Using Objective Clustering for Solving Many-Objective Optimization Problems

Table 6

Analytical model of the storm drainage problem.

Name	Function expression
Minimize 5 objectives
(1) Drainage network cost	𝑓1(𝑥)=106780.37(𝑥2+𝑥3)+61704.67
(2) Storage facility cost	𝑓2(𝑥)=3000𝑥1
(3) Treatment facility cost	𝑓3(𝑥)=(305700/(0.06∗2289)∧ 0.65)∗2289𝑥2
(4) Expected flood damage cost	𝑓4(𝑥)=250∗2289∗exp(−39.75𝑥2+9.9𝑥3+2.74)
(5) Expected economic loss cost due to flood	𝑓5(𝑥)=25∗(1.39/(𝑥1𝑥2)+4930𝑥3−80)
Subject to 7 constraints
(1) Average no. of floods/year	𝑔1(𝑥)=0.00139/𝑥1𝑥2+4.94𝑥3−0.08≤1
(2) Probability of exceeding a flood depth of 0.01 basin inches	𝑔2(𝑥)=0.0000306/𝑥1𝑥2+0.1082𝑥3−0.00986≤0.10
(3) Average no. of pounds/year of suspended solids	𝑔3(𝑥)=12.307/𝑥1𝑥2+49408.24𝑥3−4051.02≤50000
(4) Average no. of pounds/year of settleable solids	𝑔4(𝑥)=2.098/𝑥1𝑥2+8046.33𝑥3−696.71≤16000
(5) Average no. of pounds/year of BOD	𝑔5(𝑥)=2.138/𝑥1𝑥2+7883.39𝑥3−705.04≤10000
(6) Average no. of pounds/year of N	𝑔6(𝑥)=0.417/𝑥1𝑥2+1721.36𝑥3−136.54≤2000
(7) Average no. of pounds/year of PO4	𝑔7(𝑥)=0.164/𝑥1𝑥2+631.13𝑥3−54.48≤550
where 0.01≤𝑥1≤0.45, 0.01≤𝑥2,𝑥3≤0.10