#### Paper/Presentation Title

Desired Precision in Multi-Objective Optimization: Epsilon Archiving or Rounding Objectives?

#### Keywords

Multi-objective Optimization, Solution Archiving, Desired Precision, Epsilon Dominance, Rounding Objectives

#### Location

Session D3: Advances in Environmental - Decision Support - Software Systems

#### Start Date

12-7-2016 9:50 AM

#### End Date

12-7-2016 10:10 AM

#### Abstract

Multi-objective optimization (MO) aids in supporting the decision making process in environmental engineering and design problems. One of the main goals of solving a MO problem is to archive a set of solutions that are well-distributed across a wide range of all the design objectives. To this end, some of the state-of-the-art MO algorithms use the epsilon dominance concept to define a mesh-grid with pre-defined grid-cell size (often called epsilon) in the objective space and archive at most one solution in each grid-cell. Moreover, epsilon archiving helps the MO algorithm control the number of archived solutions. This is particularly important when solving problems with a large number of objectives, because as the number of objectives increases, the non-dominated portion of the objective space increases exponentially and therefore the chance of finding any dominating (new better) solution decreases.

The epsilon archiving process is a computationally demanding process. This study introduces a similar but computationally more efficient solution archiving approach where each objective function is rounded to the desired precision level before being compared to the set of archived solutions that already have rounded objective function values. The epsilon archiving and the proposed archiving approaches are compared in terms of the quality of final archived solutions for solving a five-objective benchmark mathematical test problem and a six-objective hydrologic model calibration problem. Results show promises in the proposed solution archiving approach in comparison with the epsilon archiving of ε- NSGA-II.

#### Included in

Civil Engineering Commons, Data Storage Systems Commons, Environmental Engineering Commons, Hydraulic Engineering Commons, Other Civil and Environmental Engineering Commons

Desired Precision in Multi-Objective Optimization: Epsilon Archiving or Rounding Objectives?

Session D3: Advances in Environmental - Decision Support - Software Systems

Multi-objective optimization (MO) aids in supporting the decision making process in environmental engineering and design problems. One of the main goals of solving a MO problem is to archive a set of solutions that are well-distributed across a wide range of all the design objectives. To this end, some of the state-of-the-art MO algorithms use the epsilon dominance concept to define a mesh-grid with pre-defined grid-cell size (often called epsilon) in the objective space and archive at most one solution in each grid-cell. Moreover, epsilon archiving helps the MO algorithm control the number of archived solutions. This is particularly important when solving problems with a large number of objectives, because as the number of objectives increases, the non-dominated portion of the objective space increases exponentially and therefore the chance of finding any dominating (new better) solution decreases.

The epsilon archiving process is a computationally demanding process. This study introduces a similar but computationally more efficient solution archiving approach where each objective function is rounded to the desired precision level before being compared to the set of archived solutions that already have rounded objective function values. The epsilon archiving and the proposed archiving approaches are compared in terms of the quality of final archived solutions for solving a five-objective benchmark mathematical test problem and a six-objective hydrologic model calibration problem. Results show promises in the proposed solution archiving approach in comparison with the epsilon archiving of ε- NSGA-II.