This repository contains the solutions obtained by our algorithms that compute piecewise linear approximations of nonlinear bivariate functions given a predefined absolute error and that minimize the number of pieces used.
The details of the algorithms and the description of the benchmark can be found in this paper.
The solutions obtained by algorithms DN99 and DN95 are stored in files 'DN99.txt' and 'DN95.txt' in the folder 'rawlogs'.
The file "parse_and_plot.jl" contains code in julia with a function called "parse_and_plot_instance", that plots and saves the result of an instance.
To extract information about the solution obtained by algorithm DN99 on instance N1 (f(x)=xy on [2.0,8.0]x[2.0,4.0]) with absolute error 0.05 simply do
julia> T_set, domain, delta, n_pieces, cpu_time, str_exprf = parse_and_plot_instance("DN99", "N1", 0.05)Read the README.txt file in folder src for more information about the input and output of this function
Solutions obtained on instances N1 (f(x)=xy on [2.0,8.0]x[2.0,4.0]) or N3 (f(x)=xsin(y) on [1.0,4.0]×[0.05,3.1])
[1] Aloïs Duguet and Sandra Ulrich Ngueveu (2022). Piecewise linearization of bivariate nonlinear functions: minimizing the number of pieces under a bounded approximation error. In: Ljubić, I., Barahona, F., Dey, S.S., Mahjoub, A.R. (eds) Combinatorial Optimization. ISCO 2022. Lecture Notes in Computer Science, vol 13526. Springer, Cham. https://doi.org/10.1007/978-3-031-18530-4_9