Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
Modern heuristic techniques for combinatorial problems
Modern heuristic techniques for combinatorial problems
New heuristics for packing unequal circles into a circular container
Computers and Operations Research
PERM for solving circle packing problem
Computers and Operations Research
Adaptive and restarting techniques-based algorithms for circular packing problems
Computational Optimization and Applications
A beam search algorithm for the circular packing problem
Computers and Operations Research
An augmented beam search-based algorithm for the circular open dimension problem
Computers and Industrial Engineering
A genetic algorithm with the heuristic procedure to solve the multi-line layout problem
Computers and Industrial Engineering
A probability collectives approach with a feasibility-based rule for constrained optimization
Applied Computational Intelligence and Soft Computing
High density packings of equal circles in rectangles with variable aspect ratio
Computers and Operations Research
Discrete Applied Mathematics
Solving the circular open dimension problem by using separate beams and look-ahead strategies
Computers and Operations Research
Packing unequal circles using formulation space search
Computers and Operations Research
Patterns and pathways of packing circles into a square
International Journal of Computer Applications in Technology
Computers & Mathematics with Applications
Valid constraints for the Point Packing in a Square problem
Discrete Applied Mathematics
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In this paper, we study the problem of cutting a rectangular plate R of dimensions (L, W) into as many circular pieces as possible. The circular pieces are of n different types with radii ri, i = 1 ,..., n. We solve the constrained circular problem, where di the maximum demand for piece type i is specified, using two heuristics: a constructive procedure-based heuristic and a genetic algorithm-based heuristic. Both of these approaches search for a good ordering of the pieces and use an adaptation of the best local position procedure (Studia. Inform. Univ. 2 (1) (2002) 33) to find the "best" layout of this ordered set. This positioning procedure is specifically tailored to circular cutting problems. It acts, for constrained problems, as one of the mutation operators of the genetic algorithm. We compare the performance of both proposed approaches to that of existing approximate and exact algorithms on several problem instances taken from the literature. The computational results show that the proposed approaches produce high-quality solutions within reasonable computational times. The genetic algorithm-based heuristic is easily parallelizable; one of its important features to be investigated in the near future.