1. A New multi-objective algorithm: Pareto archived dds
Masoud asadzadeh
Dr. Bryan Tolson
Department of civil and environmental engineering
Masoud Asadzadeh

2. Research goal
Develop an efficient multi-objective optimization algorithm that has few parameters.
Modify Dynamically Dimensioned Search (DDS), a simple efficient, parsimonious algorithm to solve unconstrained computationally expensive, multi-objective water resources problems.
Set up the new tool so that it can easily scale to higher dimensional problems (not only problems with two objectives).

3. Dynamically Dimensioned Search (DDS)
Background
Dynamically Dimensioned Search (DDS)
Tolson & Shoemaker [2007]
Designed for:
Single Objective Continuous Optimization
Computationally Expensive Automatic Hydrologic Model Calibration
Modified to solve problems with discrete decision variables, Tolson et al. [2008]
Single-Solution Based algorithm (not population based)
Simple & Fast Approximate Stochastic Global Optimization Algorithm
Generate Good Results in Modeller's Time Frame
Algorithm parameter tuning is unnecessary

4. Initialize starting solution Perturb the current best solution
dds description
Initialize starting solution
Perturb the current best solution Y
Globally search at the start of the search by perturbing all decision variables (DV) from their current best values
Continue?
STOP N
Locally search at the end of the search by perturbing typically only one DV from its current best value
Perturb each DV from a normal probability distribution centered on the current value of DV

5. F(x)=[f1(x),f2(x),…,fN(x)]
Problem definition
Minimize:
F(x)=[f1(x),f2(x),…,fN(x)]
Subject to:
x=[x1,x2,…,xI]  RI f1 f2

6. PA-dds description Perturb the current ND solution
Update the set of ND solutions if necessary
Search for individual minima first
Initialize starting solutions
Create the non-dominated (ND) solutions set
Pick a ND solution based on crowding distance
Pick the New solution N
New solution is ND? Y Y
STOP N
Continue?

7. PA-DDS on Bi-Objective Test Problems
Results
PA-DDS on Bi-Objective Test Problems
Zitzler [1999]
Actual Tradeoff Best Convergence Median Convergence
Average Convergence Metric Y (Deb 2001)
PA-DDS
NSGA II*
AMALGAM*
ZDT4
0.049
0.052
0.002
ZDT6
0.050
0.001
* Vrugt and Robinson [2007]

8. Higher Dimensional Problem (25000 iterations)
NEW RESULTS (TEST PROBLEMS DTLZ1)
Higher Dimensional Problem (25000 iterations)
DTLZ1, with 3 objectives Deb et. al [2002]
2D view f3 f1
Actual Tradeoff
PA-DDS result f1 f3 f2

9. New York Tunnels Problem
MORE NEW RESULTS
New York Tunnels Problem
Water Distribution Network (WDN)
Rehabilitation of an existing WDN
21 pipes (decision variables)
15 standard pipe sizes for each pipe
1 more option - no change in the pipe
1621 size of the discrete decision space
Minimum cost in the single objective version of the problem is $ million
Objectives: Cost and Hydraulic deficit

10. New York Tunnels Problem
More New Results
New York Tunnels Problem
Perelman et al. [2008]
3,360,000

11. Conclusion
PA-DDS inherits simplicity and parsimonious characteristics of DDS
Generating good approximation of tradeoff in the modeller's time frame
Reducing the need to fine tune the algorithm parameters
Solving both continuous and discrete problems
PA-DDS can scale to higher dimensional problems
Research for the efficiency assessment is ongoing

12. Thanks to our funding source
NSERC Discovery grant
Thank You

13. only modification is to discretize the DV perturbation distribution
Discrete probability distribution of candidate solution option numbers for a single decision variable with 16 possible values and a current best solution of xbest=8. Default DDDS-v1 r-parameter of 0.2*