Line blocking with vehicle interchange uses an objective function for evaluating the quality of a solution. The objective function measures solution properties where there is room for improvement. It comprises the objective function of line blocking without vehicle interchange (Construction of the graph) as a component.
The following solution properties are evaluated:
- Costs: Objective function of line blocking without vehicle interchange. This especially comprises the number of vehicles per vehicle combination as well as the service km and empty km and service times and empty times, as well as the layovers within and outside of a depot
- Number of vehicle units: Exceeding the predefined number of available vehicle units
- Consideration of volumes: Too low capacities (total or seats) regarding the OD demand
- Line purity, local definition: Number of transfers between the different lines
- Line purity, global definition: Number of different lines in a block
- Number of vehicle combinations per line: Number of different vehicle combinations used on the same line
- Regularity: Number of vehicle journey sections, who's vehicle journey section occurrence lies in at least two different blocks or blocking days
- Difference from reference solution (only when a reference solution has been specified): Difference to this reference solution in form of deviating transfers between vehicle journey sections
- State of charge: How often, how much and how long is the state of charge with respect to a user-defined line blocking item type less than the minimum required state of charge.
- Duration of the operations: Deviation of operations between two layovers in depot from the desired operating time.
The following function is used as an objective function (OF), which is based on the comparison between the calculated and the estimated values for each of the objective function components:
where
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ci |
Influential factor (Procedure parameters) for the indicator i, where ∑ci > 0 |
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ofi |
Objective function component for indicator i according to the upper list |
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comparisoni |
Comparison value for indicator i on a comparable scale |
The individual component properties are apply as follows:
|
Component |
Calculation |
|
Cost |
The objective function component costs evaluate the solution according to the same criteria as the line blocking without vehicle interchange. It therefore applies of Costs = ∑fe • Costs(e) (fe = Flow on edge e) For the comparison value, vehicle combinations are randomly selected and thus a solution calculated. The costs are then used as a comparison value. |
|
Number of vehicle units |
The sum is calculated over all vehicle units, across the number of used but not available vehicles per vehicle unit The comparison value comparisonvehicle is 1. Note: This is how you achieve very strong penalization, because this criterion must apply "hard" if it is used at all. |
|
Consideration of volumes |
For the calculation, for each vehicle journey item i first the difference between its volume and its capacity (cap) is calculated as follows
The capacity sums up from the selected capacity (seats or total) of all vehicle combinations of all vehicle journey sections that service this vehicle journey item. Due to the current parameter settings, a vehicle journey's value using option Average volume
using option Peak volume
The value
The value of this objective function component, which applies for the random solution, used for cost estimation, is used as a comparison value. |
|
Line purity, local definition |
The number of line changes between successive vehicle journeys in the block are measured. The benchmark is the number of occurrences of vehicle journey sections in total (therefore the number of all changeovers between successive vehicle journey block items). |
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Line purity, global definition |
The number is calculated minus 1 of the line per block, summed up over all blocks. The comparison value is the number minus 1 of the lines per partition, summed up over all partitions. |
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Regularity |
Dispersion of the occurrences of vehicle journey sections is measured for different blocks or optionally for different blocking days. The following applies: ofregularity = Sum of vehicle journey sections |{Blocks / blocking days which contain the VJS}| - 1 Comparisonregularity = (Sum of occurrences of the VJS in the line blocking time interval – 1) |
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Distance to starting solution |
The number of changeovers from vehicle journey section to vehicle journey section, which differ from the comparison solution, is measured. The comparison value is the number of all changeovers from vehicle journey section to vehicle journey section in the comparison solution. |
|
State of charge |
Not only a negative state of charge is penalized, but also a positive one if it is below the minimum state of charge. The supplement is quadratic when the state of charge is below zero, and linear when the state of charge is between zero and the minimum state of charge. |
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Duration of the operations |
All operations whose duration is between the lower and the upper limit for the desired operating times are neutral for evaluation. If the duration is above the upper value, it enters proportional to the exceeding. The same applies if it is too low, in which case half the proportionality factor takes effect. |
results from the particular formula below:
is the total calculated for all vehicle journeys:
Table 229: Objective function components for line blocking with vehicle interchange
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Note: Objective function components, which are not relevant to the specific planning task, can be switched off by setting the respective coefficient to 0. This is recommended, because optimization up until the solutions, considering the hidden properties, is thus suppressed. Finding good solutions regarding the remaining criteria is accelerated accordingly. |
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Note: Solutions that would be optimal with a different weighting of the objective function components (Pareto-Optima) and that are found during optimization can be saved. This helps you to estimate the optimization scope and the corresponding weights. |
