2-opt Algorithm Research Articles

ОПТИМИЗАЦИЯ ПОСЛЕДОВАТЕЛЬНОСТИ ВЫПОЛНЕНИЯ ЗАКАЗОВ ПРЕДПРИЯТИЯ ЭВРИСТИЧЕСКИМИ АЛГОРИТМАМИ

The production process of fulfilling orders with parameters that require equipment readjustment is considered. The problem of determining the optimal strategy for the production equipment changeover is an optimization problem, which is formulated as a travelling salesman problem. When solving such a task, the graph nodes are orders, the arcs are changeovers with a known cost when moving from one order to another. The optimization criterion is the minimum total cost of equipment changeovers. Based on the cost matrix of equipment changeovers when executing orders with the known parameters, research is carried out to solve the problem using the 2-opt local search algorithm and the genetic algorithm. Examples are given for estimating the total cost of changeovers for orders that have several parameters with different levels. The steps for implementing heuristic algorithms to solve the problem are presented, and the results of experiments are shown.

Optimal routing with road network for scattered farm fields: Computational experiments with the branch-and-cut and 2-opt algorithms and case study on an agricultural corporation in Japan

This study investigates optimal routing with a road network to minimize the total traveling distance among scattered farm fields for smart agriculture. Based on the case of an agricultural corporation in Japan, the shortest paths between all pairs of farm fields and their distances are obtained by utilizing road network data, and the optimal route is searched by addressing the traveling salesman problem (TSP) with an exact algorithm, which is implemented by the COIN-OR branch and cut (CBC) solver. The applicability of the TSP with the exact algorithm is verified by comparing its computational time and solution to those of the TSP with the 2-opt method, an approximation algorithm, through a computational experiment. Moreover, the effectiveness of the proposed approach is demonstrated through a case study on the agricultural corporation considered. The results of the computational experiment and case study show that the proposed approach can provide the optimal route for daily work within 7.5 seconds and can reduce 6.89% of the traveling distance from that of the route a worker creates empirically.

Optimization of Green Vehicle Paths Considering the Impact of Carbon Emissions: A Case Study of Municipal Solid Waste Collection and Transportation

In recent years, the waste produced as a result of the production and consumption activities of urban residents has led to significant environmental degradation and resource wastage. This paper focuses on the research object of municipal solid waste (MSW) collection and transportation based on the concept of “sustainable development and green economy”. Firstly, this study examines the current state of urban domestic garbage collection and transportation. It analyzes the following challenges and deficiencies of the existing collection and transportation system: (1) the operating efficiency of garbage collection vehicles is low, resulting in a significant accumulation of waste on the roadside and within the community; (2) the vehicle collection and transportation routes are fixed, and there are empty vehicles running; (3) the amount of garbage on a route exceeds the vehicle’s loading capacity, which requires the vehicle to perform a second round of collection and transportation. To enhance the efficiency of urban garbage collection and transportation and minimize the collection and transportation costs, we are investigating the problem of optimizing the path for green vehicles. To comprehensively optimize the fixed cost, variable cost, and carbon emission cost incurred during vehicle operation, a vehicle routing model with time windows is established, taking into account vehicle load constraints. Carbon emission coefficient and carbon tax parameters are introduced into the model and the “fuel-carbon emission” conversion method is used to measure the carbon cost of enterprises. An improved ant colony optimization (ACO) method is proposed: (1) the introduction of a vehicle load factor improves the ant state transfer method; (2) the updated pheromone method is improved, and additional pheromone is added to both the feasible path and the path with the minimum objective function; (3) the max–min ACO algorithm is introduced to address the issue of premature convergence of the algorithm; (4) the embedding of a 2-opt algorithm further prevents the ACO algorithm from falling into the local optimum. Finally, the calculation results based on the example data demonstrate that the algorithm has a significant advantage over the genetic algorithm (GA) and particle swarm optimization (PSO) algorithm. The total transportation distance determined by this algorithm is shorter than that of the GA and PSO methods, and the total cost of the scheme is 1.66% and 1.89% lower than that determined by GA and PSO, respectively. Compared to the data from the actual case, the number of vehicles required in the operation of this algorithm and model is reduced by three. Additionally, the total cost, fixed cost, and carbon emission cost incurred by the vehicles during operation were reduced by 31.2%, 60%, and 25.3% respectively. The results of this study help the station to collect and distribute waste efficiently, while also achieving the goals of energy saving, consumption reduction, and emission reduction.

