The area of the Pythagoras triangle is the sum of area of the Pythagoras triangle that is smaller than it except some exceptions. The exception is the case of M=2N (M,N is an independent variable of the solutions of Euclid).
Furthermore, these relations are expressed as the sequence and constructed in the Fibonacci series Next, the Pythagoras number is distributed on various parabolas group on the coordinate which assume two axes into two sides sandwiching the right angle. The degree of leaning of the axis of symmetry of the parabola group is 0 in case of the basic formula (Euclid solution) of the Pythagoras number. In addition, it is 0 and ∞ in case of “the unit formula”of sum of area. Furthermore, the axial degree of leaning converges to 2 at an early stage in case of “the general formula”.
The heuristic method we propose solves the flexible job-shop scheduling problem (FJSP) using a solution construction procedure with priority rules. FJSP is more complex than classical scheduling problems in that operations are processed on one of multiple candidate machines, one of which must be selected to get a feasible solution. The solution construction procedure with priority rules is implemented on top of the efficient existing method for solving the FJSP which consists of a genetic algorithm and a local search method. The performance of the proposed method is analyzed using various benchmark problems and it is confirmed that our proposed method outperforms the existing method on problems with particular conditions. The conditions are further investigated by applying the proposed method on newly created benchmark.