Soft security context model

1. Overview

Manages soft safety constraints including empty loading division, main deck door empty preference, and ballast weight advice — constraints that improve safety but can be relaxed if needed.

1. Dependent Contexts

1. Aircraft
2. Stowage

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2. Concepts / Entities

1. Divide Empty Loading

Ensures empty positions are divided rather than clustered for structural safety.

$positions$ : Position list.

$load$ : Load data.

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3. Variables

1. Decision Variables

This context reuses decision variables from the stowage context and does not define independent decision variables.

2. Auxiliary Variables

This context does not define independent auxiliary variables.

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4. Predicates

The business-level relation distributedEmptyPositions(J) names the divide-empty preference. In the Demo2 pipeline, that preference is realized by three source intermediate expressions and three separate soft objective inputs over adjacent position pairs; the relation itself is not a registered solver constraint.

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5. Sets

This context does not own independent sets. It uses $I$ for cargo items, $J$ for stowage positions, $A\subseteq J\times J$ for adjacent position pairs, $J^{\mathrm{emptyHated}}\subseteq J$ for positions marked EmptyHated, and $J^{\mathrm{beside}}\subseteq J$ for positions beside a main-deck door.

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6. Intermediate Values

The source DivideEmptyLoading model registers three index-aligned intermediate expressions for each $(j,k)\in A$:

1. emptyBetweenCargo[p], written $e_{jk}^{\mathrm{bc}}$, describes non-empty cargo at the first position against total cargo at the second.
2. emptyCargoBetweenCargo[p], written $e_{jk}^{\mathrm{cb}}$, describes empty cargo at the first position against non-empty cargo at the second.
3. emptyBetweenEmptyCargo[p], written $e_{jk}^{\mathrm{bb}}$, describes empty cargo at the first position against total cargo at the second.

For positions whose load is decided dynamically, the source IfFunction branches are represented by:

$$\begin{array}{rl}{e}_{jk}^{\mathrm{bc}}& =\mathrm{If}(L_j^{\mathrm{nonempty}}-(L_k^{\mathrm{all}}+1)+\tau ),\\ e_{jk}^{\mathrm{cb}}& =\mathrm{If}(L_j^{\mathrm{empty}}+L_k^{\mathrm{nonempty}}-2+\tau ),\\ e_{jk}^{\mathrm{bb}}& =\mathrm{If}(L_j^{\mathrm{empty}}-(L_k^{\mathrm{all}}+1)+\tau ).\end{array}$$

Here $\tau$ denotes the nonzero comparison offset used by the source IfFunction. Fixed-range branches in the source can instead collapse an expression to zero, a load amount, or another constant; these intermediates are model expressions, not additional solver constraints.

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7. Assertions

This context does not define independent assertions.

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8. Constraints

This section names the context's soft limits. In the Demo2 pipeline, the four entries below contribute objective terms; they are not s.t. rows. The displayed expressions use source-layer symbols and do not assert a new aggregate objective.

1. Empty Hated Limit

[CN]: 空载厌恶限制

Description: The pipeline registers a soft objective term for positions marked EmptyHated; its exact source-aligned expression, including the position coefficient and full-load expression, is given in Section 9.

2. Main Deck Door Empty Limit

[CN]: 主甲板舱门空载限制

Description: The pipeline minimizes stowage assignments beside main-deck doors (B757/B767), rather than imposing an empty_j = 1 row; the exact source-aligned expression is given in Section 9.

3. Divide Empty Loading Limit

[CN]: 空载分离限制

Description: The pipeline registers three separate soft objective inputs over adjacent pairs. distributedEmptyPositions(J) is only the business-level name for this preference, not an s.t. constraint; the three source-aligned expressions are given in Section 9.

4. Advice Ballast Weight Limit

[CN]: 建议压舱物重量限制

Description: The pipeline adds a one-sided threshold-slack objective only when an advice value exists; the negative-deviation semantics and exact source-aligned expression are given in Section 9, with no hard lower-bound s.t. row asserted here.

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9. Objective Function (if applicable)

The context contributes the following separate soft objective inputs. Their activation and any higher-level aggregation belong to the selected mode pipeline; this page does not invent a single generic penalty-sum expression, and none of these entries is a hard s.t. row.

1. Empty Hated

$$min\sum _{j\in J^{\mathrm{emptyHated}}}{c}_j(1-loa{d}_j^{\mathrm{full}})$$

Here $c_j$ is the position coefficient and $loa{d}_j^{\mathrm{full}}$ is the source full-load expression.

2. Main Deck Door Empty

$$min\sum _{i\in I}\sum _{j\in J^{\mathrm{beside}}}{c}_{i}stowag{e}_{ij}$$

Here $J^{\mathrm{beside}}$ is the set of positions whose door ubiety is Beside.

3. Divide Empty Loading

$$\begin{array}{rl}min& \sum _{(j,k)\in A}{c}_{jk}^{\mathrm{bc}}{e}_{jk}^{\mathrm{bc}},\\ min& \sum _{(j,k)\in A}{c}_{jk}^{\mathrm{cb}}{e}_{jk}^{\mathrm{cb}},\\ min& \sum _{(j,k)\in A}{c}_{jk}^{\mathrm{bb}}{e}_{jk}^{\mathrm{bb}}.\end{array}$$

These are three separate source objective inputs, with the coefficient and intermediate families defined in Section 6.

4. Advice Ballast Weight

$$min{c}_{\mathrm{ballast}}{s}_{\mathrm{ballast}}^{-},s_{\mathrm{ballast}}^{-}\ge 0$$

The term is added only when an advice value exists; $s_{\mathrm{ballast}}^{-}$ is the one-sided slack for falling below the advice threshold.

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10. Algorithm References

This context does not define an independent algorithm reference.

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11. Ubiquitous Language

Term	Symbol	Definition
Divide Empty Loading	DivideEmptyLoading	Distributed empty positions
Empty Hated	EmptyHated	Soft penalty for empty positions
Main Deck Door Empty	MainDeckDoorEmpty	Soft penalty for stowage beside main-deck doors
Advice Ballast Weight	AdviceBallastWeight	Advisory ballast weight value

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12. Design Decisions

Decision	Alternatives	Rationale
Constraint type	Hard vs Soft	Soft constraints allow relaxation when needed

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13. Change Log

No context-specific change entries are recorded on this page.