Kernighan-Lin Research Articles

Anonymous group structure algorithm based on community structure.

A social network is a platform that users can share data through the internet. With the ever-increasing intertwining of social networks and daily existence, the accumulation of personal privacy information is steadily mounting. However, the exposure of such data could lead to disastrous consequences. To mitigate this problem, an anonymous group structure algorithm based on community structure is proposed in this article. At first, a privacy protection scheme model is designed, which can be adjusted dynamically according to the network size and user demand. Secondly, based on the community characteristics, the concept of fuzzy subordinate degree is introduced, then three kinds of community structure mining algorithms are designed: the fuzzy subordinate degree-based algorithm, the improved Kernighan-Lin algorithm, and the enhanced label propagation algorithm. At last, according to the level of privacy, different anonymous graph construction algorithms based on community structure are designed. Furthermore, the simulation experiments show that the three methods of community division can divide the network community effectively. They can be utilized at different privacy levels. In addition, the scheme can satisfy the privacy requirement with minor changes.

Decomposition-Based Lin–Kernighan Heuristic With Neighborhood Structure Transfer for Multi/Many-Objective Traveling Salesman Problem

The multi/many-objective traveling salesman problem (MOTSP), which is NP-hard, can be found in many real-world applications. The Lin-Kernighan (LK) algorithm, as one of the most successful local search methods for single-objective TSP, adopts a variable neighborhood local search. However, LK cannot be directly applied to the decomposition-based multiobjective optimization framework due to its incapability of effective knowledge transfer among different subproblems, especially for problems with more than two objectives. In this paper, we propose an algorithm, called Decomposition-based Multiobjective Lin-Kernighan Heuristic with Neighborhood Structure Transfer (NST-MOLK) for MOTSP. In NST-MOLK, the knowledge of neighborhood structure has been transferred to enhance the efficiency and effectiveness of LK. The experimental studies have been conducted on both benchmark and real-world instances constructed based on the flight prices of 7 airlines and 266 airports of different cities in China. Experimental results show that NST-MOLK outperforms both classical and state-of-the-art algorithms significantly. It has also been verified that neighborhood structure transfer can effectively improve the performance of NST-MOLK.

Optimization Methods of Multi-Core Embedded System

With the development of the Internet of everything technology, embedded system has become one of the most common computing systems. Embedded system has high portability, but there are often stronger limitations in energy consumption, real-time and so on. In this work, have improved some traditional optimization algorithms, and finally get a task scheduling sequence, which can reduce the total execution time and cost of the task. Firstly, the multi-module division is used to divide multiple tasks into different modules, improve the classical Kernighan-Lin (KL) algorithm and clustering algorithm implement this process. Second, this paper invokes a series of algorithms to calculate the priority value of the task. Finally, this paper call two multi-core scheduling algorithms to schedule the tasks within each module to the Central Processing Unit (CPU) in the module. The proposed algorithm is implemented in this paper. With directed acyclic graph as input, the improvement effect of the algorithm and the direct advantages and disadvantages of different algorithms are evaluated with different task quantity.

Novel hybrid evolutionary algorithm for bi-objective optimization problems

This work considers the Bi-objective Traveling Salesman Problem (BTSP), where two conflicting objectives, the travel time and monetary cost between cities, are minimized. Our purpose is to compute the trade-off solutions that fulfill the problem requirements. We introduce a novel three-Phase Hybrid Evolutionary Algorithm (3PHEA) based on the Lin–Kernighan Heuristic, an improved version of the Non-Dominated Sorting Genetic Algorithm, and Pareto Variable Neighborhood Search, a multi-objective version of VNS. We conduct a comparative study with three existing approaches dedicated to solving BTSP. To assess the performance of algorithms, we consider 20 BTSP instances from the literature of varying degrees of difficulty (e.g., euclidean, random, mixed, etc.) and different sizes ranging from 100 to 1000 cities. We also compute several multi-objective performance indicators, including running time, coverage, hypervolume, epsilon, generational distance, inverted generational distance, spread, and generalized spread. Experimental results and comparative analysis indicate that the proposed three-phase method 3PHEA is significantly superior to existing approaches covering up to 80% of the true Pareto fronts.

