Technology
The 5 Myths of the HPCMP Optimizer
By Dr. Roy L. Campbell, Jr., Computer Engineer, CISD, ARL
Many people know that the HPCMP optimizer is used in the decision making process for annual HPCMP technology insertions (TIs), but some of the finer details of this tool are often incorrectly perceived.
Myth #1: Optimization determines the final TI-XY solution.
The HPCMP optimizer is a near-real-time, task-parallelized, linear optimization solver that uses pricing, benchmarking results, acquisition budget limitations, and a cryptic description of the target workload to determine the “ideal” quantity of each offered system that should be purchased and the “ideal” allocation of systems (both determinations being gauged solely in terms of price-per-performance). Put simply, to the extent that the application test cases constructed by the performance team are representative of the true workload, the HPCMP optimizer ranks systems and suggests how work should be distributed among the selected and already owned systems in an optimal sense when considering only bang-per-buck. Finding the optimal solution in terms of price-per-performance is, however, only one piece of the puzzle. Other considerations under the purview of the usability and collective acquisition teams introduce qualitative variables that cannot be accurately captured by a quantitative assessment. Therefore, the TI-XY problem must be solved to yield a spectrum of options beginning with the best possibility and ending (in most cases) with the ten-thousandth best possibility to provide a broad view of what is happening in the price-per-performance space so that other variables can be addressed in an educated, yet subjective manner. In other words, price-per-performance analysis is used as the framework, and qualitative issues are accommodated by finding the best price-per-performance possibility within that framework that best addresses the qualitative concerns.
Myth #2: Optimization is a new academic discipline.
Primitive forms of optimization may have actually spawned in early history with the discovery of the Golden Ratio (i.e., the convergence value of fN / fN-1 as N grows large, where fx is a member of the Fibonacci sequence). The dimensions of the Greek Parthenon, the Egyptian Pyramids, and various objects within works by Leonardo Da Vinci are claimed to comply with the value of this ratio (1.618) to maximize visual appeal. In fact, Da Vinci’s Vitruvian Man (i.e., a supposed model of the perfect male) is believed to reveal that people who possess elements of the Golden Ratio are viewed as being more attractive than those that do not. Even today, some say that society is subconsciously converging upon the Golden Ratio through the resizing of its television sets, transitioning from standard sets with a 4:3 (1.333) aspect ratio to high definition sets with a 16:9 (1.777) aspect ratio.
More sophisticated forms of optimization gained momentum in World War II as the number of logistical and tactical variables mushroomed, sowing the seed for a discipline commonly referred to as operations research. The end products of modern optimization can now be seen in many somewhat hidden but very powerful ways ranging from advertisement strategies aimed at cost-effective penetration of the consuming public to the bent wingtips typically seen on Boeing 737s.
Myth #3: The HPCMP optimizer has not changed since its advent in January of 2003.
The HPCMP optimizer was initially crafted in response to slow solution times provided by the Solver portion of Excel (the original optimization tool used by the HPCMPO), which required several days to assess the ranked possibilities of a single acquisition scenario. Therefore, in January of 2003, under the general guidance of the HPCMP Deputy Director, Dr. Larry P. Davis, a task-parallelized iterative method was developed to deliver an approximate solution within an hour, using whatever number of processors was necessary (typically 32, but sometimes as many as 256). Given the size of the acquisitions that would be impacted, an approximate solution was determined to be unacceptable. So upon the advice of Mr. John Grosh and Mr. Tom Kendall, an exacting linear programming technique (the SIMPLEX method) was adopted. This final version of the HPCMP optimizer was used to determine the price-per-performance component of both the 2004 and 2005 HPCMP Technology Insertions and has become the centerpiece for price-per-performance assessments in the TI-XY process, in general.
Myth #4: The HPCMP optimizer has been verified by the HPCMPO and ARL only.
Given the large financial impacts of a TI-XY optimization solution, external verification from the Naval Post Graduate School (NPGS) was sought. Although the methodology was initially perceived to be inefficient (since the HPCMP optimizer solves all feasible possibilities within the combinatorial space of offered system quantities and ranks the results), given the nature in which the tool is applied (as a framework to later accommodate qualitative inputs), the methodology was deemed acceptable. As further validation, a concrete example was solved by both the HPCMP optimizer and NPGS tools. The results proved to be the same (although the times-to-solution varied greatly).
Myth #5: Finding the best solution to the TI-XY problem in terms of price-per-performance requires a supercomputer.
There is some debate whether using a linear programming technique rather than an integer programming technique is a wise use of resources, since the former requires in many cases 32 or more processors to yield the top solution in near-real-time (i.e., within an hour), while the latter (for the same problem) requires a single processor producing a solution within a few seconds. The strategic selection of the former stems from the HPCMP’s desire to uncover the top 10,000 acquisition possibilities to allow exhaustive analysis of the price-per-performance space. In such a case, the time-to-solution for the linear programming technique is dilated by a few percent, while that for the integer programming technique balloons to days or weeks. As an example of how price-per-performance results might be presented to decision makers, the above chart provides a comparison of the best possibility versus the average of the top 10,000 possibilities for TI-05.