Multiple Optimal Paths Research Articles

Combining reinforcement learning algorithm and genetic algorithm to solve the traveling salesman problem

AbstractWith the growing recognition of the unique advantages of reinforcement learning and genetic algorithms in addressing combinatorial optimization problems, this study aims to integrate these two methods to collectively tackle the classic combinatorial optimization challenge of the travelling salesman problem (TSP). The TSP stands as a quintessential combinatorial optimization challenge, tasked with determining the shortest path among designated cities. This paper introduces an innovative approach by amalgamating reinforcement learning's path selection prowess with genetic algorithms' global search strategy, aiming to uncover superior solutions in TSP. Specifically, the experiment employs a dual Q‐learning algorithm within reinforcement learning to identify multiple optimal paths, serving as progenitors for the genetic algorithm to further enhance performance. The paper meticulously outlines the problem modelling process, elucidating TSP instance definitions, descriptions, and precise objective function definitions. Experimental findings underscore the substantial enhancements achievable in TSP optimization through this comprehensive approach, offering a fresh perspective and methodology for tackling combinatorial optimization challenges.

Polytomous Effectiveness Indicators in Complex Problem-Solving Tasks and Their Applications in Developing Measurement Model.

Recent years have witnessed the emergence of measurement models for analyzing action sequences in computer-based problem-solving interactive tasks. The cutting-edge psychometrics process models require pre-specification of the effectiveness of state transitions often simplifying them into dichotomous indicators. However, the dichotomous effectiveness becomes impractical when dealing with complex tasks that involve multiple optimal paths and numerous state transitions. Building on the concept of problem-solving, we introduce polytomous indicators to assess the effectiveness of problem states and state-to-state transitions . The three-step evaluation method for these two types of indicators is proposed and illustrated across two real problem-solving tasks. We further present a novel psychometrics process model, the sequential response model with polytomous effectiveness indicators (SRM-PEI), which is tailored to encompass a broader range of problem-solving tasks. Monte Carlo simulations indicated that SRM-PEI performed well in the estimation of latent ability and transition tendency parameters across different conditions. Empirical studies conducted on two real tasks supported the better fit of SRM-PEI over previous models such as SRM and SRMM, providing rational and interpretable estimates of latent abilities and transition tendencies through effectiveness indicators. The paper concludes by outlining potential avenues for the further application and enhancement of polytomous effectiveness indicators and SRM-PEI.

Three-stage multi-modal multi-objective differential evolution algorithm for vehicle routing problem with time windows

In this paper, the mathematical model of Vehicle Routing Problem with Time Windows (VRPTW) is established based on the directed graph, and a 3-stage multi-modal multi-objective differential evolution algorithm (3S-MMDEA) is proposed. In the first stage, in order to expand the range of individuals to be selected, a generalized opposition-based learning (GOBL) strategy is used to generate a reverse population. In the second stage, a search strategy of reachable distribution area is proposed, which divides the population with the selected individual as the center point to improve the convergence of the solution set. In the third stage, an improved individual variation strategy is proposed to legalize the mutant individuals, so that the individual after variation still falls within the range of the population, further improving the diversity of individuals to ensure the diversity of the solution set. Based on the synergy of the above three stages of strategies, the diversity of individuals is ensured, so as to improve the diversity of solution sets, and multiple equivalent optimal paths are obtained to meet the planning needs of different decision-makers. Finally, the performance of the proposed method is evaluated on the standard benchmark datasets of the problem. The experimental results show that the proposed 3S-MMDEA can improve the efficiency of logistics distribution and obtain multiple equivalent optimal paths. The method achieves good performance, superior to the most advanced VRPTW solution methods, and has great potential in practical projects.

A method for selecting the optimal warping path of dynamic time warping in gait analysis.

