List of Objective functions in HAS

1 Existing Optimization Models
2 New Optimization Model
- 2.1 JSON Schema

Existing Optimization Models

Minimize an unweighted value

{  
         "minimize":{  
            "attribute":  
               {  
                  "distance_between":[  
                     "customer_loc",
                     "vG"
                  ]
               }
         }
 }

Minimize a weighted value

{
    "minimize": {
        "attribute": {
            "product": [
                200,
                {
                    "distance_between": [
                        "customer_loc",
                        "vG"
                    ]
                }
            ]
        }
    }
}

Maximize an unweighted value

{
    "maximize": {
        "attribute": {
            "reliability": [
                "URLLC"
            ]
        }
    }
}

Maximize a weighted value

Minimize the sum of unweighted values

Minimize the sum of weighted values

New Optimization Model

Objective Function Object

Attribute	Required	Content	Values	Description

Attribute	Required	Content	Values	Description
goal	Y	String	minimize, maximize	The goal of the optimization
operation_function	Y	Operation function Object		The operation function that has to be optimized

Operation function object

Attribute	Required	Content	Values	Description

Attribute

Required

Content

Values

Description

operator

Y

String

sum, min, max

The operation which will be a part of the objective function

operands

Y

List of operand object

EIther an operation-function or a function

The operand on which the operation is to be performed.

The operand can be an attribute or result of a function

operation-function operand object

Attribute	Required	Content	Values	Description

Attribute	Required	Content	Values	Description
normalization	N	normalization object		Set of values used to normalize the operand
weight	N	Decimal	Default: 1.0	Weight of the function
operation_function	N	operation function object

function operand object

Attribute	Required	Content	Values	Description

Attribute	Required	Content	Values	Description
normalization	N	normalization object		Set of values used to normalize the operand
weight	N	Decimal	Default: 1.0	Weight of the function
function	N	String	distance_between, latency_between, attribute	Function to be performed on the parameters
fucntion_params	N	dict		parameters on which the function will be applied. The parameters will change for each function.

Normalization object

Attribute	Required	Content	Values	Description

Attribute	Required	Content	Values	Description
start	Y	Decimal		Start of the range
end	Y	Decimal		End of the range

JSON Schema

Examples

1. Minimize an attribute of the demand

2. Minimize the sum of the distance between the demand and the customer location.

objective function - distance_between(demand, location) + distance_between(demand, location)

Scenario:

Minimize the sum of latencies of slice subnets

objective function - latency(demand) + latency(demand)

Scenario:

Max [ sum ( W_bw * min (ran_nssi_bw, core_nssi_bw, tr_nssi_bw), 1/(W_lat * ( sum (w1 * ran_nssi_lat, w2 core_lat, W3* tn_lat)) ) ]

normalization:

function(value, range(start, end), weight)

All ranges are converted to 0 to 1. The inverse operation is not needed since it is already implied in the range.

normalized value = (value - start) / (end-start)

Eg:

latency range: 50 ms to 5 ms

candidate latency	Normalized value

candidate latency	Normalized value
20 ms	0.667
40 ms	0.222

throughput range: 100 Mbps to 1000Mbps

candidate throughput	Normalized value

candidate throughput	Normalized value
300 Mbps	0.222
800 Mbps	0.778