Hybrid Lion Swarm Optimization Algorithm for Solving Traveling Salesman Problem

Here, we develop new heuristic algorithm for solving TSP (Travelling Salesman Problem). In our proposed algorithm, the agent cannot estimate tour lengths but detect only a few neighbor sites. Under the circumstances, the agent occasionally ignores the NN method (choosing the nearest site from current site) and chooses the other site far from current site. It is dependent on relative distances between the nearest site and the other site. Our algorithm performs well in symmetric TSP and asymmetric TSP (time-dependent TSP) conditions compared with the NN algorithm using some TSP benchmark datasets from the TSPLIB. Here, symmetric TSP means common TSP, where costs between sites are symmetric and time-homogeneous. On the other hand, asymmetric TSP means TSP where costs between sites are time-inhomogeneous. Furthermore, the agent exhibits critical properties in some benchmark data. These results suggest that the agent performs adaptive travel using limited information. Our results might be applicable to nonclairvoyant optimization problems.

This paper is concerned with the discrete combinatorial optimization problem. A novel set-based differential evolution (SBDE) algorithm for traveling salesman problem (TSP) is proposed and evaluated. SBDE is based on a set-based representation scheme that enables SBDE to characterize the discrete search space of TSP. The candidate solution, vector and the arithmetical operator in SBDE are redefined. Numerical experiments are carried out using the TSPLIB of test TSP problems. The obtained results show that the proposed approach is effective in quality for solving TSP.

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

We consider in this paper the adaptation of heuristics used for programming nondeterministic games to the problems of discrete optimization. In particular, we use some “game” heuristic methods of decision-making in various discrete optimization problems. The object of each of these problems is programming anytime algorithms. Among the problems described in this paper, there are the classical traveling salesman problem and some connected problems of minimization for nondeterministic finite automata. The first of the considered methods is the geometrical approach to some discrete optimization problems. For this approach, we define some special characteristics relating to some initial particular case of considered discrete optimization problem. For instance, one of such statistical characteristics for the traveling salesman problem is a significant development of the so-called “distance functions” up to the geometric variant such problem. And using this distance, we choose the corresponding specific algorithms for solving the problem. Besides, other considered methods for solving these problems are constructed on the basis of special combination of some heuristics, which belong to some different areas of the theory of artificial intelligence. More precisely, we shall use some modifications of unfinished branchand-bound method; for the selecting immediate step using some heuristics, we apply dynamic risk functions; simultaneously for the selection of coefficients of the averaging-out, we also use genetic algorithms; and the reductive self-learning by the same genetic methods is also used for the start of unfinished branch-and-bound method again. This combination of heuristics represents a special approach to construction of anytime-algorithms for the discrete optimization problems. This approach can be considered as an alternative to application of methods of linear programming, and to methods of multi-agent optimization, and also to neural networks.

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.

The Traveling Salesman Problem (TSP) is an NP-hard graph search problem. Despite having numerous modifications of the original abstract problem, Time Dependent Traveling Salesman Problem (TD TSP) was one of the most realistic extensions under real traffic conditions. In TD TSP the edges between nodes are assigned higher costs (weights), if they were traveled during the rush hour periods, or crossed the traffic jam regions, such as the city center(s). In this paper we introduce an even more real-life motivated approach, the Intuitionistic Fuzzy Time Dependent Traveling Salesman Problem (IFTD TSP), which is a further extension of the TSP, and also of the classic TD TSP, with the additional notion of using intuitionistic fuzzy sets for the definition of uncertain costs, time, and space of the rush hour—traffic jam region affecting graph sections. In IFTD TSP we use fuzzy memberships and non-memberships sets for estimating the vague costs between nodes in order to quantify the behavior of traffic jam regions, and the rush hour periods. Since intuitionistic fuzzy sets are generalizations of classic fuzzy sets, our approach may be considered an extension and substitution of the original abstract TD TSP problem, even, of the (classic) Fuzzy TD TSP. Lastly, DBMEA (Discrete Bacterial Memetic Evolutionary Algorithm) was applied on the IFTD TSP model, the results of the simulation runs based on some extensions of the benchmarks generated from the original TD TSP data set showed quite good and promising preliminary results.

