A Genetic Algorithm with the Mixed Heuristics for Traveling Salesman Problem

2015 ◽  
Vol 14 (01) ◽  
pp. 1550003 ◽  
Author(s):  
Yong Wang
Keyword(s):  
Genetic Algorithm ◽  
Traveling Salesman Problem ◽  
Discrete Optimization ◽  
Time Complexity ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Optimization Process ◽  
Hamiltonian Cycles ◽  
Improved Genetic Algorithm ◽  
Discrete Optimization Problems

Traveling salesman problem (TSP) is one of well-known discrete optimization problems. The genetic algorithm is improved with the mixed heuristics to resolve TSP. The first heuristics is the four vertices and three lines inequality, which is applied to the 4-vertex paths to generate the shorter Hamiltonian cycles (HC). The second local heuristics is executed to reverse the i-vertex paths with more than two vertices, which also generates the shorter HCs. It is necessary that the two heuristics coordinate with each other in the optimization process. The time complexity of the first and second heuristics are O(n) and O(n3), respectively. The two heuristics are merged into the original genetic algorithm. The computation results show that the improved genetic algorithm with the mixed heuristics can find better solutions than the original GA does under the same conditions.

scholarly journals On the Classical Version of the Branch and Bound Method

2021 ◽  
pp. 21-44
Author(s):  
Boris Melnikov ◽  
◽  
Elena Melnikova ◽  
Keyword(s):  
Traveling Salesman Problem ◽  
Branch And Bound ◽  
Discrete Optimization ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Branch And Bound Method ◽  
Main Subject ◽  
Classical Version ◽  
The Traveling Salesman Problem ◽  
Discrete Optimization Problems

In the computer literature, a lot of problems are described that can be called discrete optimization problems: from encrypting information on the Internet (including creating programs for digital cryptocurrencies) before searching for “interests” groups in social networks. Often, these problems are very difficult to solve on a computer, hence they are called “intractable”. More precisely, the possible approaches to quickly solving these problems are difficult to solve (to describe algorithms, to program); the brute force solution, as a rule, is programmed simply, but the corresponding program works much slower. Almost every one of these intractable problems can be called a mathematical model. At the same time, both the model itself and the algorithms designed to solve it are often created for one subject area, but they can also be used in many other areas. An example of such a model is the traveling salesman problem. The peculiarity of the problem is that, given the relative simplicity of its formulation, finding the optimal solution (the optimal route). This problem is very difficult and belongs to the so-called class of NP-complete problems. Moreover, according to the existing classification, the traveling salesman problem is an example of an optimization problem that is an example of the most complex subclass of this class. However, the main subject of the paper is not the problem, but the method of its soluti- on, i.e. the branch and bound method. It consists of several related heuristics, and in the monographs, such a multi-heuristic branch and bound method was apparently not previously noted: the developers of algorithms and programs should have understood this themselves. At the same time, the method itself can be applied (with minor changes) to many other discrete optimization problems. So, the classical version of branch and bound method is the main subject of this paper, but also important is the second subject, i.e. the traveling salesman problem, also in the classical formulation. The paper deals with the application of the branch and bound method in solving the traveling salesman problem, and about this application, we can also use the word “classical”. However, in addition to the classic version of this implementation, we consider some new heuristics, related to the need to develop real-time algorithms.

scholarly journals Geometric and game approaches for some discrete optimization problems

2018 ◽  
Author(s):  
Boris Melnikov ◽  
◽  
Elena Melnikova ◽  
Svetlana Pivneva ◽  
Vladislav Dudnikov ◽  
...  
Keyword(s):  
Traveling Salesman Problem ◽  
Discrete Optimization ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Distance Functions ◽  
Statistical Characteristics ◽  
Discrete Optimization Problem ◽  
Geometrical Approach ◽  
Anytime Algorithms ◽  
Discrete Optimization Problems

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.

Discrete Social Spider Algorithm for Solving Traveling Salesman Problem

2021 ◽  
pp. 2150020
Author(s):  
Asieh Khosravanian ◽  
Mohammad Rahmanimanesh ◽  
Parviz Keshavarzi
Keyword(s):  
Genetic Algorithm ◽  
Discrete Optimization ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Fitness Function ◽  
Traveling Salesman ◽  
The Other ◽  
Discrete Optimization Problem ◽  
Social Spider ◽  
Social Spider Algorithm

The Social Spider Algorithm (SSA) was introduced based on the information-sharing foraging strategy of spiders to solve the continuous optimization problems. SSA was shown to have better performance than the other state-of-the-art meta-heuristic algorithms in terms of best-achieved fitness values, scalability, reliability, and convergence speed. By preserving all strengths and outstanding performance of SSA, we propose a novel algorithm named Discrete Social Spider Algorithm (DSSA), for solving discrete optimization problems by making some modifications to the calculation of distance function, construction of follow position, the movement method, and the fitness function of the original SSA. DSSA is employed to solve the symmetric and asymmetric traveling salesman problems. To prove the effectiveness of DSSA, TSPLIB benchmarks are used, and the results have been compared to the results obtained by six different optimization methods: discrete bat algorithm (IBA), genetic algorithm (GA), an island-based distributed genetic algorithm (IDGA), evolutionary simulated annealing (ESA), discrete imperialist competitive algorithm (DICA) and a discrete firefly algorithm (DFA). The simulation results demonstrate that DSSA outperforms the other techniques. The experimental results show that our method is better than other evolutionary algorithms for solving the TSP problems. DSSA can also be used for any other discrete optimization problem, such as routing problems.

Application of an Improved Genetic Algorithm with the Search Space Compression in TSP

2013 ◽  
Vol 765-767 ◽  
pp. 687-689
Author(s):  
Yi Song ◽  
Ni Ni Wei
Keyword(s):  
Genetic Algorithm ◽  
Traveling Salesman Problem ◽  
Random Search ◽  
Search Space ◽  
Traveling Salesman ◽  
Improved Genetic Algorithm ◽  
Space Compression ◽  
Accelerate Convergence ◽  
The Traveling Salesman Problem ◽  
Exponential Relation

The Traveling Salesman Problem is a combinatorial optimization problem, the problem has been shown to belong to the NPC problem, the possible solution of Traveling Salesman Problem and the scale of the cities have the exponential relation, so the more bigger of the scale. In this paper, improve the search process of the genetic algorithm by introducing the idea is to compress the search space. The simulation results show that for solving the TSP, the algorithm can quickly obtain multiple high-quality solutions. It can reduce the blindness of random search and accelerate convergence of the algorithm.

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