The Electric Vehicle Traveling Salesman Problem on Digital Elevation Models for Traffic-Aware Urban Logistics

With the increasing demand for online shopping and home delivery services, optimizing the routing of electric delivery vehicles in urban areas is crucial to reduce environmental pollution and improve operational efficiency. To address this opportunity, we optimize the Steiner Traveling Salesman Problem (STSP) for electric vehicles (EVs) in urban areas by combining city graphs with topographic and traffic information. The STSP is a variant of the traditional Traveling Salesman Problem (TSP) where it is not mandatory to visit all the nodes present in the graph. We train an artificial neural network (ANN) model to estimate electric consumption between nodes in the route using synthetic data generated with historical traffic simulation and topographical data. This allows us to generate smaller-weighted graphs that transform the problem from an STSP to a normal TSP where the 2-opt optimization algorithm is used to solve it with a Nearest Neighbor (NN) initialization. Compared to the approach of optimizing routes based on distance, our proposed algorithm offers a fast solution to the STSP for EVs (EV-STSP) with routes that consume 17.34% less energy for the test instances generated.

An Improvement to the 2-Opt Heuristic Algorithm for Approximation of Optimal TSP Tour

The travelling salesman problem (TSP) is perhaps the most researched problem in the field of Computer Science and Operations. It is a known NP-hard problem and has significant practical applications in a variety of areas, such as logistics, planning, and scheduling. Route optimisation not only improves the overall profitability of a logistic centre but also reduces greenhouse gas emissions by minimising the distance travelled. In this article, we propose a simple and improved heuristic algorithm named 2-Opt++, which solves symmetric TSP problems using an enhanced 2-Opt local search technique, to generate better results. As with 2-Opt, our proposed method can also be applied to the Vehicle Routing Problem (VRP), with minor modifications. We have compared our technique with six existing algorithms, namely ruin and recreate, nearest neighbour, genetic algorithm, simulated annealing, Tabu search, and ant colony optimisation. Furthermore, to allow for the complexity of larger TSP instances, we have used a graph compression/candidate list technique that helps in reducing the computational complexity and time. The comprehensive empirical evaluation carried out for this research work shows the efficacy of the 2-Opt++ algorithm as it outperforms the other well-known algorithms in terms of the error margin, execution time, and time of convergence.

A Hybrid Optimization Solution for UAV Network Routing

An Unmanned Aerial Vehicle (UAV) network specifies a novel type of Mobile Ad hoc Network (MANET) in which drones serve as nodes and facilitate the retransmission of messages to their final destinations. Aside from its military application, it has recently begun to seep into the civilian sector. Similar to MANET and vehicular ad hoc networks, Flying Ad hoc Networks (FANET) are a subset of ad hoc networks. An FANET is different because it is founded on UAVs. Due to the characteristics of this sort of network, which is defined by a highly changing topology in a 3D environment, we must employ an adjusted configuration method to ensure good routing performance. Therefore, to deal with this problem, a technique that responds to any change in topology by always finding the best route is required. In this work, we propose a new protocol based on the hybrid optimization of the 2-opt heuristic and Honey Badger Algorithm (HBA), called HB-AODV. In order to locate its prey, a badger must move slowly and continuously while using scent markers and mouse-digging skills to catch it. In other words, the most efficient routes in terms of the number of hops are identified. Several simulations were conducted via the 3D version of Network Simulator (NS-2) on different deployment strategies. In comparison to AODV, DSDV, and AntHocNet, the obtained results demonstrated the proposed scheme’s good performance in terms of quality of service metrics.

