PBMO™

Overview

HGL has developed an integrated system called Physics-Based Management Optimization (PBMO^TM) that links environmental modeling with management optimization focused on finding the best value solution to a challenge. This involves evaluating an objective function with multiple decision variables and practical constraints. PBMO^TM identifies optimal remedial design and operational approaches that lead to timely and cost-effective cleanups and optimal long-term management strategies.

Medallion Conceptualization

PBMO^TM is conceptualized as a medallion with two interdependent and complementary halves as shown on the figure below. One half contains a module with calibrated physics-based, multi-media, flow and transport models that seamlessly interacts with the second half housing the computational optimization module. By linking modeling and computational optimization with decision science, PBMO^TM realistically captures important site physics, managerial and stakeholder requirements, with financial constraints and implementability considerations; achieves a coherent interpretation of disparate site data; and produces structured, credible solutions acceptable to stakeholders and regulators.

PBMO™ P&T Remedy Optimization Problem Statement
Assignment:
Maximize or Minimize the Objective Function Subject to Specific Constraints
Objective Function:
Defined in Terms of Performance, Cost or Time
•	Minimize remedy cost	•	Maximize contaminant mass removal
•	Minimize remedy time frame
Decision Variables and Constraints:
May Incorporate Practical Limitations, Available Budget, and Regulatory Requirements
•	Well extraction/injection locations & rates	•	Budget
•	Clean up goal	•	Land use
•	Elapsed time	•	Existing infrastructure

Objective Function Complexity

Environmental systems design can be some of the most challenging problems to solve optimally, as the solution surface (aka objective function) is unknown at the start of the analysis. Objective functions for environmental system problems are often very bumpy; they have non-smooth surfaces with sharp changes in values.

**Objective Function F with Decision Variables X and Y**

This bumpy characteristic renders many common optimization solution techniques, such as subjective engineering judgement (aka SME trial-and-error), or gradient-based searches (commonly used in parameter estimation software) ineffective in finding the best solution for a given problem.

PBMO^TM Optimization Methodology

PBMO^TM uses a blended suite of global optimization techniques that search through these many apparent “good” peaks to find the best one, which is the global optimal solution. PBMO^TM accomplishes this by using a “breadth search” to examine many different ways of solving the problem and a “depth search” to focus on finding the best solution in various regions that contain promising approaches. It provides the computational optimal and the near-optimal solutions for inspection, evaluation, and consideration for use. Since implementability is a prerequisite requirement of the analysis setup, all the feasible PBMO^TM-generated solutions are also implementable and usable, as produced.

High-Performance Computing

PBMO^TM takes advantage of modern high-performance distributed computing capabilities on desktops, internal network clusters, and Cloud environments, independently or as a hybrid computational system, which permits timely evaluation of many hundreds to hundreds- of -thousands of candidate solutions. PBMO^TM can perform both deterministic or stochastic optimization on sites with single or multiple plumes present. PBMO^TM can also assess the robustness of solutions by using multiple geostatistical realizations of aquifer properties.

PBMO^TM Technology Recognition

In 2017, HGL received the Grand Prize in the Innovative Research category of the Excellence in Environmental Engineering and Science^™ competition for its PBMO^TM technology. The annual international competition, organized by the American Academy of Environmental Engineers & Scientists^®, has been rewarding the best in current environmental engineering and science since 1989.