Maplesoft's Global Optimization Toolbox Plays Significant Role in Solving a Global Challenge - User Case Studies - Maplesoft

User Case Study: Maplesoft's Global Optimization Toolbox Plays Significant Role in Solving a Global Challenge

In a paper submitted at the 2006 INFORMS Annual Conference, Larry M. Deschaine presented an approach to solving the challenge of accurately locating and discriminating unexploded ordnance (explosives). He, along with colleagues Frank D. Francone and János D. Pintér, has developed a solution that fuses knowledge from Physics, Genetic Programming and Global Optimization. Maplesoft’s Global Optimization Toolbox is an important part of this solution.

The Problem

A report by the Defense Science Board Task Force on Unexploded Ordnance, Department of Defense, laid out the problem in December 2003 as follows. “The UXO clean-up problem is a very large-scale undertaking involving 10 million acres of land at some 1400 sites. One of the key problems is … [that] instruments that can detect the buried UXOs also detect numerous scrap metal objects and other artifacts, which leads to an enormous amount of expensive digging. Typically 100 holes may be dug before a real UXO is unearthed.”

Though discriminating non-ordnance from ordnance is a very important step, in many instances the desired performance level is not reached. During a published test sponsored by the US Government at the Jefferson Proving Grounds, all contractors fell below the accuracy criteria, and most solutions were hardly better than random guessing.

Larry and his colleagues set out to remove the inefficiencies in UXO detection through tools that provably locate and identify UXOs with high accuracy. Their solution also determines when a UXO field is cleared, thus eliminating the issue of digging up unnecessary holes. The UXO challenge is solved – but only after a 7-year research and development project that first started as a PhD dissertation topic at Chalmers University of Technology (Göteborg, Sweden) expanded to a production tool at SAIC and RMLT. The project was recently validated on blind field data at a large UXO project at FE Warren Air Force Base, Wyoming, USA.

The next phase of locating and identifying dangerous subsurface objects is the detection of landmines. Millions of landmines are buried in more than 80 countries, which result in 20,000 civilian victims every year. The landmine detection project is in the R&D phase and Maplesoft software is providing key value in this project as well.

The Solution

The proposed solution is a subsurface object location and identification method using a technique for modeling and identifying objects on the basis of noisy, sparse data. The solution approach fuses physics, data, and human expertise models, and determines best algorithms for each challenge. The techniques used include information theory, physics based modeling, signal processing cognitive modeling, signal filtering and global optimization. The challenge was to integrate these techniques, and to determine the key information content, in order to extend the accuracy of predictive modeling.

The solution is based on the fundamental geo-electromagnetic equations and involves the following steps:

  • Solid understanding of the physics; derivation and key assumptions in the mathematical equations
  • Steady and dynamic signal interpretation
  • Insights from human expertise
  • Development of optimal predictions via an extended approach inspired by Kalman filtering theory
  • Fusing the information in the analysis to create the decision support tool UXO MineFinder (UXOMF™)

Use of Maple and the Global Optimization Toolbox from Maplesoft

Optimization was chosen to fit a model of the expected physics of the UXO or non-UXO response as observed in the geo-electromagnetic data. The model calibration problems were solved by the seamlessly integrated global + local optimization software suite LGO. LGO was chosen after an exhaustive search and testing of available optimization algorithms. This powerful optimization package is implemented for Maple (Maplesoft’s flagship product) as the Global Optimization Toolbox. Maple and the Global Optimization Toolbox (GOT) were selected for their depth of mathematical and scientific resources, and ease of use. Maple and its extensions (such as the GOT) enable the efficient development and preservation of knowledge.

The Result

The project outcome was outstanding. Performance (detection accuracy and reliability) results were better than all earlier published results. It was established that UXOMF™ provides highest accuracy of UXO discrimination, and its usage has led to a reduced need to dig test holes. Overall, the results reduced excavation costs by at least 30-50%.

The current toolkit will be further refined, extended and improved as the data, physics or subject matter expert analysis-models improve, leading to better and more accurate results. This includes ongoing R&D for the analysis and resolution of both landmine and underwater UXO challenges.

Maplesoft ( is a leading provider of high-performance software tools for engineering, science, and mathematics
PCS ( provides advanced nonlinear optimization software products and services
RMLT ( is the developer of the Discipulus linear genetic programming software.
SAIC ( is a leading systems, solutions and technical services company.