An Adaptive Layered Clustering Framework with Improved Genetic Algorithm for Solving Large-Scale Traveling Salesman Problems

Traveling salesman problems (TSPs) are well-known combinatorial optimization problems, and most existing algorithms are challenging for solving TSPs when their scale is large. To improve the efficiency of solving large-scale TSPs, this work presents a novel adaptive layered clustering framework with improved genetic algorithm (ALC_IGA). The primary idea behind ALC_IGA is to break down a large-scale problem into a series of small-scale problems. First, the k-means and improved genetic algorithm are used to segment the large-scale TSPs layer by layer and generate the initial solution. Then, the developed two phases simplified 2-opt algorithm is applied to further improve the quality of the initial solution. The analysis reveals that the computational complexity of the ALC_IGA is between O(nlogn) and O(n2). The results of numerical experiments on various TSP instances indicate that, in most situations, the ALC_IGA surpasses the compared two-layered and three-layered algorithms in convergence speed, stability, and solution quality. Specifically, with parallelization, the ALC_IGA can solve instances with 2×105 nodes within 0.15 h, 1.4×106 nodes within 1 h, and 2×106 nodes in three dimensions within 1.5 h.

A Biogeography-Based Optimization with a Greedy Randomized Adaptive Search Procedure and the 2-Opt Algorithm for the Traveling Salesman Problem

We develop a novel method to improve biogeography-based optimization (BBO) for solving the traveling salesman problem (TSP). The improved method is comprised of a greedy randomized adaptive search procedure, the 2-opt algorithm, and G2BBO. The G2BBO formulation is derived and the process flowchart is shown in this article. For solving TSP, G2BBO effectively avoids the local minimum problem and accelerates convergence by optimizing the initial values. To demonstrate, we adopt three public datasets (eil51, eil76, and kroa100) from TSPLIB and compare them with various well-known algorithms. The results of G2BBO as well as the other algorithms perform close enough to the optimal solutions in eil51 and eil76 where simple TSP coordinates are considered. In the case of kroa100, with more complicated coordinates, G2BBO shows greater performance over other methods.

Reposition optimization in the free-floating bike-sharing system considering transferring travels from urban rail transit

The popular free-floating bike-sharing (FFBS) system serves as a first- and last-mile solution to connect urban rail transit (URT). Recently, a number of studies have investigated how to enhance the integration between FFBS and URT. Nevertheless, how to reposition the FFBS system to promote URT ridership is still a challenge. This study proposes a bike-sharing repositioning framework to balance the demand and supply of FFBS and promote URT ridership. First, a repositioning quantity determination method based on the geographically weighted regression model is applied to determine the number of bikes to be delivered to or collected from each transfer area. Second, we establish an optimization model to minimize the total repositioning cost considering carbon price. Both the repositioning of normal bikes and recycling of broken bikes are included in this model. Subsequently, a hybrid Cuckoo Search algorithm is designed to solve the problem. The extended 2-opt, random removal and insertion algorithms are introduced to generate new solutions, which enhance the search ability. Finally, several numerical studies are conducted using data collected in Shenzhen, China, to verify the effectiveness of the proposed methods. The results demonstrate that the methodology proposed in this study is reasonable and effective. The findings are expected to guide traffic authorities to get environmental and highly utilized scheduling schemes for the integration between FFBS and URT systems.

Discrete Salp Swarm Algorithm for symmetric traveling salesman problem.

In the Salp Swarm Algorithm (SSA), the update mechanism is inspired by the unique chain movement of the salp swarm. Numerous versions of SSA were already put forward to deal with various optimization problems, but there are very few discrete versions among them. d-opt is improved based on the 2-opt algorithm: a decreasing factor d is introduced to control the range of neighborhood search; TPALS are modified by Problem Aware Local Search (PALS) based on the characteristics of Travelling Salesman Problem (TSP); The second leader mechanism increases the randomness of the algorithm and avoids falling into the local optimal solution to a certain extent. We also select six classical crossover operators to experiment and select Subtour Exchange Crossover (SEC) and the above three mechanisms to integrate them into the SSA algorithm framework to form Discrete Salp Swarm Algorithm (DSSA). In addition, DSSA was tested on 23 known TSP instances to verify its performance. Comparative simulation studies with other advanced algorithms are conducted and from the results, it is observed that DSSA satisfactorily solves TSP.

