2-opt Search Research Articles

Hybrid Genetic Algorithms for the Asymmetric Distance-Constrained Vehicle Routing Problem

We aim to suggest a simple genetic algorithm (GA) and other four hybrid GAs (HGAs) for solving the asymmetric distance-constrained vehicle routing problem (ADVRP), a variant of vehicle routing problem (VRP). The VRP is a difficult NP-hard optimization problem that has numerous real-life applications. The VRP aims to find an optimal tour that has least total distance (or cost) to provide service to n customers (or nodes or cities) utilizing m vehicles so that every vehicle starts journey from and ends journey at a depot (headquarters) and visits every customer only once. The problem has many variations, and we consider the ADVRP for this study, where distance traveled by every vehicle must not exceed a predefined maximum distance. The proposed GA uses random initial population followed by sequential constructive crossover and swap mutation. The HGAs enhance the initial solution using 2-opt search method and incorporate a local search technique along with an immigration procedure to obtain effective solution to the ADVRP. Experiments have been conducted among the suggested GAs by solving several restricted and unrestricted ADVRP instances on asymmetric TSPLIB utilizing several vehicles. Our experiments claim that the suggested HGAs using local search methods are very effective. Finally, we reported a comparative study between our best HGA and a state-of-the-art algorithm on asymmetric capacitated VRP and found that our algorithm is better than the state-of-the-art algorithm for the instances.

Comparison of a Bat and Genetic Algorithm Generated Sequence Against Lead Through Programming When Assembling a PCB Using a Six-Axis Robot With Multiple Motions and Speeds

An optimal component feeder arrangement and robotic placement sequence are both important for improving assembly efficiency. Both problems are combinatorial in nature and known to be NP-hard. This article presents a novel discrete hybrid bat-inspired algorithm for solving the feeder slot assignment and placement sequence problem encountered when planning robotic assembly of electronic components. In our method, we use the concepts of swap operators and swap sequence to redefine position and velocity operators from the basic bat algorithm (BA). Furthermore, we propose an improved local search method based on genetic operators of crossover and mutation enhanced by the 2-opt search procedure. The algorithm is formulated with the objective of minimizing the total traveling distance of the pick-and-place device. Through numerical experiments, using a real printed circuit board (PCB) assembly scenario, we demonstrate the considerable effectiveness of the proposed discrete BA to improve the selection of feeder arrangement and placement sequence in PCB assembly operations and achieve high throughput production. The results also highlighted that even though the algorithms outperformed traditional lead through programming techniques, the programmer must consider the influence of different robot motions and speeds.

Experimental Study of Hybrid Genetic Algorithms for the Maximum Scatter Travelling Salesman Problem

We consider the maximum scatter travelling salesman problem (MSTSP), a travelling salesman problem (TSP) variant. The problem aims to maximize the shortest edge in the tour that travels each city only once in the given network. It is a very complicated NP-hard problem, and hence, exact solutions are obtainable for small sizes only. For large sizes, heuristic algorithms must be applied, and genetic algorithms (GAs) are observed to be very successful in dealing with such problems. In our study, a simple GA (SGA) and four hybrid GAs (HGAs) are proposed for the MSTSP. The SGA starts with initial population produced by sequential sampling approach that is improved by 2-opt search, and then it is tried to improve gradually the population through a proportionate selection procedure, sequential constructive crossover, and adaptive mutation. A stopping condition of maximum generation is adopted. The hybrid genetic algorithms (HGAs) include a selected local search and perturbation procedure to the proposed SGA. Each HGA uses one of three local search procedures based on insertion, inversion and swap operators directly or randomly. Experimental study has been carried out among the proposed SGA and HGAs by solving some TSPLIB asymmetric and symmetric instances of various sizes. Our computational experience reveals that the suggested HGAs are very good. Finally, our best HGA is compared with a state-of-art algorithm by solving some TSPLIB symmetric instances of many sizes. Our computational experience reveals that our best HGA is better.

