Table 3 Algorithms parameters used in the simulation.

Case 1

Hidden layer size

20

-

Min. Cost, Min. emissions, Min. LESP, Min. deviation between actual and optimal levels of energy demands as a single objective function

No. neurons

10

No. epochs

1000

\(\:{iter\:}^{\text{m}\text{a}\text{x}}\)

100

Learning rate

0.1000

Batch size

20

Train function

trainlm

Goal error

1\(\:{e}^{-4}\)

Train ratio

0.7

Validation ratio

0.15

Test ratio

0.15

RMSE

19.0333

Case 2

Hidden layer size

20

Time interval

24

Obj. function

Min. Cost, Min. emissions, Min. LESP, Min. deviation between actual and optimal levels of energy demands as a multi-objective function

No. neurons

10

No. epochs

1000

Population size

100

\(\:{iter\:}^{\text{m}\text{a}\text{x}}\)

100

Learning rate

0.1000

Max. generations

200

Batch size

20

Train function

trainlm

\(\:{iter\:}^{\text{m}\text{a}\text{x}}\)

1000

\(\:{l}_{b}\)

\(\:\left[0\:0\:35\:6.8\:2\right]\)

Goal error

1\(\:{e}^{-4}\)

\(\:{u}_{b}\)

\(\:\left[0.6\:0.4\:40\:7.4\:5\right]\)

Train ratio

0.7

Crossover fraction

0.6

Validation ratio

0.15

Test ratio

0.15

Pareto fraction

0.3

RMSE

0.2828

Case 3

Hidden layer size

[5 30]

Time interval

24

Obj. function

Min. Cost, Min. emissions, Min. LESP, Min. deviation between actual and optimal levels of energy demands as a multi-objective function

no. epochs

[100 1000]

train function

trainlm

Population size

100

Query budget

50

\(\:{iter\:}^{\text{m}\text{a}\text{x}}\)

100

Max. generations

200

Best hidden layer size

30 neurons

Num. scenarios

1000

Training goal

\(\:2.72\text{*}{10\:}^{-6}\)

\(\:{l}_{b}\)

\(\:Varied\)

Training epoch

647

normrnd

(Mean, std)

\(\:{u}_{b}\)

\(\:\text{V}\text{a}\text{r}\text{i}\text{e}\text{d}\)

Best RMSE

0.2356