An Improved Farmland Fertility Algorithm with Hyper-Heuristic Approach for Solving Travelling Salesman Problem

Travelling Salesman Problem (TSP) is a discrete hybrid optimization problem considered NP-hard. TSP aims to discover the shortest Hamilton route that visits each city precisely once and then returns to the starting point, making it the shortest route feasible. This paper employed a Farmland Fertility Algorithm (FFA) inspired by agricultural land fertility and a hyper-heuristic technique based on the Modified Choice Function (MCF). The neighborhood search operator can use this strategy to automatically select the best heuristic method for making the best decision. Lin-Kernighan (LK) local search has been incorporated to increase the efficiency and performance of this suggested approach. 71 TSPLIB datasets have been compared with different algorithms to prove the proposed algorithm’s performance and efficiency. Simulation results indicated that the proposed algorithm outperforms comparable methods of average mean computation time, average percentage deviation (PDav), and tour length.

Hyper-Heuristic Based on ACO and Local Search for Dynamic Optimization Problems

Hyper-heuristics comprise a set of approaches that are motivated (at least in part) by the objective of intelligently combining heuristic methods to solve hard optimization problems. Ant colony optimization (ACO) algorithms have been proven to deal with Dynamic Optimization Problems (DOPs) properly. Despite the good results obtained by the integration of local search operators with ACO, little has been done to tackle DOPs. In this research, one of the most reliable ACO schemes, the MAX-MIN Ant System (MMAS), has been integrated with advanced and effective local search operators, resulting in an innovative hyper-heuristic. The local search operators are the Lin–Kernighan (LK) and the Unstringing and Stringing (US) heuristics, and they were intelligently chosen to improve the solution obtained by ACO. The proposed method aims to combine the adaptation capabilities of ACO for DOPs and the good performance of the local search operators chosen in an adaptive way and based on their performance, creating in this way a hyper-heuristic. The travelling salesman problem (TSP) was the base problem to generate both symmetric and asymmetric dynamic test cases. Experiments have shown that the MMAS provides good initial solutions to the local search operators and the hyper-heuristic creates a robust and effective method for the vast majority of test cases.

A linearithmic heuristic for the travelling salesman problem

A linearithmic (nlogn) randomized method based on POPMUSIC (Partial Optimization Metaheuristic Under Special Intensification Conditions) is proposed for generating reasonably good solutions to the travelling salesman problem. The method improves a previous work with empirical algorithmic complexity in n1.6. The method has been tested on instances with billions of cities. For a lot of problem instances of the literature, a few dozens of runs are able to generate a very high proportion of the edges of the best solutions known. This characteristic is exploited in a new release of the Helsgaun’s implementation of the Lin-Kernighan heuristic (LKH) that is also able to produce rapidly extremely good solutions for non-Euclidean instances. The practical limits of the proposed method are discussed on a new type of problem instances arising in a manufacturing process, especially in 3D extrusion printing.

Evolutionary algorithm hybridized with local search and intelligent seeding for solving multi-objective Euclidian TSP

Multi-objective Euclidian TSP (ETSP) has several practical applications such as mobile computing and maritime surveillance. This problem has complexity not only in terms of combinatorial constraints but also in terms of multiple objectives. The local heuristic-based algorithms are extremely efficient in solving the single-objective ETSPs. However, their efficacy is limited in solving the multi-objective ETSPs due to the presence of multiple objectives. To bridge this gap, a two-stage evolutionary algorithm (TSEA) is developed to solve multi-objective ETSPs. In this algorithm, the first stage involves the use of a hybrid local search evolutionary algorithm (HLS-EA) which incorporates the local heuristic of nearest neighbor and 2-opt in the framework of real-coded NSGA-II to solve the individual objectives of multi-objective ETSP. These individual single-objective solutions which represent the corner solutions of the Pareto optimal front are used in the second stage as seed solutions in seeded HLS-EA (SHLS-EA) for solving the corresponding multi-objective ETSP. The developed algorithm is tested on 17 two-objective, 6 three-objective, and 2 four-objective ETSPs to show the superior performance over multi-objective variants of the Lin-Kernighan algorithm. Also, the developed algorithm is compared with several variants of DE and GA to illustrate the superior performance over the variants of evolutionary algorithms. Further, the algorithm is extended to the multi-objective ETSPs up to 10,000 cities.