Improved genetic algorithms for the travelling salesman problem

The travelling salesman problem (TSP) is a benchmark problem in which a salesman has to visit all nodes (cities) in a network exactly once except the starting node, come back to the starting node and find the shortest tour. Genetic algorithm (GA) is one of the best algorithms to deal with the travelling salesman problem (TSP). In GA, crossover operator plays a vital role and the sequential constructive crossover (SCX) is one of the best crossover operators for solving the TSP. Several improvements have been proposed for other crossover operators. In this paper we propose four improved genetic algorithms using three local search methods – 2-opt search, a hybrid mutation, and a combined mutation operator, and incorporate them into SCX. The experimental results on some TSPLIB instances show that our improved GAs can significantly improve simple GA using SCX in terms of solution quality.

The Ordered Clustered Travelling Salesman Problem: A Hybrid Genetic Algorithm

The ordered clustered travelling salesman problem is a variation of the usual travelling salesman problem in which a set of vertices (except the starting vertex) of the network is divided into some prespecified clusters. The objective is to find the least cost Hamiltonian tour in which vertices of any cluster are visited contiguously and the clusters are visited in the prespecified order. The problem is NP-hard, and it arises in practical transportation and sequencing problems. This paper develops a hybrid genetic algorithm using sequential constructive crossover, 2-opt search, and a local search for obtaining heuristic solution to the problem. The efficiency of the algorithm has been examined against two existing algorithms for some asymmetric and symmetric TSPLIB instances of various sizes. The computational results show that the proposed algorithm is very effective in terms of solution quality and computational time. Finally, we present solution to some more symmetric TSPLIB instances.

An experimental study of a hybrid genetic algorithm for the maximum traveling salesman problem

Purpose: In this paper, we consider the maximum traveling salesman problem, a variation of the usual traveling salesman problem, in which the objective is to maximize the cost of a tour of the salesman. The main purpose of this paper is to develop a hybrid genetic algorithm (GA) for obtaining a heuristically optimal solution to the problem. Methods: First, a simple GA and then a hybrid GA have been proposed to solve the problem. As crossover operator plays a vital role in GAs, we modify the sequential constructive crossover operator for our simple GA to solve the problem. To improve the quality of the solution obtained by the crossover operator, restricted 2-opt search is applied. Then a hybrid GA is developed by incorporating a new local search algorithm to the simple GA in order to obtain a heuristic solution to the problem. Results: We compare the efficiency of our hybrid GA against an existing heuristic algorithm for symmetric traveling salesman problem library (TSPLIB) instances. Finally, we present solutions to the problem for asymmetric TSPLIB instances. Since, to the best of our knowledge, no literature presents solution for asymmetric instances, hence, we could not carry out any comparative study to show the efficiency of our hybrid GA for the asymmetric instances. Conclusions: The comparative study shows the effectiveness of our hybrid GA.

A Hybrid Genetic Algorithm for the Bottleneck Traveling Salesman Problem

The bottleneck traveling salesman problem is to find a Hamiltonian circuit that minimizes the largest cost of any of its arcs in a graph. A simple genetic algorithm (GA) using sequential constructive crossover has been developed to obtain heuristic solution to the problem. The hybrid GA incorporates 2-opt search, another proposed local search and immigration to the simple GA for obtaining better solution. The efficiency of our hybrid GA to the problem against two existing heuristic algorithms has been examined for some symmetric TSPLIB instances. The comparative study shows the effectiveness of our hybrid algorithm. Finally, we present solutions to the problem for asymmetric TSPLIB instances.

New heuristics for solving the economic lot scheduling problem with reworks

In this study, we are interested in the economic lot scheduling problem (ELSP) that considers manufacturing of the serviceable products and remanufacturing of the rework products. In this paper, we formulate a mathematical model for the ELSP with reworks using the common cycle approach in which only one manufacturing lot and only one rework lot for each product exist during a common cycle. In order to solve this problem, we propose two heuristics that not only search for the optimal cycle time and an optimal production sequence, but also utilize a simple scheduling heuristic to schedule the starting time of all the manufacturing and rework lots so as to minimize the average total costs. The first heuristic is a simple heuristic that employs a 2-opt search to obtain a close-to-optimal production sequence. The second heuristic, which is a refined version of the simple heuristic, employs a bisection search to look for an optimal cycle time. In our numerical experiments, we compare the effectiveness of both heuristics using randomly generated instances.