Optimization functions

This page documents all constraint and objective functions that form the mathematical core of the transport component model.

Overview

The optimization functions are organized into several categories:

Model Definition: Functions for creating the optimization model and defining decision variables
Constraints: Mathematical constraints that ensure feasible and realistic solutions, covering demand coverage, vehicle sizing, infrastructure limitations, and policy restrictions
Objective Function: The cost minimization function that drives the optimization
Workflow Runners: High-level functions that combine constraints and objectives for specific modeling scenarios

Each constraint function adds specific mathematical relationships to the optimization model, allowing users to build models of varying complexity depending on their analysis needs. The workflow runners provide pre-configured combinations of constraints for common use cases, from simple demand coverage to complex multi-modal infrastructure planning.

Model definition

TransComp.create_model — Function

create_model(data_structures, case_name::String, optimizer)

Definition of JuMP.model and adding of variables.

Arguments

data_structures: dictionary with the input data and parsing of the input parameters
case_name::String: name of the case
optimizer: optimizer to use for the model

Returns

model::JuMP.Model: JuMP model with the variables added
data_structures::Dict: dictionary with the input data

TransComp.base_define_variables — Function

base_define_variables(model::Model, data_structures::Dict)

Defines the variables for the model.

Arguments

model::Model: JuMP model
data_structures::Dict: dictionary with the input data

Constraints

TransComp.constraint_demand_coverage — Function

constraint_demand_coverage(model::JuMP.Model, data_structures::Dict)

Creates constraint for demand coverage.

Arguments

model::JuMP.Model: JuMP model
data_structures::Dict: dictionary with the input data

TransComp.constraint_vehicle_sizing — Function

constraint_vehicle_sizing(model::JuMP.Model, data_structures::Dict)

Creates constraint for vehicle sizing.

Arguments

model::JuMP.Model: JuMP model
data_structures::Dict: dictionary with the input data

TransComp.constraint_vehicle_aging — Function

constraint_vehicle_aging(model::JuMP.Model, data_structures::Dict)

Creates constraints for vehicle aging.

Arguments

model::JuMP.Model: JuMP model
data_structures::Dict: dictionary with the input data

Returns

model::JuMP.Model: JuMP model with the constraints added

TransComp.constraint_monetary_budget — Function

constraint_vehicle_purchase(model::JuMP.Model, data_structures::Dict)

Creates constraints for monetary budget for vehicle purchase by route.

Arguments

model::JuMP.Model: JuMP model
data_structures::Dict: dictionary with the input data

TransComp.constraint_fueling_infrastructure — Function

constraint_vehicle_purchase(model::JuMP.Model, data_structures::Dict)

Constraints for the sizing of fueling infrastructure at nodes and edges.

Arguments

model::JuMP.Model: JuMP model
data_structures::Dict: dictionary with the input data

TransComp.constraint_supply_infrastructure — Function

constraint_supply_infrastructure(model::JuMP.Model, data_structures::Dict)

Constraints for sizing of supply infrastructure at nodes and edges.

Arguments

model::JuMP.Model: JuMP model
data_structures::Dict: dictionary with the input data

TransComp.constraint_mode_infrastructure — Function

constraintmodeinfrastructure(model::JuMP.Model, data_structures::Dict)

Constraints for sizing of mode infrastructure at nodes and edges.

Arguments

model::JuMP.Model: JuMP model
data_structures::Dict: dictionary with the input data

TransComp.constraint_fueling_demand — Function

constraint_fueling_demand(model::JuMP.Model, data_structures::Dict)

Constraints for fueling demand at nodes and edges.

Arguments

model::JuMP.Model: JuMP model
data_structures::Dict: dictionary with the input data

TransComp.constraint_vehicle_stock_shift — Function

constraint_vehicle_stock_shift(model::JuMP.Model, data_structures::Dict)

Constraints for vehicle stock turnover.

Arguments

model::JuMP.Model: JuMP model
data_structures::Dict: dictionary with the input data

TransComp.constraint_mode_shift — Function

constraint_mode_shift(model::JuMP.Model, data_structures::Dict)

Constraints for the rate of the mode shfit.

Arguments

model::JuMP.Model: JuMP model
data_structures::Dict: dictionary with the input data

TransComp.constraint_mode_share — Function

constraint_mode_share(model::JuMP.Model, data_structures::Dict)

If share are given for specific modes, this function will create constraints for the share of the modes. When this constraint is active, it can be a source of infeasibility for the model as it may be not possible to reach certain mode shares due to restrictions in the shift of modes (see parametrization of parameters alphaf and betaf). Especially also when constraints for minimum/maximum mode shares are active.

