Rule context model

1. Overview

The rule context defines link, restriction, flow-control, and feasibility services used to judge whether a recovered task sequence is legal. It supplies predicates and costs to bunch generation; it is not an independent master model.

1. Dependent Contexts

Task, aircraft, and infrastructure time/cost types.

2. Concepts / Entities

1. Link

$p r e v_{l}$ , $s u c c_{l}$ : predecessor and successor tasks;

$s p l i t C o s t_{l}$ : link split cost; $t y p e_{l}$ : connecting, stopover, or connection-time-ignoring link.

2. Restriction

$c a t e g o r y_{r}$ : restriction category; $w e i g h t_{r}$ : violation weight;

$c o s t_{r}$ : optional violation cost; $c o n d i t i o n_{r}$ : task/airport/aircraft condition.

3. Flow control

$a i r p o r t_{f}$ , $s c e n e_{f}$ , $t i m e_{f}$ , and $c a p a c i t y_{f}$ describe an arrival/departure flow window and its capacity.

3. Variables

No decision or auxiliary variables are registered by RuleContext.

4. Predicates

linkType(l) classifies link semantics. violates(t,r) means task t violates restriction r. flowClosed(f) means the flow capacity is zero. feasible(t,t') means the connection time, rule, and aircraft tests pass.

5. Sets

$L$ : links; $L^{c o n n}$ , $L^{s t o p}$ , and $L^{i g n o r e}$ are link subsets. $R$ : restrictions; $F$ : flow-control windows; $T^{f e a s}$ : task transitions accepted by all enabled rules.

6. Intermediate Values

The connection service derives a transition time and total violation cost:

Δ (t, t^{'}) = s t a r t_{t^{'}} - e n d_{t}, c o s t (t, t^{'}) = \sum_{r \in R} w e i g h t_{r} 1 [v i o l a t e s (t, t^{'}, r)]

7. Assertions

Every link has two task endpoints, and a connecting link only connects tasks whose airport/time data are defined. A flow window has nonnegative capacity and nonempty time range.

8. Constraints

No independent solver rows are registered. Feasibility is a service predicate:

s . t . f e a s i b l e (t, t^{'}) ⟺ Δ (t, t^{'}) \geq r e q u i r e d C o n n e c t i o n T i m e (t, t^{'}) \land \neg v i o l a t e s (t, t^{'}, r) \forall r \in R^{h a r d}

9. Objective Function (if applicable)

None. Transition and restriction costs are inputs to a bunch cost calculator.

10. Algorithm References

No standalone algorithm document; FeasibilityJudger, connection-time, and cost calculators implement the predicates.

11. Ubiquitous Language

Term	Symbol	Definition
link	`l`	relation between consecutive tasks
restriction	`r`	rule limiting a task transition
flow control	`f`	airport/time capacity window
feasibility	`feasible`	all enabled rules pass

12. Design Decisions

Decision	Alternative	Rationale
evaluate rules before column insertion	add invalid bunches then filter in master	keeps generated columns feasible

13. Change Log

Version	Change	Reason
1.0	Documented rule predicates as a service boundary	Separate feasibility from master variables

Rule context model ​

1. Overview ​

1. Dependent Contexts ​

2. Concepts / Entities ​

1. Link ​

2. Restriction ​

3. Flow control ​

3. Variables ​

4. Predicates ​

5. Sets ​

6. Intermediate Values ​

7. Assertions ​

8. Constraints ​

9. Objective Function (if applicable) ​

10. Algorithm References ​

11. Ubiquitous Language ​

12. Design Decisions ​

13. Change Log ​