Solving Capacitated Vehicle Routing Problem with route optimization using Swarm Intelligence

Fuzzy systems (FSs) have been extensively applied to automatic control, pattern recognition, and decision analysis. However, a common bottleneck is encountered in the derivation of fuzzy rules, which is often difficult, time consuming, and relies on expert knowledge. To automate the design of FSs, many metaheuristic learning algorithms have been proposed. One major optimization category uses Swarm Intelligence (SI) model (Kennedy et al., 2001). The SI technique studies collective behavior in decentralized systems. Its development was based on mimicking the social behavior of animals or insects in an effort to find the optima in the problem space. SI models are initialized with a population of random solutions. One well-known SI model is particle swarm optimization (PSO) (Kennedy & Eberhart, 1995). Many modified PSO models have been proposed and successfully applied to different optimization problems (Clerc & Kennedy, 2002; Bergh & Engelbrecht, 2004; Ratnaweera et al., 2004; Juang, 2004; Kennedy & Mendes, 2006; Parrott & Li, 2006; Chen & Li, 2007). FS design using PSO has also been proposed in several studies (Juang, 2004; Chatterjee et al., 2005; Juang et al., 2007; Araujo & Coelho, 2008; Sharma et al., 2009). Another well-known SI is ant colony optimization (ACO) (Dorigo & Stutzle, 2004). The ACO technique is inspired by real ant colony observations. It is a multi-agent approach that was originally proposed to solve difficult discrete combinatorial optimization problems, such as the traveling salesman problem (TSP) (Dorigo et al., 1996; Dorigo & Gambardella, 1997). In the original ACO meta-heuristic, artificial ant colonies cooperate to find good solutions for difficult discrete optimization problems. Different ACO models have been applied to FS design problems (Cassillas et al., 2000; Cassillas et al., 2005; Mucientes & Casillas; 2007; Juang & Lo, 2007; Juang et al., 2008; Juang & Lu; 2009). In (Cassillas et al.,2000; Mucientes & Casillas; 2007; Juang et al., 2008; Juang & Lu; 2009), the FS input space was partitioned in grid type with antecedent part parameters of an FS manually assigned in advance. In (Juang & Lo, 2007), the FS input space was flexibly partitioned using a fuzzy clustering-like algorithm in order to reduce the total number of rules. For all of these studies, the consequent part parameters were optimized in discrete space using ACO. Since only the consequent part parameters are optimized, and the optimization space is restricted to be discrete, the designed FSs are unsuitable for problems where high accuracy is a major concern. Source: Fuzzy Systems, Book edited by: Ahmad Taher Azar, ISBN 978-953-7619-92-3, pp. 216, February 2010, INTECH, Croatia, downloaded from SCIYO.COM

The Capacitated Vehicle Routing Problem (CVRP) presents significant challenges in shipping route optimization and logistics management. These challenges include balancing vehicle capacity, minimizing travel distance, and efficiently grouping delivery points, all of which are crucial for enhancing operational efficiency and reducing costs. This research aims to apply a combination of the Sweep and Nearest Neighbor algorithms to address the CVRP, seeking to improve route efficiency and manage vehicle capacity effectively. The Sweep algorithm is employed to cluster pickup points based on their polar angle from the depot, facilitating efficient grouping and optimal vehicle capacity management. Within each cluster, the Nearest Neighbor algorithm is implemented to optimize the sequence of visits, minimizing total travel distance by sequentially selecting the next closest point. The Haversine Distance is used to calculate the distances between points, ensuring geographical accuracy compared to the Euclidean method. Experimental results demonstrate that this hybrid approach yields shorter routes. Quantitative analysis shows a significant reduction 13% in total travel distance when using this combination of algorithms, highlighting its effectiveness in solving the CVRP. This research demonstrates that combining the Sweep and Nearest Neighbor algorithms provides an efficient solution to the CVRP, improving route optimization and vehicle capacity management. The findings contribute valuable insights to logistics management, with practical implications for enhancing shipping route efficiency.

