Introduction to operations research, 4th ed.
Introduction to operations research, 4th ed.
Combinatorial optimization
Integer Programming Formulation of Traveling Salesman Problems
Journal of the ACM (JACM)
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms and Manufacturing Systems Design
Genetic Algorithms and Manufacturing Systems Design
Genetic Algorithms for the Travelling Salesman Problem: A Review of Representations and Operators
Artificial Intelligence Review
Finding Cuts in the TSP (A preliminary report)
Finding Cuts in the TSP (A preliminary report)
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This paper examines the problem of determining the sequence in which to cast aluminium ingots such that setup times are minimized. The aluminium ingots are of different size and consist of different alloys; this poses constraints on the allowable ordering of casting jobs. The sequencing problem can be formulated as an asymmetric traveling salesman problem with additional constraints. Two different methods are used to formulate and solve this problem, a genetic algorithm (GA) and an integer programming approach (IP). A new method for detecting sub-tours in the IP formulation is set forth and used. Both the GA and IP approach are implemented in a software tool that is being used in the aluminium production industry. The results show that even though the integer programming formulation can be used to solve the problem to optimality, the size of the problem is a limiting factor for practical implementation. Therefore, the genetic algorithm is used in the industrial implementation with good results.