MODIFICATION OF CROSSOVER OPERATOR ON GA APPLICATION FOR TSP

Genetic Algorithm (GA) has been widely used in many fields of optimization; one of them is Traveling Salesman Problem (TSP). GA in the TSP is primarily used in cases involving a lot of vertices, which is not possible to enumerate the shortest route. One of stages in GA is crossover operation to generate offspring’s chromosome based on parent’s. Example of some crossover operators in GA for TSP are Partially Mapped Crossover (PMX), Order Crossover (OX), Cycle Crossover (CX), and some others. However on constructing the route, they are not considering length of the route to maximize its fitness. The use of random numbers on constructing the route likely produces offspring (a new route) that is not better than its parent. Sequence of nodes in the route affects the length of the route. To minimize uncertainty, then the crossover operation should consider a method to arrange the chromosomes. This article studied incorporating two methods into crossover stage, in order to ensure the offspring has good fitness. Methods to be combined with algorithms are commonly used in the route searching; those are Nearest Neighbor algorithm, and Sequential Insertion. Operators used are CSI (Crossover combined with Sequential Insertion) and CNN (Crossover combined with Nearest Neighbor), named after the method used. Those operators are compared with PMX operator on test using benchmark data from TSPLIB on some independent executions. The tests showed that CSI are better than two other and length of its route was relatively equal to optimal length recorded. Keywords: Genetic Algorithm, Traveling Salesman Problem, Crossover operato

The Traveling Salesman Problem: An Analysis and Comparison of Metaheuristics and Algorithms

One of the most investigated topics in operations research is the Traveling Salesman Problem (TSP) and the algorithms that can be used to solve it. Despite its relatively simple formulation, its computational difficulty keeps it and potential solution methods at the forefront of current research. This paper defines and analyzes numerous proposed solutions to the TSP in order to facilitate understanding of the problem. Additionally, the efficiencies of different heuristics are studied and compared to the aforementioned algorithms’ accuracy, as a quick algorithm is often formulated at the expense of an exact solution

Traveling Salesman Problem

The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance

Determine the Optimal Sequence-Dependent Completion Times for Multiple Demand with Multi-Products Using Genetic Algorithm

Sequencing is the most impact factor on the total completion time , the products sequences inside demands that consist from muti-product and for multiple demands . It is very important in assembly line and batch production . The most important drawback of existing methods used to solve the sequencing problems is the sequence must has a few products and dependent completion time for single demand . In this paper we used genetic algorithm –based Travelling Salesman Problem with Precedence Constraints Approach ( TSPPCA)  to minimize completion time . The main advantage of this new method , it is used to solve the sequencing problems for multiple demand with multi-product In this paper , we compare between modify the assignment method ( MAM ) and genetic algorithm  depend on least completion time , the results discern that   GA  has minimum completion time Keywords: products sequences , completion time , travel salesman problem (TSP ) , TSPPCA , genetic algorithm. 

The Anglerfish algorithm: A derivation of randomized incremental construction technique for solving the traveling salesman problem

Combinatorial optimization focuses on arriving at a globally optimal solution given constraints, incomplete information and limited computational resources. The combination of possible solutions are rather vast and often overwhelms the limited computational power. Smart algorithms have been developed to address this issue. Each offers a more efficient way of traversing the search landscapes. Critics have called for a realignment in the bio-inspired metaheuristics field. We propose an algorithm that simplifies the search operation to only randomized population initialization following the Randomized Incremental Construction Technique, which essentially compartmentalizes optimization into smaller sub-units. This relieves the need of complex operators normally imposed on the current metaheuristics pool. The algorithm is more generic and adaptable to any optimization problems. Benchmarking is conducted using the traveling salesman problem. The results are comparable with the results of advanced metaheuristic algorithms. Hence, suggesting that arbitrary exploration is practicable as an operator to solve optimization problems. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature

HamLib: A library of Hamiltonians for benchmarking quantum algorithms and hardware

In order to characterize and benchmark computational hardware, software, and algorithms, it is essential to have many problem instances on-hand. This is no less true for quantum computation, where a large collection of real-world problem instances would allow for benchmarking studies that in turn help to improve both algorithms and hardware designs. To this end, here we present a large dataset of qubit-based quantum Hamiltonians. The dataset, called HamLib (for Hamiltonian Library), is freely available online and contains problem sizes ranging from 2 to 1000 qubits. HamLib includes problem instances of the Heisenberg model, Fermi-Hubbard model, Bose-Hubbard model, molecular electronic structure, molecular vibrational structure, MaxCut, Max-k-SAT, Max-k-Cut, QMaxCut, and the traveling salesperson problem. The goals of this effort are (a) to save researchers time by eliminating the need to prepare problem instances and map them to qubit representations, (b) to allow for more thorough tests of new algorithms and hardware, and (c) to allow for reproducibility and standardization across research studies