Tourism Route Selection Model for Tourism Sustainable Development Based on Improved Genetic Algorithm

The improvement of people’s quality of life also promotes the development of tourism. The traditional travel mode is no longer suitable for the needs of modern people. How to quickly determine the optimal tourist route according to the needs of different families is the current sustainable development direction of tourism. Scientific planning of tourist routes to minimize the cost and time of tourists is very important for the improvement of tourism experience. This study employs an improved genetic algorithm (IGA) to find the best tourist route based on this requirement. With the increase of tourist attractions, routes, and demands, the traditional genetic algorithm (GA) has problems such as premature convergence and poor local search ability when planning the tourist route. The existence of these problems will affect the effect of route planning. IGA proposes three improvements to traditional GA. One is to introduce the ant colony algorithm (ACA) to initialize the parameters in the GA. This algorithm is introduced to alleviate the over-reliance of GA on initializing the population and the poor adaptability of individual populations. Second, because the crossover probability parameter in GA has such a large influence on the final solution, this study proposes an adaptive strategy for adjusting the crossover probability to improve population fitness. Third, considering the weak local search ability of GA and the problem of premature convergence, this study introduces the 2-opt optimization algorithm to improve the quality of the solution. The results of the experimental analysis confirm the effectiveness of the proposed method.

Optimizing the path of seedling transplanting with multi-end effectors by using an improved greedy annealing algorithm

Automated transplanters perform the repetitive task of replugging bad or missing cells with healthy seedlings in greenhouses. The work efficiency of transplanters can be improved by optimizing the transplanting paths of manipulators. In this study, an improved greedy simulated annealing algorithm (IGSA) based on MTSP model was proposed for path optimization. Aimed at improving the computation speed of the algorithm, a new improved 2-Opt algorithm based on the metropolis criterion was utilized. Moreover, the greedy algorithm (GRA) and the greedy genetic algorithm (GGA) were modified to adapt to the multi-end effectors’ replugging operation. The performance of IGSA and those of the GGA, GRA, and common sequence method (CSM) in path planning for replugging transplanting were compared in terms of their optimization effects and computation times. Then, manipulators with different numbers of end effectors (four, five, and six end effectors) were used to verify the increased effect of the path planning. Under the verification test conditions, the comparative average optimization ratios of GRA, GGA, and IGSA compared to the CSM were 4.87 %, 10.64 %, and 20.07 %, respectively. The performance ranking of the methods with short average paths was in the order of IGSA, GGA, GRA, and CSM. Compared with the average path shortening ratio of the four end effectors, those of the five and six end effectors were 11.44 % and 18.68 %, respectively. The average computation times of CSM, GRA, GGA, and IGSA were 0.002, 0.007, 6.94, and 3.49 s in MATLAB (R2019a), respectively. All of them can meet the real-time operation requirements except for GGA. In contrast to GGA, GRA, and CSM, the proposed IGGA performed effectively in the path planning of the seedlings’ replug transplanting owing to its comprehensive performance derived from its path optimization ratio and low cost in terms of computation time.

Parameter adaptation-based ant colony optimization with dynamic hybrid mechanism

In this paper, a parameter adaptation-based ant colony optimization (ACO) algorithm based on particle swarm optimization (PSO) algorithm with the global optimization ability, fuzzy system with the fuzzy reasoning ability and 3-Opt algorithm with local search ability, namely PF3SACO is proposed to improve the optimization ability and convergence, avoid to fall into local optimum. In the PF3SACO, a new dynamic parameter adjustment mechanism by the PSO and the fuzzy system is designed to adaptively adjust the pheromone importance factor α, pheromone volatilization coefficient ρ and the heuristic function importance factor β to accelerate the convergence, improve the search ability, enhance the local search ability and avoid premature. This is achievable by parameter adaptation to reflect the dynamic search characteristic by exploring and exploiting in the search process for the parameter values to be close to the optimal values. In addition, 3-Opt algorithm is applied to optimize the generated path to eliminate the cross path, obtain the optimal path and avoid to fall into local optimum. The optimization performance of the PF3SACO is investigated on fifteen travelling salesman problems (TSPs) with the scales from 42 to 783 cities. The experiment results show that the PF3SACO has better optimization performance by comparing with ABC, NACO, HYBRID, ACO-3Opt, PACO-3Opt, PSO-ACO-3Opt and some other well-known algorithms in most TSP in term of the solution quality, robustness and space distribution. It provides a reference to solve the large-scale TSP for obtaining better path length.