Graph-Based Application Partitioning Approach for Computational Offloading in Mobile Cloud Computing

Background: Computational offloading is emerging as a popular field in Mobile Cloud Computing (MCC). Modern applications are power and compute-intensive which leads to the energy, storage and processing issues in mobile devices. Using the offloading concept, a mobile device can offload its computation to the cloud servers and receives back the results on the device. Objective: The main objective of the work is to provide a solution of an important question that arises in the offloading scenario is that which part of the application needs to be offloaded remotely and which part would run locally. Methods: In order to identify remote and local code, the application needs to be partitioned. In this paper, the graph partitioning approach is considered which is based upon the spectral graph partitioning with the Kernighan Lin algorithm. An application is assumed to be a graph and each node of the graph is assumed as a method. Results: Experimental results show that the proposed hybrid approach performs optimally in partitioning the application. The results indicate that considering the combination of spectral approach with the Kernighan Lin algorithm performs optimally as compared to random and multilevel partitioning in a mobile cloud scenario. Conclusion: The proposed technique gave better results than the existing techniques in terms of edge cut which is less, concluding minimum communication cost among components and thus save energy of the mobile device.

A Double Traveling Salesman Problem With Three-Dimensional Loading Constraints for Bulky Item Delivery

This article considers bulky item delivery problems in which multiple items are retrieved and loaded onto a vehicle from different warehouses and then delivered. This problem is described as a double traveling salesman problem with three-dimensional container loading constraints with multiple stacks. The double TSP with multiple stacks is used to determining the shortest route performing pickups and deliveries in two separated networks (one for pickups and one for deliveries) using only one container. Repacking is not allowed after loading the items into the container. An integer linear programming model is proposed to solve this problem, a standard genetic algorithm and an improved genetic algorithm is designed. In the improved genetic algorithm, a Lin-Kernighan algorithm is used to improve the delivery route, a k-means clustering algorithm, and a heuristic packing scheme improvement rules work together to improve the loading route. The results show that the improved genetic algorithm is superior to the standard genetic algorithm in large scale problems.

On Randomness and Structure in Euclidean TSP Instances: A Study With Heuristic Methods

Prediction of the quality of the result provided by a specific solving method is an important factor when choosing how to solve a given problem. The more accurate the prediction, the more appropriate the decision on what to choose when several solving applications are available. In this article, we study the impact of the structure of a Traveling Salesman Problem instance on the quality of the solution when using two representative heuristics: the population-based Ant Colony Optimization (ACO) and the local search Lin-Kernighan (LK) algorithm. The quality of the result for a solving method is measured by the computation accuracy, which is expressed using the percent error between its solution and the optimum one. We classify the instances in structured, semi-structured, and unstructured and perform a between classes and inside-classes analysis. All the structured instances were solved to optimality by the ACO implementation, which was not the case for the LK application. On small random instances, the ACO implementation used in this paper also optimally found the solutions. We show that the quality of the results on semi-structured and unstructured instances can be predicted using some instance parameters when using the ACO implementation. Using the same parameters, the accuracy of the solutions provided by the Lin-Kernighan application cannot be predicted. We also propose several new structured, clustered, and unstructured 2D Euclidean Traveling Salesman Problem instances that can be used by the research community for further investigations.

A parcel network flow approach for joint delivery networks using parcel lockers

Current courier networks in metropolitan areas are characterised by utilising fleets of vans that perform collection and distribution routes independently. This results in long stem distances, low load factors and high environmental costs. Joint delivery systems have the potential to reduce the distances of pick-up and drop-off routes. In this context, parcel lockers can be utilised to transfer goods between vans, electrical vehicles and bikes to improve the efficiency and sustainability of courier networks. This paper presents a model for designing joint delivery networks in urban areas by utilising parcel lockers. This model has a two-level structure: the lower level dealing with multi-depot capacitated vehicle routing problems (MDCVRP) for a set of depots and lockers whilst the upper level being a (minimum-cost) parcel network flow problem (PNFP) considering goods delivered between depots and lockers and the selection of lockers’ positions and sizes. A hybrid algorithm integrating a Genetic Algorithm with the Lin-Kernighan Heuristic has been developed. The GA focuses on finding solutions for the PNFP. Once the paths of parcel flow are determined, the LKH optimises vehicle flow. This paper is the first to consider the use of parcel lockers for business-to-business networks in the form of MDCVRP.