<p><strong>Context and relevance.</strong>The traveling salesman problem (TSP) is one of the key NP-hard combinatorial optimization problems with wide applications in logistics, transportation planning, and other fields. Exact methods for solving TSP become inefficient as the problem dimension increases, making the use of metaheuristic methods such as simulated annealing (SA), ant colony optimization (ACO), and particle swarm optimization (PSO) relevant. <strong>Objective. </strong>To conduct a comparative analysis of the effectiveness of SA, ACO and PSO for solving the traveling salesman problem with 100 points, to evaluate their convergence and to identify the optimal parameters. <strong>Hypothesis. </strong>The ant algorithm, due to the pheromone trail mechanism, will provide higher accuracy of solutions compared to SA and PSO, but will require more computational resources. <strong>Methods and materials. </strong>The study conducted computational experiments with varying parameters of each algorithm. For SA, the initial temperature and cooling coefficient were analyzed, for ACO, the influence of pheromones and distances, for PSO, the cognitive and social coefficients. <strong>Results. </strong>ACO showed the best results, finding a route with a length of 9.23, demonstrating high efficiency for medium-sized problems. PSO took an intermediate position with a route length of 32.64, making it suitable for moderately complex problems. SA was the least effective, with a route length of 45.2, which limits its use for complex routing networks. <strong>Conclusions. </strong>The ant algorithm demonstrated the greatest efficiency due to the balance between exploring the solution space and exploiting the found routes, which is especially important for maritime Arctic logistics, where sustainable route optimization is required under high uncertainty. PSO showed good convergence, but it is inferior to ACO in terms of accuracy. SA, despite its simplicity, is less effective for high-dimensional problems. The obtained results are of particular practical value for route optimization in the Arctic region, where traditional methods often prove to be ineffective.</p>

The capacitated vehicle routing problem (CVRP) is regarded as an NP-hard problem. Moreover, the CVRP is described as a model that can be used in many applications such as transport, logistics, and distribution. The exact algorithms can find exact optimal solutions on the small-sized problem instances; however, for large-sized instances it is difficult to find the exact optimal solutions in polynomial time. This reason motivated the researchers to present heuristic/metaheuristic algorithms to solve large-sized problem instances within a reasonable computational time. One of the good algorithms that deal with the CVRP is the ant colony optimization (ACO) algorithm. Several ACO algorithms have been suggested in the literature, such as the ant system (AS) algorithm, ant colony system (ACS) algorithm, and so on. On the other hand, ACO is designed to solve the path problem that finds the best way. However, this algorithm still lacks exploratory mechanisms, which results in premature convergence and stagnation issues. Therefore, we propose to develop an enhanced ACS (EACS) algorithm for solving the CVRP based on subpaths. In our proposed algorithm, we propose to utilize the K-nearest neighbour (KNN) algorithm for finding the best initial solution and then enhance the diversity mechanism of the proposed algorithm by avoiding the generation of the same solution using subpaths. This uses the diversity of the generated solution to find a better solution with a shorter route in a reasonable amount of computational time. Furthermore, we propose to apply the three-opt algorithm to the completed subtour and the k-opt algorithm to the subpath gained from the experience of the subpath. Finally, to verify the effectiveness of the proposed EACS algorithm, the algorithm is tested on some CVRP instances and is compared with one of the state-of-the-art methods, namely, the enhanced simulated annealing algorithm. The comparative study showed a better performance of our EACS compared to the enhanced simulated annealing algorithm.

Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO) algorithms have attracted the interest of researchers due to their simplicity, effectiveness and efficiency in solving real world optimization problems. Swarm-inspired optimization has recently become very popular. Both ACO and PSO are successfully applied in the Traveling Salesman Problem (TSP). Our approach consists in combining Fuzzy Logic with ACO (FACO - Fuzzy Ant Colony Optimization) and PSO (FPSO - Fuzzy Particle Swarm Optimization) for solving the TSP. Experimental results and comparative studies illustrate the importance of Fuzzy logic in reducing the time and the best length for the TSP problems considered.

This chapter presents a hybrid method of swarm intelligence current. Intelligence represented by ant colonies has been enriched with fuzzy logic arithmetics. In this case Kosinski’s Ordered Fuzzy Numbers were specifically used. Apart from a fuzzy decision model of a single ant used earlier by other researchers, the author used the order as a trend support. By associating the direction of a number in Ordered Fuzzy Numbers (OFNs) with the trend observed in the ant colony it is possible to provide a unique description of a fuzzy observation of a colony behavior. The experiments were carried out in the area of searching for the optimal connecting route in the field. The experiment covered 10 complex issues of searching for the optimal route. All are benchmarks from the TSPlib repository which are well known among researchers. They represent the actual problems of route selection such as transport connections depending on geographic conditions and optimizing the machining process or the layout of the power networks. The complexity level of optimal solutions for problems to be solved amounted from several hundred to several thousand connections. Each of them was solved using six swarm intelligence methods and five well-known classical methods dedicated to the traveling salesman problem (TSP). The results were presented in the form of tables and graphs, and some of the routes were shown in graphical form. Final conclusions of the experiment indicate the superiority of methods based on ant colony optimization as regards closeness to optimal solutions. The results achieved by the OFNAnt method are generally better (in 92% of cases) than those achieved by classic methods and are in the forefront of solutions from the swarm intelligence group.