In this paper we present two recent metaheuristics, particle swarm optimization and differential evolution algorithms, to solve the single machine total weighted tardiness problem, which is a typical discrete combinatorial optimization problem. Most of the literature on both algorithms is concerned with continuous optimization problems, while a few deal with discrete combinatorial optimization problems. A heuristic rule, the smallest position value (SPV) rule, borrowed from the random key representation in genetic algorithms, is developed to enable the continuous particle swarm optimization and differential evolution algorithms to be applied to all permutation types of discrete combinatorial optimization problems. The performance of these two recent population based algorithms is evaluated on widely used benchmarks from the OR library. The computational results show that both algorithms show promise in solving permutation problems. In addition, a simple but very efficient local search method based on the variable neighbourhood search (VNS) is embedded in both algorithms to improve the solution quality and the computational efficiency. Ultimately, all the best known or optimal solutions of instances are found by the VNS version of both algorithms.

The Traveling Salesman Problem (TSP) is a classical discrete combinatorial optimization problem that is widely applied in various domains, including robotics, transportation, networking, etc. Although existing studies have provided extensive discussions of the TSP, the issues of improving convergence and optimization capability are still open. In this study, we aim to address this issue by proposing a new algorithm named IDINFO (Improved version of the discretized INFO). The proposed IDINFO is an extension of the INFO (weighted mean of vectors) algorithm in discrete space with optimized searching strategies. It applies the multi-strategy search and a threshold-based 2-opt and 3-opt local search to improve the local searching ability and avoid the issue of local optima of the discretized INFO. We use the TSPLIB library to estimate the performance of the IDINFO for the TSP. Our algorithm outperforms the existing representative algorithms (e.g., PSM, GWO, DSMO, DJAYA, AGA, CNO_PSO, Neural-3-OPT, and LIH) when tested against multiple benchmark sets. Its effectiveness was also verified in the real world in solving the TSP in short-distance delivery.

<p indent="0mm">As a high-performance general-purpose form of parallel solvers, parallel algorithm portfolios (PAPs) have recently shown great performance for solving decision, counting, continuous, and discrete optimization problems. However, the manual construction of PAPs is laborious work, which typically requires substantial domain knowledge and human effort. To address this issue, this paper proposes AutoPAP, an evolutionary intelligence-based method for PAP construction. Overall, AutoPAP follows the (<italic>n</italic>+1) evolutionary framework, i.e., in each generation, <italic>n</italic> candidate algorithms are generated, and the best one among them is retained in the PAP. Considering that the algorithm configuration space is typically very large, this study designs a highly effective mutation operator to improve the practical performance of AutoPAP and further theoretically proves that AutoPAP can achieve (1−1/<italic>e</italic>) approximation. Finally, to validate the effectiveness of AutoPAP, this study uses it to build a PAP, namely, TSP_PAP, for traveling salesman problems (TSPs). The test results show that TSP_PAP significantly outperforms state-of-the-art TSP solvers EAX and LKH in terms of efficiency (runtime) and effectiveness (solution quality). On 128 TSP instances of sizes ranging from 1000 to 30000, compared with LKH and EAX, TSP_PAP can reduce the average runtime by at least 45.71% and lower the average deviation ratio by at least 87.50%, indicating the huge potential of AutoPAP in automatic algorithm design and evolution.

