Genetic Algorithm Constraint Graph for Dynamic Air Mission Scheduling

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Solution Overview

Problem

Optimization problems with dynamic constraints, such as Air Tasking Order planning in wartime air campaigns, face challenges in efficiently generating feasible solutions that adapt to changing objectives and resource availability, as existing methods struggle to handle real-time modifications and large, nonlinear solution spaces.

Innovation Solution

A genetic algorithm-based method that utilizes a constraint graph to ensure feasibility of solutions, where each solution corresponds to a connected subgraph, and allows for dynamic constraint modification between iterations, enabling real-time adaptation and efficient solution generation.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If a genetic algorithm is used to solve optimization problems with dynamic constraints, then the ability to handle large, nonlinear solution spaces is improved, but the difficulty of ensuring feasibility under changing constraints increases

Engineering Contradiction:

Improveability to handle large, nonlinear solution spacesVSAvoiddifficulty of ensuring feasibility under changing constraints

Core Design Contradiction:

Adaptability or versatilityVSDevice complexity

Solution Approach 1:

The constraint system is segmented into static constraints and dynamic constraints. Static constraints remain fixed throughout the optimization process, while dynamic constraints can be modified between generations. This segmentation allows the genetic algorithm to handle the large solution space effectively while managing constraint complexity through organized categorization.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The system implements dynamic constraint modification between generations of the genetic algorithm. Constraints can be added, removed, or modified based on changing problem conditions, allowing the optimization process to adapt to dynamic environments while maintaining feasibility through systematic constraint management.

Inventive Principle:

Principle #15Dynamics

2Productivity

If dynamic constraints are modified between iterations, then real-time adaptation to changing objectives is improved, but the time required to re-evaluate solution feasibility increases

Engineering Contradiction:

Improvereal-time adaptation to changing objectivesVSAvoidtime required to re-evaluate solution feasibility

Core Design Contradiction:

ProductivityVSLoss of time

Solution Approach 1:

The system performs preliminary evaluation of constraint changes between generations. By assessing which constraints have changed and which solutions are affected before full re-evaluation, the system reduces the time required to maintain feasibility while still achieving real-time adaptation to changing objectives.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The system implements feedback mechanisms where constraint modifications trigger targeted re-evaluation of affected solutions. This feedback loop allows the genetic algorithm to efficiently adapt to changing constraints by focusing computational effort only on solutions that need re-assessment, rather than re-evaluating the entire population.

Inventive Principle:

Principle #23Feedback

3Manufacturing precision

If infeasible solutions are discarded, then solution quality is improved, but the population size and diversity may decrease

Engineering Contradiction:

Improvesolution qualityVSAvoidpopulation size and diversity

Core Design Contradiction:

Manufacturing precisionVSQuantity of substance

Solution Approach 1:

The system discards infeasible solutions from the population while implementing mechanisms to recover diversity. This may involve generating new feasible solutions through constraint-based initialization or using archive structures to preserve genetic material from previously feasible solutions, thereby maintaining population diversity despite selective discarding.

Inventive Principle:

Principle #34Discarding and recovering

Data Source

PatentUS8069127B2Method and system for solving an optimization problem with dynamic constraints

Publication Date: 2011.11.29 21ST CENTURY TECH

AI summary

A method and system for solving an optimization problem comprising a plurality of dynamic constraints. A genetic algorithm is used to iteratively generate potential solutions to the problem. A constraint graph is used to model the plurality of dynamic constraints, and any potential solution that does not correspond to a connected subgraph of the constraint graph is infeasible and discarded. Real-time changes in dynamic constraints are incorporated by modification of the constraint graph between iterations of the genetic algorithm. An exemplary embodiment comprising the scheduling of air missions is presented.