It's now time to conclude our demonstration of a faster method for pit optimization with the pseudoflow method. Read the last part of this series and download the full article at the bottom of this post.
In our previous post we examined the maximum flow problem and introduce the pseudoflow engine in Whittle, comparing the pseudoflow vs LG. method. Today, we will list the factors impacting the speed of optimization, answer the precision question and memory requirements before concluding on the method.
Authors: Victor Xiaoyu Bai, George Turczynski, Nathaniel Baxter, @HS , @SR, @DP
Factors Impacting the Speed of Optimization
In general, the computation time of the optimization process can be impacted by a variety of factors including:
- The number of blocks
- The number of arcs, related to slope setting and block size
- Distribution of block values
- Computer hardware and system
The testing done here is not exhaustive for all factors, but focuses on showing the time comparison over different sized block models, which is usually the dominant factor. For some small or intermediate block models, the pseudoflow engine may not produce significant speed improvement over LG. The reason is that the LG engine is already very fast in solving these cases, and the majority of processing time is taken up by data reading/writing instead of optimization. But for larger sized block models, the speed improvements are significant.
Precision Question
With the recent exposure of pseudoflow in the mining industry, one common question continues to be raised: “Does pseudoflow always produce exactly the same result as LG?” The answer is “Yes” and “No”. Mathematically, “Yes”, it has been proven that the pseudoflow algorithm and LG generate the same result. When it relates to software implementation, it is not always true. The reason is that the Whittle pseudoflow engine approximates the value of blocks as integers, while LG deals with them as floating point numbers. In both cases, using floating point numbers or integers, the block value encoding will introduce imprecision in the block value. The pseudoflow engine neglected the value in the scale of cents, which is usually marginal to the block value. In some rare cases, this approximation can result in a pit slightly different from the LG result. However, even if different pits occur, the pit values should be very close. In the context of strategic mine planning, considering that the actual block values have much greater uncertainty when comparing to the marginal value neglected here, the approximation of value hardly impacts on the NPV report and is definitely tolerable.
Memory Requirements
The pseudoflow engine utilizes more physical memory via RAM than LG does. For some large cases, the pseudoflow engine may reach the memory limit of the computer. In general, the memory usage grows almost linearly with the number of active arcs, as shown in Figure 9.
The information of active arcs is reported in the pit optimization message tab for both LG and pseudoflow. Table 3 lists typical memory requirements to efficiently solve problems of different sizes (measured by the number of active arcs). Here, the term “efficiently” means “processing without using virtual memory”. Using virtual memory can drastically slow down the optimization and therefore add significant time to the overall optimization process. On the other hand, a slightly larger case can also be solved by using a small amount of virtual memory, with a trade off of speed. For example, with a 32 GB RAM computer, a problem with less than 509 million active arcs can be efficiently solved; and a problem of 550 million active arcs is still solvable by using virtual memory.
CONCLUSION
The pseudoflow algorithm is a fast new vehicle for delivering optimal pit solutions. In Whittle, the pseudoflow engine has inherited the same usability as the entrusted Pit Optimization Engine, which allows users to configure comprehensive practical slope settings for a variety of geotechnical needs, and achieves identical results to the LG method. Speed improvements open up the opportunity to solve problems that were previously too large for Whittle and the traditional LG engine. Furthermore, the pseudoflow algorithm also enables some interesting collaboration possibilities. Dassault Systèmes is now connecting GEOVIA’s offerings to the likes of SIMULIA® Process Automation and Simulation technologies on the 3DEXPERIENCE® platform. This enables running hundreds to thousands of “What if?” scenarios and analyzing them within the same timeframe that it took to run a handful in the past. With the 3DEXPERIENCE platform, it is possible to even further automate and improve the performance seen with GEOVIA Whittle, and GEOVIA continues searching for faster, practical and easy-to-use strategic mine planning solutions for the future.
▶ Download the White Paper
References
[1] H. Lerchs and I. F. Grossmann, “Optimum design of open-pit mines,” Transactions CIM, vol. LXVIII, pp. 17–24, 1965.
[2] J. C. Picard, “Maximal closure of a graph and applications to combinatorial problems,” Management Science, vol. 22, no. 11, pp. 1268–1272, 1976.
[3] A. V. Goldberg and R. E. Tarjan, “A new approach to the maximum-flow problem,” Journal of the Association for Computing Machinery, vol. 35, no. 4, pp. 921–940, Oct. 1988.
[4] D. S. Hochbaum, “The Pseudoflow Algorithm: A New Algorithm for the Maximum-Flow Problem,” Operations Research, vol. 56, no. 4, pp. 992–1009, Aug. 2008.
[5] B. G. Chandran and D. S. Hochbaum, “A Computational Study of the Pseudoflow and Push-Relabel Algorithms for the Maximum Flow Problem,” Operations Research, vol. 57, no. 2, pp. 358–376, Jan. 2009.
[6] D. C. W. Muir, “Pseudoflow, New Life for Lerchs-Grossmann Pit Optimisation,” in Orebody Modelling and Strategic Mine Planning Conference, Perth, Australia, 2004, vol. 14, pp. 97–104.
[7] C. H. Papadimitriou and K. Steiglitz, “The Max-Flow, Min-Cut Theorem,” in Combinatorial Optimization: Algorithms and Complexity, Unabridged edition., Mineola, N.Y: Dover Publications, 1998, pp. 120–128.
GEOVIA Whittle pit optimization best practice