This study aims to demonstrate that when performing dynamic time warping (DTW) on gait data, multiple optimal warping paths (OWPs) with a minimum sum of local costs can occur and to propose an additional OWP selection method to address this problem. A 3-dimensional motion analysis experiment was conducted on 55 adult participants, including both males and females, to acquire gait data. This study analyzed 990 instances of DTW on gait data to examine the occurrence of multiple OWPs with the minimum sum of local costs. We subsequently applied an additional selection method to the multiple OWPs to determine the feasibility of identifying a single OWP. Multiple OWPs through DTW were observed 82 times, accounting for 8.28%. Notably, on the ankle joint of males, the rate was the highest at 11.11%. Cases with two multiple OWPs were the most prevalent at 56.10%, and cases with ten or more multiple OWPs accounted for 19.51%. The additional selection method proposed in this study was applied to the 82 instances in which multiple OWPs occurred. The results demonstrated the ability to identify a unique OWP in all cases. These results hold significance in identifying the shortcomings of conventional OWP selection methods previously employed and proposing solutions. It enhances the reliability, validity, and accuracy of studies utilizing DTW.

Cross-Layer Based QoS Aware Load-balancing Multi-Path Routing Protocol over Wireless Multimedia Sensor Networks

Abstract: Currently, the utilization of WMSNs in different real-time and non-real-time applications requires an excessive amount of bandwidth for reliable data delivery. The unique features of WMSNs are significantly challenging in satisfying the QoS requirements in such application-specific environments and balancing the traffic load among the devices. The provision of reliable multipath routing is a cornerstone in fulfilling the QoS requirements of WMSNs. Selecting multiple optimal paths between a source and destination based on peculiar routing metrics enhances the performance of QoS routing. Generally, routing protocols exploit several routing metrics, such as delay, remaining energy of nodes, hop count, available bandwidth, and packet loss rate in path selection to attain high reliability in data delivery. Many existing routing protocols only consider the network layer parameters, whereas it lacks focus on the data link and physical layer parameters, which creates a severe impact on the degradation of QoS. In addition to that, varying bandwidth channels create interference in multimedia data delivery and degrade the network performance. Designing a multipath routing protocol by considering cross-layer parameters offer a promising solution to optimize the WMSN performance. In cross-layer design, diverse protocol layers support the routing decisions adaptively by perceiving the dynamic characteristics of the wireless medium, resulting in fair use of scarce resources with high QoS. A Cross-Layer Based QoS Aware Load-Balancing Multipath Routing Protocol over Wireless Multimedia Sensor Networks was the goal of the study's five design objectives. The study and analysis of QoS and cross-layer-based routing algorithms for WMSNs was the initial goal. Secondly, a Deep Learning prioritization-based packet classifier to divide traffic according to priority. To ensure fair resource consumption and distribution of multimedia traffic, the third goal was to design and create a cross-layer optimizer model for optimal multiple disjoint route selection using machine learning techniques. The development of a cutting-edge channel-scheduling algorithm was goal four. It was designed to efficiently assign low-interference channels to communication devices in order to lower the packet drop rate in real-time packet delivery. Last but not least, a security method for Wireless Multimedia Sensor Networks' Cross-Layer based multipath routing protocol.

Time-Optimal Path Planning in an Evolving Ocean Wave Field Based on Reachability Theory

We consider the navigation of surface vessels in an evolving ocean wave field, where the detrimental extreme waves are treated as moving and deforming obstacles. We propose a new time-optimal path planning algorithm with avoidance of such obstacles based on the reachability theory. In our framework, the mathematical optimization problem is boiled down to: 1) forward propagation of reachable set described by a variational inequation (VI), which is numerically solved through the level set method combined with a prediction-correction scheme and 2) a backtracking procedure to find the optimal path. The new path planner is tested in a number of cases including one with realistic ocean waves. We demonstrate that our algorithm can provide correct paths avoiding high waves and achieve multiple optimal (equivalent in time) paths when available. Finally, the framework can be straightforwardly extended to other problems involving collision avoidance with moving and deforming obstacles.

Energy-Efficient LoRa Routing for Smart Grids.