Particle swarm optimization (PSO) is adopted to solve capacitated vehicle routing problems (CVRPs). A nonlinear S decrease curve is employed to adjust the inertia weight of PSO to balance global and local searches. Meanwhile, local search and path relink are also involved to improve the quality of solutions. Experiments were conducted on Auger at problems in the OR Library. Experimental results will were compared with those from other studies. Experimental results prove the algorithm designed in this article can effectively solve capacitated type vehicle routing problems.

Swarm intelligence is a relatively new approach to problem solving that takes inspiration from the social behaviors of insects and other animals. Ants, in particular, have inspired a number of methods and techniques among which the most studied and successful is the general-purpose optimization technique, also known as ant colony optimization, In computer science and operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs. Ant Colony Optimization (ACO) algorithm is used to arrive at the best solution for TSP. In this article, the researcher has introduced ways to use a great deluge algorithm with the ACO algorithm to increase the ability of the ACO in finding the best tour (optimal tour). Results are given for different TSP problems by using ACO with great deluge and other local search algorithms.

Ant colony optimization (ACO) algorithm is a metaheuristic inspired by the behavior of real ants in their search for the shortest path to food sources. The ACO algorithm takes on these characteristics of robust, positive feedback distributed computing, easy fusing with other algorithms. But the basic ACO algorithm has some deficiencies of premature and stagnation phenomenon in the evolution process, and is easily trapped into local optimal solution. And it is difficult to explore other solutions in the neighbor space. So a improved ACO(DPSEMACO) algorithm based on dual population strategy, bi-directional dynamic adjust evaporation factor strategy of the pheromone and parallel strategy is proposed to solve the traveling salesman problem(TSP). In the DPSEMACO algorithm, the ants are divided into the two subpopulations by borrowing the mutual cooperation mechanism of biological community, which evolve separately and exchange information timely. The bi-directional dynamic adjusting evaporation factor strategy of the pheromone is used to change the corresponding path pheromone of different subpopulations in order to avoid to trap into a local optimum. The parallel strategy can avoid falling into a local optimum. And the DPSEMACO algorithm can expand the search space and improve the overall searching performance by repeated changing the pheromone of the each subpopulation and adaptive adjusting evaporation factor. Finally, in order to prove the optimization performance of the proposed DPSEMACO algorithm, some classic TSP instances are selected from the TSPLIB in this paper. And some existing methods are selected to compare the optimization performance with the proposed DPSEMACO algorithm. The experimental results demonstrate that the proposed DPSEMACO algorithm is feasible and effective in solving TSP, and takes on a good global searching ability and high convergence speed.

Fuzzy C-Means (FCM) clustering technique is among the most effective partitional clustering algorithms available in the literature. The Capacitated Vehicle Routing Problem (CVRP) is an important industrial logistics and managerial NP-hard problem. Cluster-First Route-Second Method (CFRS) is one of the efficient techniques used to solve CVRP. In CFRS technique, customers are first divided into clusters in the first phase, then each cluster is solved independently as a Traveling Salesman Problem (TSP) in the second phase. This research is concerned with the clustering phase of CFRS, and TSP is then solved using a traditional optimization method. Three supervised FCM based techniques are proposed to solve the clustering phase at reduced cost via centroids (pre-FCM) initialization phase. The proposed pre-FCM initialization techniques are developed to be problem dependent. Hence, three initialization techniques are first developed using K-means technique, spatially equally distributed, and demand weighted center of mass. Then, a modified demand weighted fuzzy c-means objective function is employed to assign customers to clusters. To compare the performance of the proposed supervised FCM techniques, forty-two CVRP benchmark problems are solved using the traditional fuzzy C-means algorithm and the developed algorithms. Extensive comparisons are conducted between the traditional fuzzy C-means algorithm, the three proposed initialization techniques, and other fuzzy C-means techniques available in the literature. Results show that the proposed three initialization techniques are efficient in terms of solution quality and computational cost.

The Traveling Salesman Problem (TSP) is a combinatorial optimization problem which has a plethora of real-world applications in various domains. Since large scale TSP problems are difficult to be solved by deterministic algorithms in a reasonable amount of time, heuristic and meta-heuristic algorithms such as swarm intelligence algorithms are usually used for solving TSP. These algorithms provide near-optimal solutions in a feasible amount of time. The Dragonfly Algorithm (DA) is a recent swarm intelligence algorithm and it has shown to have a higher performance as compared to other swarm intelligence algorithms in various applications. Since the original DA algorithm is proposed for solving continuous optimization problems, it cannot be used for solving TSP and although a binary version of the algorithm, called BDA, is also proposed, it is not suitable for solving TSP. Hence, in this paper, a variant of the DA algorithm is proposed. DA is adapted for solving TSP by adapting its equations and making use of the method of swap sequences to update the position of the artificial dragonflies in the search space. The algorithm is employed to solve a TSP problem which consists of four cities and the results show that the proposed algorithm is able to provide the optimal TSP path.

