Annealing strategy-based layout method for circle packing problem

Abstract

The invention relates to an annealing strategy-based layout method for a circle packing problem, and the problem is that n given round cakes are arranged in a regular triangle container in a way that every two round cakes are not embedded mutually, wherein the side length of the triangle is L, and the minimal value of the L is determined. The method comprises the following steps: A, reading an input file, namely, data including the number of the round cake to be arranged and the Ri thereof (i is larger than or equal to 1 and smaller than or equal to n) for test cases; B, converting the problem of the circle packing problem in the triangular container into an unconstrained layout optimization problem through a quasi content strategy; C, solving the circle packing problem in the triangular container through a heuristic simulated annealing algorithm; D, taking the final layout obtained from the algorithm as an initial layout, and carrying out binary search to the side length L; and E, outputting the final result in a way of graphics and documents. The method provided by the invention has high feasibility and high processing speed, can obtain the result closer to a global optimal solution, and can be widely used to solve other layout optimization problems.

Description

technical field [0001] The invention relates to a layout method for a circular packing problem based on an annealing strategy, which is mainly used in the fields of object stacking, transportation, raw material blanking, spacecraft layout design, industrial layout planning and the like. Background technique [0002] The packing problem studies the placement of multiple circular objects in a large space or container without embedding each other, and it is required to maximize the utilization of the space or container. The circular packing problem is a kind of packing problem, which has a wide range of applications in the fields of object stacking, transportation, raw material cutting, spacecraft layout design and industrial layout planning. In theory, this problem belongs to NP-hard problem [1]. At the same time, in recent years, the industry has spent a lot of money on research. The reason is that effectively solving this type of problem can not only save a lot of resources,...

AI Technical Summary

Problems solved by technology

Compared with the random algorithm, the deterministic algorithm has fast search speed and high precision, but its universality is not strong, and it is easy to fall into the trap of local minimum points; the random algorithm has the advantages of global search and wide adaptability, but lacks effective Local search mechanism, and the convergence speed is slow

[0004] Analyzing the advantages and disadvantages of the above two types of algorithms, it can be seen that it is difficult to effectively obtain the optimal solution of the circular packing problem by using any algorithm alone.

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