Energy-efficient routing protocols in Internet of Things (IoT) applications are always of colossal importance as they improve the network's longevity. The smart grid (SG) application of the IoT uses advanced metring infrastructure (AMI) to read and record power consumption periodically or on demand. The AMI sensor nodes in a smart grid network sense, process, and transmit information, which require energy, which is a limited resource and is an important parameter required to maintain the network for a longer duration. The present work discusses a novel energy-efficient routing criterion in an SG environment realised using LoRa nodes. Firstly, a modified LEACH protocol-cumulative low-energy adaptive clustering hierarchy (Cum_LEACH) is proposed for cluster head selection among the nodes. It uses the cumulative energy distribution of the nodes to select the cluster head. Furthermore, for test packet transmission, multiple optimal paths are created using the quadratic kernelised African-buffalo-optimisation-based LOADng (qAB_LOADng) algorithm. The best optimal path is selected from these multiple paths using a modified version of the MAX algorithm called the SMAx algorithm. This routing criterion showed an improved energy consumption profile of the nodes and the number of active nodes after running for 5000 iterations compared to standard routing protocols such as LEACH, SEP, and DEEC.

An Adaptive Multipath Routing Method Based on Improved GA and Information Entropy

With the development of artificial intelligence technology, some emerging applications (such as computation offloading and digital twin) require higher transmission quantity and quality for wireless sensor networks (WSNs). The increasing amount of data aggravates the imbalance of node energy consumption. In the single-path routing, nodes on the optimal path consume too much energy, which leads to the premature failure of the network. In addition, the transmission protocols based on the acknowledge character (ACK) mechanism ensure the quality of service, but bring additional energy overhead. In this article, an adaptive multipath routing method based on balanced energy consumption (AMRBEC) is proposed for WSNs that significantly reduce energy consumption and prolong network lifetime. We design a new multidimensional fitness function based on the path energy, distance, hops and the lowest energy node, which servers to an improved genetic algorithm (GA) to select the multiple optimal paths. The packet loss rate is predicted by random forest to realize the non-feedback transmission. According to the residual energy and the information entropy of each path, the amount of data transmitted is dynamically adjusted, and the optimal paths are updated to balance the energy consumption of the whole network. A simulation analysis shows that the proposed AMRBEC performs better than other algorithms from the literature by improving the lifetime by 20% and reducing energy consumption by more than 20%.

A Prehistorical Approach to Optimal Fluctuations for General Langevin Dynamics with Weak Gaussian White Noises

The dynamics of a stochastic system that exhibits large fluctuations to a given state are almost deterministic due to weak random perturbations. Such large fluctuations occur with overwhelming probability in the vicinity of the so-called optimal path, which is a vital concept in physics, chemistry, and biology, as it uncovers the way in which a physical process escapes from the attractive domain of a metastable state and transitions between different metastable states. In this paper, we examine the prehistorical description of the optimal fluctuation with the unifying framework of Langevin dynamics by means of a quantity called prehistory probability density. We show that the optimal fluctuation has a strong connection with the time reversal of the associated diffusion process. Specifically, in the stationary or quasi-stationary cases, it is found that the prehistory probability density actually acts as the transition probability density of the reversed process. As noise intensity approaches zero, it focuses on the average dynamics of the reversed process due to the law of large numbers, which is then shown to coincide with the time reversal of the optimal path. The local dispersion of the prehistory probability density can thus be reformulated as a Gaussian distribution corresponding to the linearized part of the reversed process. In addition, as an analogue of the original definition in the stationary states, it is proven that the concept of prehistory probability density can also be extended to nonstationary cases where similar properties are still valid. Based on these theoretical results, an algorithm is designed and then successfully applied to a one-dimensional example at the end, showing its accuracy for pinpointing the location of the optimal path and its efficacy in cases where multiple optimal paths coexist.