Arguments

model::JuMP.Model: JuMP model
data_structures::Dict: dictionary with the input data

TransComp.constraint_max_mode_share — Function

constraint_max_mode_share(model::JuMP.Model, data_structures::Dict)

If share are given for specific modes, this function will create constraints for the share of the modes. When this constraint is active, it can be a source of infeasibility for the model as it may be not possible to reach certain mode shares due to restrictions in the shift of modes (see parametrization of parameters alphaf and betaf). Or when multiple constraints for the mode share are active.

Arguments

model::JuMP.Model: JuMP model
data_structures::Dict: dictionary with the input data

TransComp.constraint_min_mode_share — Function

constraint_min_mode_share(model::JuMP.Model, data_structures::Dict)

If share are given for specific modes, this function will create constraints for the share of the modes. When this constraint is active, it can be a source of infeasibility for the model as it may be not possible to reach certain mode shares due to restrictions in the shift of modes (see parametrization of parameters alphaf and betaf). Or when multiple constraints for the mode share are active.

Arguments

model::JuMP.Model: JuMP model
data_structures::Dict: dictionary with the input data

TransComp.constraint_market_share — Function

constraint_market_share(model::JuMP.Model, data_structures::Dict)

If share are given for specific vehicle types, this function will create constraints for the newly bought vehicle share of vehicles the modes.

Arguments

model::JuMP.Model: JuMP model
data_structures::Dict: dictionary with the input data

TransComp.constraint_emissions_by_mode — Function

constraint_emissions_by_mode(model::JuMP.Model, data_structures::Dict)

Emissions given per mode for a specific year. Attention: This constraint may be a source for infeasibility if mode or technology shift cannot be achieved due to restrictions in the shift of modes (see parametrization of parameters alphaf and betaf), or due to the lifetimes of technologies as well as the lack of available low emission or zero emission technologies.

Arguments

model::JuMP.Model: JuMP model
data_structures::Dict: dictionary with the input data

Objective

TransComp.objective — Function

objective(model::Model, data_structures::Dict)

Definition of the objective function for the optimization model.

Arguments

model::Model: JuMP model
data_structures::Dict: dictionary with the input data

Workflow Runners

TransComp.run_minimum_viable_case — Function

run_minimum_viable_case(data_structures::Dict, optimizer)

Runs the minimum viable case: creates the model, applies demand coverage constraint, and sets the objective.

Arguments

data_structures::Dict: dictionary with the input data
optimizer: JuMP optimizer

Returns

model::JuMP.Model: JuMP model with constraints and objective set
data_structures::Dict: dictionary with the input data

TransComp.run_vehicle_stock_sizing — Function

run_vehicle_stock_sizing(data_structures::Dict, optimizer)

Creates model, applies demand coverage and vehicle sizing constraints, and sets the objective. Output: Cost-optimal coverage of travel demand with sizing of required vehicle stock.

TransComp.run_vehicle_stock_aging — Function

run_vehicle_stock_aging(data_structures::Dict, optimizer)

Creates model, applies demand coverage, vehicle sizing, and vehicle aging constraints, and sets the objective. Output: Cost-optimal coverage of travel demand with sizing of required vehicle stock under the consideration of the age structure of the vehicles.

TransComp.run_constrained_technology_shift — Function

run_constrained_technology_shift(data_structures::Dict, optimizer)

Creates model, applies demand coverage, vehicle sizing, vehicle aging, and vehicle stock shift constraints, and sets the objective. Output: Cost-optimal coverage of travel demand with sizing of required vehicle stock under the consideration of the age structure of the vehicles and limitations on the speed of vehicle stock shift.

TransComp.run_fueling_infrastructure_sizing — Function

run_fueling_infrastructure_sizing(data_structures::Dict, optimizer)

Creates model, applies demand coverage, vehicle sizing, fueling demand constraints, and sets the objective. Output: Cost-optimal coverage of travel demand with sizing of required vehicle stock and expansion of fueling infrastructure.

TransComp.run_constrained_mode_shift — Function

run_constrained_mode_shift(data_structures::Dict, optimizer)

Creates model, applies demand coverage, vehicle sizing, mode shift constraints, and sets the objective. Output: Cost-optimal coverage of travel demand with sizing of required vehicle stock and constrained mode shift.

TransComp.run_mode_infrastructure_sizing — Function

run_mode_infrastructure_sizing(data_structures::Dict, optimizer)

Creates model, applies demand coverage, mode shift constraints, and sets the objective. Output: Cost-optimal coverage of travel demand under limitation of speed of shift.