A combination k-means clustering and 2-opt algorithm for solving the two echelon e-commerce logistic distribution

A combination k-means clustering and 2-opt algorithm for solving the two echelon e-commerce logistic distribution

NoC Application Mapping Optimization Using Reinforcement Learning

Application mapping is one of the early stage design processes aimed to improve the performance of Network-on-Chip. Mapping is an NP-hard problem. A massive amount of high-quality supervised data is required to solve the application mapping problem using traditional neural networks. In this article, a reinforcement learning–based neural framework is proposed to learn the heuristics of the application mapping problem. The proposed reinforcement learning–based mapping algorithm (RL-MAP) has actor and critic networks. The actor is a policy network, which provides mapping sequences. The critic network estimates the communication cost of these mapping sequences. The actor network updates the policy distribution in the direction suggested by the critic. The proposed RL-MAP is trained with unsupervised data to predict the permutations of the cores to minimize the overall communication cost. Further, the solutions are improved using the 2-opt local search algorithm. The performance of RL-MAP is compared with a few well-known heuristic algorithms, the Neural Mapping Algorithm (NMA) and message-passing neural network-pointer network-based genetic algorithm (MPN-GA). Results show that the communication cost and runtime of the RL-MAP improved considerably in comparison with the heuristic algorithms. The communication cost of the solutions generated by RL-MAP is nearly equal to MPN-GA and improved by 4.2% over NMA, while consuming less runtime.

Path planning of patrol robot based on improved discrete electrostatic discharge algorithm

Safety is the premise of the stable and sustainable development of the chemical industry, safety accidents will not only cause casualties and economic losses, but also cause panic among workers and nearby residents. Robot safety inspection based on the fire risk level in a chemical industrial park can effectively reduce process accident losses and can even prevent accidents. The optimal inspection path is an important support for patrol efficiency, therefore, in this study, the fire risk level of each location to be inspected, which is obtained by the electrostatic discharge algorithm (ESDA)–nonparallel support vector machine evaluation model, is combined with the optimisation of the inspection path; that is, the fire risk level is used to guide the inspection path planning. The inspection path planning problem is a typical travelling salesman problem (TSP). The discrete ESDA (DESDA), based on the ESDA, is proposed. In view of the shortcomings of the long convergence time and ease of falling into the local optimum of the DESDA, further improvements are proposed in the form of the IDESDA, in which the greedy algorithm is used for the initial population, the 2-opt algorithm is applied to generate new solutions, and the elite set is joined to provide the best segment for jumping out of the local optimum. In the experiments, 11 public calculation examples were used to verify the algorithm performance. The IDESDA exhibited higher accuracy and better stability when solving the TSP. Its application to chemical industrial parks can effectively solve the path optimisation problem of patrol robots.

A multi-product multi-layer urban freight distribution problem solved using a hybrid metaheuristic procedure

The pick-up and delivery routing problem has received special attention thanks to its application to urban freight distribution processes. However, due to the multiple levels involved in those processes, modeling and analyzing urban distribution networks in urban contexts are complex tasks. As a result, efficient and robust solution methods should be proposed according to the dynamic and uncertain conditions that characterize this type of problems. This article presents a new formulation for the pick-up and delivery problem in a logistics distribution network composed of 3 levels: n: 1: m (n suppliers, 1 urban consolidation center, and m customers). In addition, an algorithm based on GRASP heuristic and 2-opt algorithm was implemented here to find solutions to problem, which were compared with the results of the same algorithm for a two-layer vehicle routing problem in several instances. Thus, the proposed procedure achieved a 22% improvement over such algorithm.