Application Aware Multiple Constraint Optimal Paths for Transport Network Using SDN

The backhaul networks for the 5G networks consist of different links that handle massive heterogeneous traffic. Fulfilling the QoS requirement of users to comply with the growth and increasing revenue is a challenge for the service providers. We address QoS parameters like bandwidth and delay for the user’s transport network. We use Software-Defined Networking and solve this problem. We have added a component Flowlet based Multiple Constraint Optimal Paths (MCOP) for packet forwarding by taking input as QoS requirements and creating a logical network in backhaul transport networks when needed for the elephant traffic. Due to security reasons, the transport network cannot access L7 to identify the application type. We have added an application identification component to detect the traffic type. We use an experimental platform using mininet and OpenFlow. Our proposed algorithm has higher QoS performance than the conventional method after the primary link exhaust capacity. It takes around 20 to 30 packets to learn the traffic type up to L6 parameters. Our approach identifies 73.10% of traffic type. The multipath usage helps improve revenue growth by assuring the dynamic allocation of the resources to the customer for elephant flow with the required QoS.

Multi-Objective Function-Based Node-Disjoint Multipath Routing for Mobile Ad Hoc Networks

The main goal is to find multiple node-disjoint paths that meet the multi-objective optimization problem in terms of energy consumption minimization and network lifetime improvement. Due to the battery-dependent nodes in mobile ad hoc networks, the performance of the network will degrade. Hence, it is necessary to choose multiple optimal node-disjoint paths between source and destination for data transfer. Additionally, it improves the Quality of Service (QoS) of wireless networks. Multi-objective function is used to select a path such that it gives an optimum result based on the energy consumption, hop, and traffic load. From the simulation results, it is proved that the proposed system is achieving less energy consumption and improved network lifetime compared with existing Dynamic Source Routing (DSR), Hopfield Neural Network-based Disjoint Path set Selection (HNNDPS) and Multipath DSR (MDSR).

Volcano Routing: A Multi-Pipe High-Throughput Routing Protocol with Hole Avoidance for Multi-Beam Directional Mesh Networks

The emergence of multi-beam directional antennas (MBDAs) has paved the way for fast and high-throughput data communications by providing concurrent multi-directional transmissions. However, the existing routing protocols are not capable of utilizing the advantages of MBDAs. In this paper, we have developed a new routing scheme, called volcano routing, which can exploit the concurrent packet dispatching capability of MBDAs for high-throughput data delivery. Its topology resembles the flow of volcano lava and several routing “pipes” are used, which can detour around the network “holes” or blocked areas. The routing process consists of two phases: 1) Main path search phase: There is a main path at the core of each pipe. Multiple optimal main paths are formed that have a high potential of adding side nodes to enable multi-beam communications. A hierarchical scoring system and the performance metrics are used to evaluate the quality of the main paths. 2) Volcano establishment phase: The top-quality main paths are selected, and side paths are formed around each main path to establish the volcano pipes. A multi-beam traffic scheduling and dispatching policy is also proposed to achieve better performance. Our results show that the volcano routing scheme can exploit the advantages of MBDAs for achieving high data rates.

Pairwise Sequence Alignment by Differential Evolutionary Algorithm with New Mutation Strategy

Sequence alignment is a significant facet in the bio-informatics research field for the molecular sequence analysis. Arrangement of two biological sequences by maximizing the similarities between the sequences by incorporating and adjusting gaps is Pairwise Sequence Alignment (PSA). Arrangement of multiple sequences is Multiple Sequence Alignment (MSA). Though Dynamic programming can produce optimal sequence alignment for PSA it suffers from a problem when multiple optimal paths are present and trace back is required. Back tracking becomes complex and it is also not suitable for MSA. So many meta-heuristic algorithms like Genetic Algorithm (GA) and Differential Evolutionary Algorithm (DE) are developed in the recent years to resolve the issue of optimization. Both GA and DE are used to produce optimal sequence alignment. But Compared to GA, DE is able to produce more optimal sequence alignment. To further enhance the performance of DE a new mutant is proposed by considering best, worst and a random candidate solution and applied on DE. It is named as New Differential Evolutionary Algorithm (NDE). By taking the test sequences from a bench mark data set “prefab4ref” tests are performed on GA, All DE mutants and NDE and it is observed that the proposed algorithm NDE outperformed all the other algorithms.