A Novel Approach to Optimize Numerical Control Codes Using a Systematic Block Management Method

The numerical control (NC) codes generated from Computer Aided Manufacturing (CAM) software follow the sequence of adding elements to the design. As an alternative, it would be quite beneficial in cost-reduction to optimize the manufacturing sequence to minimize the run time. Accordingly, this paper introduces a novel approach to optimize the numerical control codes generated from a CAM software package using a systematic block management method. To improve the drilling sequence, contours are also considered as block entities in a traveling salesman problem (TSP) with modifications to systematically manage the blocks of code that define the contours. A MATLAB program was created to automatically optimize the numerical codes from a CAM software translator. Because of easier usage and good performance, a partitioned approach for the λ-opt algorithm was implemented instead of the Lin-Kernighan Heuristic (LKH) that has been extensively proven to be effective in optimizing the traveling salesman problem. The new approach was simulated on sample designs and has been shown to achieve at least 15.52% reduction in airtime and 11.32% reduction in tool travel distance. Experimental data showed a 13.45% decrease in total milling time. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License .

The approximation ratio of the 2-Opt Heuristic for the metric Traveling Salesman Problem

The 2-Opt heuristic is one of the simplest algorithms for finding good solutions to the metric Traveling Salesman Problem. It is the key ingredient to the well-known Lin–Kernighan algorithm and often used in practice. So far, only upper and lower bounds on the approximation ratio of the 2-Opt heuristic for the metric TSP were known. We prove that for the metric TSP with n cities, the approximation ratio of the 2-Opt heuristic is n∕2 and that this bound is tight.

Efficient hybrid local search heuristics for solving the travelling thief problem

Real-world problems often consist of several interdependent subproblems. The degree of interaction of the subproblems is associated with the complexity of the problem and solving each subproblem optimally not ensure the optimal solution of the overall problem. The Travelling Thief Problem (TTP) integrates two well-known combinatorial optimization problems namely the classical Travelling Salesman Problem (TSP) and the 0–1 Knapsack Problem (KP). TTP was introduced to represent the complication of a real-world combinatorial optimization problem. The goal of this problem is to provide a tour to a thief over all the cities and a picking plan that determines which item should be taken from which city to achieve the maximum benefits. The KP component of the TTP is more efficient as compared to the TSP component for optimization. Our proposed method mainly focuses on constructing a picking plan for a near-optimal tour generated by Chained Lin–Kernighan Heuristic (CLKH). In this picking plan, items are picked up according to their scoring value which is calculated by our proposed formulation. Additionally, bit-flip is used for a better solution that can give a more profitable picking plan. The experimental results suggest that our proposed approach can meet or beat current state-of-the-art methods for a large number of TTP instances.

Region Division in Logistics Distribution With a Two-Stage Optimization Algorithm

When facing the problem of modern logistics distribution under the large-scale network, the reasonable delivery task allocation has become an important part. For this problem, this paper uses the idea of decentralized control to establish a region division model in logistics distribution and transforms it into the multiple traveling salesmen problem with constraints of the road network and task allocation. The optimization goal of the model is to minimize the sum of the distances for logistics transport agents traveling all demand points in the system, with the constraints on the equilibrium of commodity requirements in each sub region. Then, a two-stage algorithm is proposed to solve the model. In the first stage, the $K$ -means clustering method is used to obtain a highly feasible initial solution; In the second stage, the initial solution is optimized by the algorithm which is combining swap algorithm and tabu search algorithm. In the two-stage solution evaluation, the TSP solution based on the Lin-Kernighan algorithm is applied to obtain the sets of demand points with ranking of the route and the corresponding shortest distances for each divided sub region. Finally, to verify the effectiveness of the proposed model and solving method, two cases are presented in this paper. The region division method in logistics distribution proposed in this paper not only helps to reduce the total distance, but also helps to balance the workload of the logistics transport agents, thereby making great potential to reduce logistics costs and improving the overall operational efficiency of logistics distribution.