Research on improved ant colony optimization for traveling salesman problem.

As one of the most popular combinatorial optimization problems, Traveling Salesman Problem (TSP) has attracted lots of attention from academia since it was proposed. Numerous meta-heuristics and heuristics have been proposed and used to solve the TSP. Although Ant Colony Optimization (ACO) is a natural TSP solving algorithm, in the process of solving it, there are also some shortcomings such as slow convergence speed and prone to fall into local optimum. Therefore, this paper proposes an improved ant colony optimization based on graph convolutional network: Graph Convolutional Network Improved Ant Colony Optimization (GCNIACO). The graph convolutional network is introduced to generate a better solution, and the better solution is converted into the pheromone on the initial path of the ACO. Thereby, the guiding effect of the pheromone concentration for the ants at the beginning of the algorithm is enhanced. In the meantime, through adaptive dynamic adjustment of the pheromone volatility factor and the introduction of the 3-opt algorithm, the algorithm's ability to jump out of the local optimum is enhanced. Finally, GCNIACO is simulated on TSP datasets and engineering application example. Comparing the optimization results with other classical algorithms, it is verified that the graph convolutional network improved ant colony optimization has better performance in obtaining the optimal solution.

Artificial Bee Colony Algorithm with Proposed Discrete Nearest Neighborhood Algorithm for Discrete Optimization Problems

Travelling salesman problem (TSP) is one the problems of NP-complete family, which means finding shortest complete close tour in the graph. This study seeks to solve this problem using Artificial Bee Colony (ABC) Algorithm along with the proposed Discrete Nearest Neighborhood Algorithm (DNNA). DNNA finds shortest path among points by starting from an arbitrary point. In next steps this links will be a guide to make complete tour. In other words the links in partial tours have higher chance to be in the final solution. In order to improve the final solutions of a single created tour, The employee bees’ movement radius has been limited, because of avoidance of long random jump between nodes. To reduce the optimization time of the tours created by the artificial bee colony algorithm, the fixed-radius near neighbor 2-opt algorithm was used as well. In addition, 2 types of scout bee were used for to intensify the probability property of the algorithm. Also, convergence in the probability function of employee bees’ movement was prevented by increasing the number of route-creating tours. The first scout bee applies the proposed DNNA and the secondary scout bee improves the partial tours of employee bees in a probable way. Although Althought the average error of proposed ABC algorithm has been 0.371% higher than best solution of all methods, it could improve the solution of 3 problems with average of 3.305%. The proposed algorithm has been better than basic ABC in all tested problems with average of 0.570%.

Transformation operators based grey wolf optimizer for travelling salesman problem

In the field of swarm intelligence, the Grey Wolf Optimizer (GWO) is a popular algorithm based on leadership hierarchy. Primarily, GWO was proposed to solve continuous optimization problem. However, in recent years, GWO has been extensively explored to deal with a wide variety of real world problem regardless the nature of problem. GWO has received a lot of attention from researchers because of its advantages over other swarm intelligence approaches and its simplicity. The classical GWO is redesigned in this paper by incorporating the swap, shift and symmetry transformation operators to solve permutation-coded travelling salesman problem (TSP), and it is named as transformation operator based grey wolf optimizer (TO-GWO). In TO-GWO, each wolf represents a possible solution of TSP and using swap, shift and symmetry operators wolves interact with leader wolves in order to obtain optimal solution for TSP. In order to improve the proposed algorithm’s local search capability when solving discrete problems, 2-opt algorithm have also been adapted. The TO-GWO is implemented in MATLAB environment. In this study, the TO-GWO is tested over 50 TSP instances. Also, the results of proposed algorithm are compared with 12 state-of-the-art algorithms for TSP instances with various numbers of cities in order to evaluate its performance. For the majority of the TSP instances used in the experiment, the TO-GWO significantly outperforms other algorithms in terms of quality of solutions and efficiency.