Two kinds of sensors will be discussed in some sort of wireless sensor networks (WSNs). One is named a normal sensor (called A_nodes) with fixed initial energy, which can get perception data from the surrounding environment and have functions of storage and forwarding. The other is named relay sensor (called B_node) with sufficient energy, which only can store data and forward data. Cluster heads (called A_heads) are chosen among A_nodes by probability mode to create clusters first. Local adjustments would be done inter-cluster. Then the sink is selected as the root and a backbone shortest path tree with hops limited is built dynamically from A_heads, B_Nodes and sink. Inside the backbone shortest path aggregation tree, two steps are done. The first step, select some B_node as cluster head (denoted as B_node) and make local adjustment intra-clusters if it is possible. The second step, adjust the shortest path aggregation tree. By using both particle swarm optimization (PSO) and ant colony optimization (ACO), a traveling salesman problem (TSP) cycle with shorter path length is obtained (this method is noted as TSP_PSO_ACO). This TSP cycle consists of all nodes in the aggregation backbone tree. Along this cycle, energy is offered to nodes except sink. The above strategy would be discussed for its feasibility and time complexity. The experimental results imply that the energy consumption is reduced by using local adjustment. The relative failure rate of nodes can be reduced in the later stage of WSN survival. Offering energy to a small number of nodes several times has no obvious impact on the overall energy consumption and survival time of WSN. The case with some small-sized obstacles in WSN area is also discussed. There are little affections on TSP cycles both from results on theoretical analysis and simulation if there are some obstacles with small size in WSN area.

The capacitated Vehicle Routing Problem with structured Time Windows (cVRPsTW) is concerned with finding optimal tours for vehicles with given capacity constraints to deliver goods to customers within assigned time windows. In our problem variant these time windows have a special structure, namely they are non-overlapping and each time window holds several customers. This is a reasonable assumption for Attended Home Delivery services. Sweep algorithms are known as simple, yet effective heuristics for the classical capacitated Vehicle Routing Problem. We propose variants of the sweep algorithm that are not only able to deal with time windows, but also exploit the additional structure of the time windows in a cVRPsTW. Afterwards we suggest local improvement heuristics to decrease our objective function even further. A carefully constructed benchmark set that resembles real-world data is used to prove the efficacy of our algorithms in a computational study.

The Vehicle Routing Problem (VRP) is an important problem occurring in many distribution systems, which is also defined as a family of different versions such as the Capacitated Vehicle Routing Problem (CVRP) and the Vehicle Routing Problem with Time Windows (VRPTW). The Ant Colony Optimization (ACO) is a metaheuristic for combinatorial optimization problems. Given the ACO inadequacy, the vehicle routing optimization model is improved and the transfer of the algorithm in corresponding rules and the trajectory updated regulations is reset in this paper, which is called the Improved Ant Colony Optimization (I-ACO). Compared to the calculated results with genetic algorithm (GA) and particle swarm optimization (PSO), the correctness of the model and algorithm is verified. Experimental results show that the I-ACO can quickly and effectively obtain the optimal solution of VRFTW.

Objectives: A well-known NP-complete problem is the travelling salesman problem (TSP). It has numerous engineering and scientific applications. In this article, we have proposed a multi-conveyance TSP where different conveyances are present to travel from one city to another city. This is an extension to classical TSP. In this TSP, the salesman visits all the cities only once during his/her tour, using different conveyances to travel from one city to another. The cost of travelling between cities using various modes of conveyance varies. The objective of this research is to find the minimum cost tour using an ant colony optimization (ACO) based approach by satisfying the constraints of the proposed multi-conveyance TSP. Method: The considered TSP has been solved using a novel ACO technique. The proposed ACO is adopted with the Roulette-wheel selection and “tuning solution” techniques. We have used a few benchmark datasets from TSPLIB to check the effectiveness of the proposed algorithm. The experimental findings for a few benchmarks TSP instances show that almost always, the proposed ACO is able to find a better result. Then, we used some redefined and randomly generated datasets for experiments. The experimental outcomes for various input datasets are also very encouraging. Findings: The goal of the proposed TSP is to find a complete tour with a minimum cost without exceeding the total travel cost and total travel time. Thus, there are two novel constraints in the classical TSP. Novelty: A unique aspect of the proposed research is the use of several conveyance facilities and a fixed total travel time and cost. This is new, as these three factors are integrated into a single TSP model. Keywords: Travelling Salesman Problem; Travel Cost; Travel Time; MultiConveyance TSP; Ant Colony Optimization