(528f) Numerical Simulation and Optimization of Environmental Treatment Design Using Parallel Computational Methods: Theory and Application

Environmental remediation has been ongoing in the Unites States for several decades and has produced some successes. However, the more difficult sites remain challenging and resistant to efficient and effective remediation. These are precisely the environmental problems that remain as persistent fiscal and technological challenges as the success of the heuristic trial-and-error approach, which assisted in remediating the simpler sites, has reached it a limit of applicability on these cases. These tools herein enable formal, physically consistent and robust analysis of optimal remedial designs for environmental contamination problems of any level of complexity.

This paper discusses and demonstrates fast computational simulation and optimization technologies used for optimally managing environmental remediation project and programs by reducing remediation design analysis timeframes and costs. Those responsible for managing or remediating chemical or radionuclide impacted sediments, soils, surface or groundwater including designing remedial design and operation projects will benefit from tools that will help them find acceptable, efficient and effective solutions to complex and multi-faceted planning challenges at efficient cost points. A new universal optimization system is developed which has successfully been deployed on environmental and radionuclide impacted sites across a variety of computational environments including desktops and the high performance elastic Cloud-based computing platforms.

This computational advancement removes the impediment of burdensome and unpredictable runtime requirements for optimizing the design of these types of projects, which have typically consumed weeks or months of calendar time using heuristic trial-and-error or even automated serial computation approaches. These new optimization methods return results in minutes to hours for simulations and optimal solutions in hours to at most a few days for medium and larger size projects which here-to-fore required months to solve.

Computational Approach

PBMO^TM is a universal optimization tool. Capabilities include optimizing linear or non-linear elliptic, parabolic and hyperbolic models and objective functions that are continuous, non-continuous and mixed integer. It is a tool system that helps users perform complex high-level tasks with amazing simplicity. Modes of operation include standard and expert modes, and it runs on computers with single and multiple CPUs, including local area grids and the Cloud. Because it is programmed as a set of modules using standard FORTRAN, it is platform independent. It has the capability for including applications with mixed operating systems and can deploy with multiple, independent or blended process models including subject matter expert (SME), data-driven (DD), Physics-based (PB) or integrated model (IM). Analysis can begin with the best result from a trial-and-error approach, or from a random starting point so efforts engaged to date by the design teams can be fully used. The optimal solution search relies on evaluations of candidate solutions, which can be entirely physics-based or response function or minorant approximated solution search (Deschaine, 2014).

This is accomplished by developing both a parallel optimal search strategy and the numerical matrix solver in the groundwater flow and transport modeling code. The parallel distributed optimization method will execute on one to several hundred (or more as needed) CPUs while the parallel numerical solver that has been added to the subsurface flow and transport simulator MODFLOW-SURFACT^TM has demonstrated speedups as high as a factor of 9.8. Hence, the integrated parallel simulation and optimization method uses the breadth and depth search approach; iteratively producing sets of tens or 100s of candidate investigation points that are evaluated concurrently instead of the previous and widely used sequential approach (i.e. one model evaluation at a time). This enables 80-100% globally optimal solutions are regularly found expending only 5-10% of the common computational effort using this new parallel optimization method (reducing computation effort by 10 to 20 times and calendar time by a factor of 100 or more).

Additionally, practitioners conducting conceptual site model development, model calibration by auto-calibration methods and remedial design by heuristics can enjoy solution speedups by using the parallel numerical matrix solver in the physics-based simulator as well as automated uncertainty analysis using the Latin Hypercube, Monte-Carlo or geostatistical realization techniques. Combining investigation and design analysis with breadth and depth parallel optimization methods, projects at the fringe of practical optimization, along with projects that here-to-fore were beyond the reach of formal optimization methods are now wholly feasible and tractable optimization problems.

Remedial Design Approach

PBMO^TM project design involves selecting the appropriate combination of its fully comprehensive solution options, including the full capability of mixing and matching various approaches.

• Select proper descriptive model or model set that adequately describes the system to be optimized

• Select optimization algorithm or set of proper optimization algorithms to optimize the system best.

• Select computer operation system or a mixture of operating systems, to enable the integrated system to run as-is.

It is important to note that â??optimizationâ? refers not just to cost minimization but also to the effective and efficient balance of cost, performance, risk, management, and societal priorities along with uncertainty analysis. To wit, the PBMO^TM process formally integrates the stakeholder input into the analysis and provides not only the "optimal solution" but also "what-if" capability that includes management override control on remedial design analysis. This approach integrates all of these elements into a single decision framework that is tractable, traceable, and defensible. The approach is modular and scalable. It can be applied either as individual components or in total. This solution methodology represents a significant improvement over the non-optimal â??trial and errorâ? approach to developing environmental response(s).

METHODS

Understanding optimization rationale and theory, methodological strength, applicability, and limitations, is critical for understanding why optimization is valuable and how to successfully and deploy computational optimization analysis on projects. Project implementation experience has shown that several effective optimization methods exist that are routinely successful when used on projects and are included in this system. Exhibition of case histories demonstrates their value for developing optimal solutions not obtainable by traditional subjective design methods (a.k.a. manual trial and error).

PBMO^TM uses a breadth and depth search strategy. The breadth search identifies good solution quickly, whereas the local search drills down to find the optimal value. The optimization methods use include:

• Derivative-based global methods

  • Linear programming (LP)

  • Sequential linear approximation (SLA)

  • Sequential Quadratic Programming (SQP)

  • Generalized Reduced Gradient (GRG)

• Derivative-free global methods

  • Adaptive Design of Experiment (ADOE)

  • Adaptive Global Random Search (AGRS)

  • Branch and Bound (B&B)

  • Global Adaptive Random Search (GARS)

Table 1 depicts the applicability of the PBMO^TM system (Deschaine, 2014).

Table 1. PBMO^TM Solution Scope and Analysis Results

The solution from the PBMO^TM methodology has always exceeded the subjective engineering solution when available for comparison (Deschaine, 2014).

CONCLUSIONS

The basic PBMO^TM methodology has been previously tested, verified, validated and documented using a broad range of industrial projects. Those results indicate that it meets or exceeds the best available solution either in use (i.e. as an RIP), proposed by the subject matter experts or developed by other optimization methods. These two new parallelization methods now allow for the optimization of remedial designs for the more complicated problems. These are precisely the environmental problems that remain in the environmental contamination site portfolio as persistent challenges. The earlier successes of the heuristic trial-and-error approach - which assisted in remediating the simpler sites - has reached it limit of applicability in these cases. By simultaneously combining project level optimization with optimal programmatic design, the optimal design and implementation of environmental challenge response are now computationally tractable, practical and viable.

REFERENCES

Deschaine, L. M. (2014). Decision support for complex planning challenges. Ph.D. Dissertation, Chalmers University of Technology, Göteborg, Sweden. 233p.

Deschaine, L. M., Lillys, T. P., & Pintér, J. D. (2013). Groundwater remediation design using physics-based flow, transport, and optimization technologies. Environmental Systems Research, 2(1), 1-21. http://www.environmentalsystemsresearch.com/content/pdf/2193-2697-2-6.pdf