Optimal Route Searching with Multiple Dynamical Constraints—A Geometric Algebra Approach

The process of searching for a dynamic constrained optimal path has received increasing attention in traffic planning, evacuation, and personalized or collaborative traffic service. As most existing multiple constrained optimal path (MCOP) methods cannot search for a path given various types of constraints that dynamically change during the search, few approaches for dynamic multiple constrained optimal path (DMCOP) with type II dynamics are available for practical use. In this study, we develop a method to solve the DMCOP problem with type II dynamics based on the unification of various types of constraints under a geometric algebra (GA) framework. In our method, the network topology and three different types of constraints are represented by using algebraic base coding. With a parameterized optimization of the MCOP algorithm based on a greedy search strategy under the generation-refinement paradigm, this algorithm is found to accurately support the discovery of optimal paths as the constraints of numerical values, nodes, and route structure types are dynamically added to the network. The algorithm was tested with simulated cases of optimal tourism route searches in China’s road networks with various combinations of constraints. The case study indicates that our algorithm can not only solve the DMCOP with different types of constraints but also use constraints to speed up the route filtering.

An on-demand power and load-aware multi-path node-disjoint source routing scheme implementation using NS-2 for mobile ad-hoc networks

Ad-hoc network consists of a group of mobile nodes with a restricted power supply resources that can communicate with each other without any established infrastructure or centralized administration. The unbalanced distribution of traffic loads among network's nodes led to a power dissipation of overloaded nodes, the loss of these vital nodes causes link failure which could lead to critical topological changes, affect the network operations and its lifetime. This paper summarized the energy consumption problem in ad-hoc wireless networks and the existing power aware routing protocols classification. The main objective of this paper is to introduce and implement a new power and load-aware routing scheme that is based on DSR protocol's scheme. A new cost function was drawn, that allows source nodes to find a multiple node-disjoint power and load aware optimal paths to their destinations, as a way to extend the operational life of nodes and thereby maximize the network lifetime. Simulation results showed that the protocol that is based on this proposed scheme can prolong network lifetime by almost 30% with low traffic loads, and by 40% with high traffic loads compared to pure DSR.

A novel hybrid algorithm for generalized traveling salesman problems in different environments

A swap sequence-based particle swarm optimization (SSPSO) technique and genetic algorithm (GA) are used in tandem to develop a hybrid algorithm to solve generalized traveling salesman problem. Local search algorithm K-Opt is occasionally used to move any stagnant solution. Here, SSPSO is used to find the sequence of groups of a solution in which a tour to be made and cities from different groups of the sequence are selected using GA. The K-Opt algorithm (for K=3) is used periodically for a predefined number of iterations to improve the quality of the solutions. The algorithm is capable of solving the problem in crisp as well as in imprecise environment. For this purpose, a general fitness evaluation rule for the solutions is proposed. The efficiency of the algorithm is tested in crisp environment using different size benchmark problems available in TSPLIB. In crisp environment, the algorithm gives 100% success rate for problems up to considerably large sizes. Imprecise problems are generated from crisp problems randomly using a rule and are solved using the proposed approach. The obtained results are discussed. Moreover it is observed that the proposed algorithm finds multiple optimal paths, when they exist, both for the crisp problems and their fuzzy variations.