Traveling salesman problem (TSP) means that a travelling salesman needs to promote products in n cities (including the city where he lives). After visiting each city (each city can be visited once), he returns to the departure city. Let’s suppose that there is one road to connect each two cities. What is the best route to follow in order to minimize the distance of the journey? TSP has been proven to be a NP-hard problem, i.e. failure of finding a polynomial time algorithm to get a optimal solution. TSP is easy to interpret, yet hard to solve. This problem has aroused many scholars’ interests since it was put forward in 1932. However, until now, no effective solution has been found. Though TSP only represents a problem of the shortest ring road, in actual life, many physical problems are found to be the TSP. Example 1, postal route. Postal route problem is a TSP. Suppose that a mail car needs to collect mails in n places. Under such circumstances, you can show the route through a drawing containing n+1 crunodes. One crunode means a post office which this mail car departures from and returns to. The remaining n crunodes mean the crunodes at which the mails need to be collected. The route that the mail car passes through is a travelling route. We hope to find a travelling route with the shortest length. Example 2, mechanical arm. When a mechanical arm is used to fasten the nuts for the ready-to-assembling parts on the assembly line, this mechanical arm will move from the initial position (position where the first nut needs to be fastened) to each nut in proper order and then return to the initial position. The route which the mechanical arm follows is a travelling route in the drawing which contains crunodes as nuts; the most economical travelling route will enable the mechanical arm to finish its work within the shortest time. Example 3, integrated circuit. In the course of manufacturing the integrated circuit, we often need to insert thousands of electrical elements. It will consume certain energy when moving from one electrical element to the other during manufacturing. How can we do to arrange the manufacturing order to minimum the energy consumption? This is obviously a solution for TSP. Except for the above examples, problems like route distribution of transportation network, choice of tourist route, laying of pipelines needed for city planning and engineering construction are interlinked with the problems of finding the shortest route. So, it is of significance to make a study on the problem of the shortest route. This renders us a use value. As finding a solution for TSP plays an important role in the real life, since the TSP appeared, it has attracted many scholars to make a study on it.

The traveling salesman problem (TSP) is a classic problem in optimization, frequently used for measuring the performance of optimization algorithms. The goal in solving the TSP is to determine the lowest-cost circuit through a set of cities on a graph. Ant colony optimization (ACO) algorithms, inspired by nature, use simulated ants that modify their environment through laying and removing pheromone, represented by weights on the edges of the graph connecting each city. In this study, a novel algorithm is developed, Multi-Colony System (MCS), which uses multiple colonies of simulated ants in combination to produce superior solutions to the TSP. In comparison with Ant Colony System (ACS), a standard well-performing ACO algorithm, MCS has displayed improved performance, producing tours up to 19.4% shorter than those of ACS in the same amount of time. The performance of MCS in this study presents potential advantages in applications beyond the TSP, including the ability of multiple colonies to both develop a greater number of solutions simultaneously and to more efficiently avoid local maxima in the search space.

The traveling salesman problem (TSP) is one of the most studied problems in combinatorial optimization. Given a set of nodes and the distances between them, it consists in finding the shortest route that visits each node exactly once and returns to the first. Nevertheless, more flexible and applicable formulations of this problem exist and can be considered. The Steiner TSP (STSP) is a variant of the TSP that assumes that only a given subset of nodes must be visited by the shortest route, eventually visiting some nodes and edges more than once. In this paper, we adapt some classical TSP constructive heuristics and neighborhood structures to the STSP variant. In particular, we propose a reduced 2‐opt neighborhood and we show that it leads to better results in smaller computation times. Computational results with an implementation of a GRASP heuristic using path‐relinking and restarts are reported. In addition, ten large test instances are generated. All instances and their best‐known solutions are made available for download and benchmarking purposes.

Most discrete optimization problems belong to the NP-complete or NP-hard classes. A benchmark problem to assess the performance of new heuristics to solve these classes of problems is the traveling salesman problem (TSP). This paper proposes some modifications on a self-organizing network, named RABNET- TSP, to solve TSP problems. The modified algorithm is compared, with encouraging results, to other proposals from the literature on a number of different TSP instances.

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

Many real-world problems, like microchip design, can be modeled by means of the well-known traveling salesman problem (TSP). Many instances of this problem can be found in the literature. Although several optimization algorithms have been applied to TSP instances, the selection of the more promising algorithm is, in practice, a difficult decision. In this paper, a new meta-learning-based approach is investigated for the selection of optimization algorithms for TSP instances. Essentially, a learning model is trained with TSP instances for which the performance of a set of optimization algorithms is known a priori. Then, the learned model is used to predict the best algorithm for a new TSP instance. Each instance is described by meta-features that capture characteristics of the TSP that affect the performance of the optimization algorithms. Given that the best solution for a given TSP instance can be obtained by several algorithms, the meta-learning problem is considered here to be a multi-label classification problem. Several experiments illustrate the performance of the proposed approach, with promising results.