature, rapid design of nucleotide sequences with many overlapping sites remains a challenge. Here, we show that this is an NP-hard problem, coined here as the nucleotide String Packing Problem (SPP). We then introduce a computational technique that efficiently assembles sets of DNA-protein binding sites into dense, contiguous stretches of double-stranded DNA. For the efficient design of nucleotide sequences spanning hundreds of base pairs, we reduce the SPP to an Orienteering Problem with integer distances, and then leverage modern integer linear programming solvers. Our method optimally packs sets of 20-100 binding sites into dense nucleotide arrays of 50-300 base pairs in 0.05-10 seconds. Unlike approximation algorithms or meta-heuristics, our approach finds provably optimal solutions. We demonstrate how our method can generate large sets of diverse sequences suitable for library generation, where the frequency of binding site usage across the returned sequences can be controlled by modulating the objective function. As an example, we then show how adding additional constraints, like the inclusion of sequence elements with fixed positions, allows for the design of bacterial promoters. The nucleotide string packing approach we present can accelerate the design of sequences with complex DNA-protein interactions. When used in combination with synthesis and high-throughput screening, this design strategy could help interrogate how complex binding site arrangements impact either gene expression or biomolecular mechanisms in varied cellular contexts.

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.

GSHFA-HCP: a novel intelligent high-performance clustering protocol for agricultural IoT in fragrant pear production monitoring

The agriculture Internet of Things (IoT) has been widely applied in assisting pear farmers with pest and disease prediction, as well as precise crop management, by providing real-time monitoring and alerting capabilities. To enhance the effectiveness of agriculture IoT monitoring applications, clustering protocols are utilized in the data transmission of agricultural wireless sensor networks (AWSNs). However, the selection of cluster heads is a NP-hard problem, which cannot be solved effectively by conventional algorithms. Based on this, This paper proposes a novel AWSNs clustering model that comprehensively considers multiple factors, including node energy, node degree, average distance and delay. Furthermore, a novel high-performance cluster protocol based on Gaussian mutation and sine cosine firefly algorithm (GSHFA-HCP) is proposed to meet the practical requirements of different scenarios. The innovative Gaussian mutation strategy and sine–cosine hybrid strategy are introduced to optimize the clustering scheme effectively. Additionally, an efficient inter-cluster data transmission mechanism is designed based on distance between nodes, residual energy, and load. The experimental results show that compared with other four popular schemes, the proposed GSHFA-HCP protocol has significant performance improvement in reducing network energy consumption, extending network life and reducing transmission delay. In comparison with other protocols, GSHFA-HCP achieves optimization rates of 63.69%, 17.2%, 19.56%, and 35.78% for network lifespan, throughput, transmission delay, and packet loss rate, respectively.

A multi-ship power sharing strategy: Using two-stage robust optimization and Shapley value approach

In recent years, the use of cold ironing (CI) has effectively reduced the carbon emissions of ships in port areas. However, due to the limitation of port CI quantity and power supply capacity, the power demand of some ships cannot be met. To solve this problem, this paper proposes a multi-ship power sharing strategy based on two-stage robust optimization and improved Shapley value method. Firstly, considering the uncertainty of ship photovoltaic power generation, a multi-ship power sharing model based on two-stage robust optimization is established. This model is a three-level optimization model with mixed integer variables, which is a NP-hard problem. In this paper, the nested column-and-constraint generation algorithm combined with duality theory and big-M method is used to obtain the optimal scheduling strategy of ship shared power, CI power and load demand response power. Secondly, an improved Shapley value method considering berth and remaining berthing time is proposed to realize the cost allocation in the process of ship power sharing. Finally, the effectiveness of the multi-ship power sharing strategy in reducing berthing costs and carbon emissions is verified by simulation. This method is expected to provide a new idea for the development of green ports.

A new heuristic for the continuous fixed-radius disc cover problem

The continuous fixed-radius disc cover (CFDC) problem is a location model to cover the given demand points by finding the minimum number of fixed-radius discs in the plane. It is an NP-hard problem, and only a few approximate algorithms have been proposed over the past three decades. In the article, a new heuristic called dynamic reduction (DR) is introduced. The heuristic works by initiating an upper bound on the number of discs, and then reducing the number by removing redundant discs during updates to the disc centres. Experimental results, using different radius settings on some datasets of a travelling salesman problem library (TSP-Lib), show that the proposed heuristic greatly outperforms the recent approximation algorithm in accuracy. Notably, an enhancement of the heuristic is also provided.

An OGSM-based multi-objective optimization model for partner selection in fresh produce supply chain considering carbon emissions

Incorporating partner selection with environmental commitment is recognized as a crucial aspect of green development in fresh produce supply chains. This paper presents a multi-objective programming (MOP) model for partner selection considering carbon emissions based on the ‘Objectives, Goals, Strategies, Measures’ (OGSM) framework. The OGSM serves as a strategic scheme to identify the long-term green development vision of a supply chain, ensuring that the activities of supply chain partners are aligned with common goals. Driven by the OGSM design, the MOP model is formulated with three conflicting objective functions to maximize profit, minimize carbon emission, and maximize the quality of fresh produce. The model helps decision-makers address decisions on partner selection with determined logistics volumes, transportation modes and packaging types under carbon emission constraints. To tackle the NP-hard problem, we develop an effective hybrid meta-heuristic algorithm called ɛ-NSGA, which complements the advantages of the ɛ-constraint method and NSGA-II (Non-dominated Sorting Genetic Algorithm-II). The experimental results based on parameter calibration of the Taguchi method and the Kruskal–Wallis test demonstrate that the proposed ɛ-NSGA outperforms other four heuristic algorithms in terms of the performance indices of GD (Generational Distance), spacing, IGD (Inverted Generational Distance), and HV (Hyper Volume). The implementation of the OGSM-MOP together with ɛ-NSGA in a real-world apple supply chain illustrates the effectiveness and practicality of the model. Finally, managerial insights into the utilization of the model are discussed and suggestions for decision-making to fulfill corporate environmental obligations are provided.