The translation has been made by Svetoslav Slavkov. We are grateful for his help on improving our programs.
Archive for the ‘Real Cut 1D’ Category
We have just released version 10 of our linear optimization software.
We have a lot of new things and improvements here:
– fractional input (now you can enter the data either as real values: 100.5 or as fractional ones: 100 1/2)
– advanced import from Excel: you can choose what is on each column of your table, you can also skip rows etc.
We invite you to test this new version …
Thanks to Andrew Athanasiadis we now have Greek translation for our optimization programs. Thanks a lot Andrew!
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In version 9 of the Real Cut 1D we have changed the order of columns for Demand parts. We did that in order to improve data exchange with Excel.
If you previously saved your data in native files (with extension 1d) you dont have to do anything. Real Cut 1D knows how to load its own files.
However, if you did saved your data in csv or excel files, you will have to modify them by reordering the columns.
Here is what you have to do:
– open the csv or xls file in Excel.
– move the angle1 and angle 2 columns at the right of the existing columns.
– delete the empty columns 3 and 4 which have resulted as effect of moving columns with angles.
– exchange the height column with quantity column.
Here is an example:
– csv file from version 8 or less:
in version 9 this becomes:
Pay a special attention to list separator. In some regions the separator is “,”. In some others is “;”. If the separator is incorrectly set you will get an error.
You may change the separator from menu Start | Control panels | Region and language | Additional settings| List separator of the Windows 7.
We have reduced the running time of 1d optimization for large data. Here is a test with RealCut1D which has to cut 174000 demand parts from 200000 inventory bars.
The optimization took only 0.33 seconds, however in the end-user software (Real Cut 1D) few more seconds are needed to compute all statistics and to display the results.
The cutting optimization problem belongs to the class of Nondeterminist Polynomial Complete (NP-Complete) problems . Other problems in this class are the Hamiltonian path, Travelling Salesman, Subset sum, Clique, Independent set, Graph colouring etc. All these problems have been deeply analyzed by a huge number of researchers, but no polynomial-time algorithm was discovered for them. This has a direct consequence over the running time and the quality of the optimization.
A polynomial-time algorithm is that one whose running time is bounded by a polynomial function of its input size. For instance, if we have n = 1000 pieces to cut and the cutting algorithm would have the complexity O(n2), then the running time would have been directly and linear proportional to 10002 which is (106) units of time. Assuming that our computers can perform 109 operations per second, the cutting optimization algorithm would run in less than a fraction of a second. Sadly, this is not the case for the cutting optimization problem. There is no such fast algorithm for solving it.
The only perfect algorithm for solving the cutting optimization problem is an exponential one. An exponential algorithm will run in an exponential amount of time (2n, 3n, n! – where n is the number of pieces to be optimized). Thus, even for small instances (lets say 1000 pieces) an exponential algorithm will run as follows:
These algorithms run in an impressive number of years. Even if we put all computers in the world to solve the problem in parallel we still don’t get a significant improvement in speed.
This is why another possibility (which is employed by our software too) is to use heuristics or approximation algorithms. A heuristic is an algorithm which is fast and returns a good solution (often the best one) of the problem. However,there is no guarantee that the obtained solution is the optimal one.
An important parameter of the software is the OptimizationLevel. This will basically tell how many configurations are explored before the best found solutions is outputted. If you set the OptimizationLevel to very low value you will obtain a solution very fast. But the quality of the solution might be not so good. If you set the OptimizationLevel to very high value you will obtain a good solution but not so fast. Thus, one must employ a trade-off between the quality of the solutions and the running time.
. Garey, M.R., Johnson D.S., Computers and Intractability: A Guide to NP-completeness, Freeman & Co, San Francisco, USA, 1979.