Malfatti’s constrained optimization problem
DOI:
https://doi.org/10.5564/jimdt.v5i1.3205Keywords:
Malfatti’s problem, Nonconvex optimization, circle, triangleAbstract
In 1803 Italian mathematician Malfatti posed the following problem how to pack three non-overlapping circles of maximum total area in a given triangle. Malfatti originally assumed that the solution to this problem are three circles inscribed in a triangle such that each circle tangent to other two and touches two sides of the triangle. Now it is well known that Malfatti’s solution is not optimal. The problem for the first time was treated as a global optimization problem in Enkhbat [9]. In this paper, we consider a new formulation of Malfatti’s problem called Malfatti’s constrained optimization problem. The new problem is formulated as a nonconvex optimization problem with nonlinear constraints. Numerical experiments were conducted on Python for the cases.
Мальфаттын зааглалтай бодлого
Хураангуй: 1803 онд анх Италийн математикч Мальфатт өгөгдсөн гурвалжинд хамгийн их талбайтай, давхцахгүйгээр гурван тойргийг хэрхэн байрлуулах вэ? гэсэн бодлогыг тавьж байсан бөгөөд энэхүү бодлогын шийд нь гурвалжинд багтсан гурван тойргуудын тойрог бүр нөгөө хоёр тойргийг, гурвалжны хоёр талыг шүргэсэн байна гэж үзсэн.
Энэ нь хараахан оновчтой шийд биш байсан ба [9] ажилд анх Мальфаттын бодлогыг бодох глобал оновчлолын бодлогыг томьёолж шийдийг олох арга алгоритм боловсруулсан. Энэхүү судалгаанд бид Мальфаттын бодлогын шинэ томьёолол буюу Хөдөлгөөнт Мальфаттын бодлогыг авч үзсэн. Тус бодлого нь шугаман бус хязгаарлалттай гүдгэр бус оновчлолын бодлого юм. Тоон туршилтыг Python дээр хийсэн.
Түлхүүр үгс: Мальфаттын бодлого, гүдгэр бус оновчлол, тойрог, гурвалжин
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