SIMULATION AND PERFORMANCE ANALYSIS EVALUATION FOR MULTIPATH EXTENSION OF AODV TO IMPROVE END TO END DELAY, ROUTE ERROR SENT, ROUTING LOAD AND PACKET DROP RATIO

This paper describes improvement in standard routing protocol AODV for mobile ad-hoc networks. Our mechanism setups multiple optimal paths based on bandwidth and delay. It allows to store multiple optimal paths based on Bandwidth and delay. At time of link failure, it will switch to next available path. To set up multiple paths, we have used the information that we get in the RREQ packet and also send RREP packet to more than one path. It reduces overhead of local route discovery at the time of link failure and because of this End to End Delay and Drop Ratio decreases. The main feature of our mechanism is that it is simple, efficient. We evaluate through simulations the performance of the AODV routing protocol including our scheme and we compare it with HLSMPRA (hot link split multi-path routing algorithm) Algorithm. Indeed, our scheme reduces routing load, End to End Delay, route error sent, and Packet drop ratio. The simulations have been performed using network simulator OPNET-14.0. The network simulator OPNET is discrete event simulation software for network simulations which means it simulates events such as sending, receiving, forwarding and dropping packets.

Optimal Route Based Advanced Algorithm using Hot Link Split Multi-Path Routing Algorithm

Abstract —Present research work describes advancement in standard routing protocol AODV for mobile ad-hoc networks. Our mechanism sets up multiple optimal paths with the criteria of bandwidth and delay to store multiple optimal paths in the network. At time of link failure, it will switch to next available path. We have used the information that we get in the RREQ packet and also send RREP packet to more than one path, to set up multiple paths, It reduces overhead of local route discovery at the time of link failure and because of this End to End Delay and Drop Ratio decreases. The main feature of our mechanism is its simplicity and improved efficiency. This evaluates through simulations the performance of the AODV routing protocol including our scheme and we compare it with HLSMPRA (Hot Link Split Multi-Path Routing Algorithm) Algorithm. Indeed, our scheme reduces routing load of network, end to end delay, packet drop ratio, and route error sent. The simulations have been performed using network simulator OPNET. The network simulator OPNET is discrete event simulation software for network simulations which means it simulates events not only sending and receiving packets but also forwarding and dropping packets. This modified algorithm has improved efficiency, with more reliability than Previous Algorithm.

Generalized multipath planning model for ride-sharing systems

Ride-sharing systems should combine environmental protection (through a reduction of fossil fuel usage), socialization, and security. Encouraging people to use ride-sharing systems by satisfying their demands for safety, privacy and convenience is challenging. Most previous works on this topic have focused on finding a fixed path between the driver and the riders either based solely on their locations or using social information. The drivers' and riders' lack of options to change or compute the path according to their own preferences and requirements is problematic. With the advancement of mobile social networking technologies, it is necessary to reconsider the principles and desired characteristics of ride-sharing systems. In this paper, we formalized the ride-sharing problem as a multi source-destination path planning problem. An objective function that models different objectives in a unified framework was developed. Moreover, we provide a similarity model, which can reflect the personal preferences of the rides and utilize social media to obtain the current interests of the riders and drivers. The model also allows each driver to generate sub-optimal paths according to his own requirements by suitably adjusting the weights. Two case studies have shown that our system has the potential to find the best possible match and computes the multiple optimal paths against different user-defined objective functions.

OPTIMAL ROUTE SELECTION STRATEGY FOR QOS IMPROVEMENT

An ad-hoc mobile network is a collection of mobile nodes that are dynamically and arbitrarily located in such a manner that the interconnections between nodes are capable of changing on a continual basis. Ad hoc nodes operating in a single path, single channel model might experience packet loss and high latency due to the congestion caused. Nodes along the heavy traffic path could reach the maximum bandwidth limit and experience undesirable amounts of packet drop. In Ad hoc networks the nodes are mobile and contain no infrastructure. Certain emergency messages have to be delivered with very low latency and high reliability. An efficient routing protocol should ensure reliable packet delivery in a timely manner. Our Proposed solution is to setup multiple optimal paths based on bandwidth and delay. It allows storing multiple optimal paths based on Bandwidth and delay. At time of link failure, it will switch to next available path. To set up multiple paths, we have used the information that we get in the RREQ packet and also send RREP packet to more than one path It reduces overhead of local route discovery at the time of link failure. We investigated the performance metrics namely Retransmission Attempt, Media Access Delay, Network Load by through OPNET simulation.