Economical connections between several European countries based on TSP data

AbstractA fluent economical collaboration between countries is a major need. European flows of trade and people are supported by efficient connections between main localities from a geographic region, in many cases overriding national borders. This paper introduces three traveling salesmen problem instances based on freely available geographic coordinates of the main cities of France, Portugal and Spain. These instances are unified, generating other four larger instances: three with all pairs of countries and one instance with the settlements from all the three countries. The study includes an analysis of quality of solutions for a version of branch & cut algorithm and some hybrid heuristics including the Lin–Kernighan algorithm. $Bor\mathring{u}vka$, Quick$Bor\mathring{u}vka$ and Greedy algorithms are also used in the hybrid approaches in order to obtain a potential beneficent initial solution for the Lin–Kernighan algorithm. Concorde solver, nowadays state-of-the-art exact software, together with the already mentioned algorithms, is used to test and furthermore analyze the new TSP instances. Some results are represented using online services such as Google Maps, showing the potential integration of the Concorde’s optimum results into commercial routing applications. The very good results provided by the Lin–Kernighan method allow its usage for real medium-sized routing instances.

A Novel Hybrid Metaheuristic for Solving Automobile Part Delivery Logistics With Clustering Customer Distribution

With the continuous maturity of the automobile industry, the cluster network effect has been gradually formed among automobile parts' suppliers. How to carry out reasonable and efficient distribution in the cluster network has become one of the greatest challenges in today's automobile manufacturers. In this paper, we conducted a field survey of a real-world automobile logistics company and collected data. After analyzing the relevant transportation modes, we concluded that the problem could be classified as a clustered vehicle routing problem (CluVRP). A CluVRP considers gathering customers according to geographical proximity on the basis of the classical capacitated vehicle routing problem (CVRP). An accompanying problem is that there is a hard constraint that all customers in a cluster must be served consecutively by the same vehicle. Because the CluVRP is NP-hard, a hybrid metaheuristic solution approach was proposed. First, the shortest distance best fit decreasing (SD-BFD) algorithm was used to construct an initial solution. Second, a clustering feature was considered in order to divide the problem into two levels for optimization: the intra-cluster level and the inter-cluster level. For the intra-cluster level, the variable neighborhood search (VNS) was applied; for the inter-cluster level, the Lin-Kernighan (LK) considering dummy point was employed for optimizing. The computational performances of the hybrid metaheuristic algorithms are tested on three sets of instances and compared with the results from previous papers and the company's manually calculated solutions. The results show that the proposed algorithm is excellent in both the operation time and the final solution value, which is significant to improve distribution efficiency, reduce transportation costs, and improve customer satisfaction.

Computational Intelligence for Solving Difficult Transportation Problems

Intelligent Transportation Systems (ITSs) are providing a broad range of services to all the actors involved in any type of transportation activities. Path planning is a common transportation problem, which can be extremely difficult when an exact solution is sought. The quality of heuristic approaches to this problem is therefore important, as they are now implemented as planning modules into almost all the ITSs on the market. The goal of this paper is to analyze several distributed reinforcement learning techniques involving the collective experience of artificial ants when approaching a transportation problem. Traveling Salesman Problem (TSP), a well-known NP-hard transportation problem, was chosen for computational experiments. In order to assess the behavior of the investigated solving methods, two medium-size TSP instances, covering large areas, are proposed. The results are compared with those provided by a state-of-the-art technique, namely the highly effective Lin-Kernighan(LK) heuristic procedure for generating optimum and near-optimum solutions for the TSP. This paper connects the academic Operational Research with societal needs in Transportation and Logistics.

Kernighan-Lin算法的改进对图划分问题的研究

Kernighan-Lin算法的改进对图划分问题的研究