SKILL.md
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⚡ Sublinear Optimization
- Action-state graph optimization using advanced matrix operations
- Cost-benefit analysis through diagonally dominant system solving
- Real-time plan optimization with minimal computational overhead
- Temporal advantage planning for predictive action execution
🎯 Intelligent Prioritization
- PageRank-based action and goal prioritization
- Multi-objective optimization with weighted criteria
- Critical path identification for time-sensitive objectives
- Resource allocation optimization across competing goals
🔮 Predictive Planning
- Temporal computational advantage for future state prediction
- Proactive action planning before conditions materialize
- Risk assessment and contingency plan generation
- Adaptive replanning based on real-time feedback
🤝 Multi-Agent Coordination
- Distributed goal achievement through swarm coordination
- Load balancing for parallel objective execution
- Inter-agent communication for shared goal states
- Consensus-based decision making for conflicting objectives
Primary Tools
Sublinear-Time Solver Tools
mcp__sublinear-time-solver__solve- Optimize action sequences and resource allocation
mcp__sublinear-time-solver__pageRank- Prioritize goals and actions based on importance
mcp__sublinear-time-solver__analyzeMatrix- Analyze goal dependencies and system properties
mcp__sublinear-time-solver__predictWithTemporalAdvantage- Predict future states before data arrives
mcp__sublinear-time-solver__estimateEntry- Evaluate partial state information efficiently
mcp__sublinear-time-solver__calculateLightTravel- Compute temporal advantages for time-critical planning
mcp__sublinear-time-solver__demonstrateTemporalLead- Validate predictive planning scenarios
Claude Flow Integration Tools
mcp__flow-nexus__swarm_init- Initialize multi-agent execution systems
mcp__flow-nexus__task_orchestrate- Execute planned action sequences
mcp__flow-nexus__agent_spawn- Create specialized agents for specific goals
mcp__flow-nexus__workflow_create- Define repeatable goal achievement patterns
mcp__flow-nexus__sandbox_create- Isolated environments for goal testing
Workflow
1. State Space Modeling
// World state representation
const WorldState = {
current_state: new Map([
['code_written', false],
['tests_passing', false],
['documentation_complete', false],
['deployment_ready', false]
]),
goal_state: new Map([
['code_written', true],
['tests_passing', true],
['documentation_complete', true],
['deployment_ready', true]
])
};
// Action definitions with preconditions and effects
const Actions = [
{
name: 'write_code',
cost: 5,
preconditions: new Map(),
effects: new Map([['code_written', true]])
},
{
name: 'write_tests',
cost: 3,
preconditions: new Map([['code_written', true]]),
effects: new Map([['tests_passing', true]])
},
{
name: 'write_documentation',
cost: 2,
preconditions: new Map([['code_written', true]]),
effects: new Map([['documentation_complete', true]])
},
{
name: 'deploy_application',
cost: 4,
preconditions: new Map([
['code_written', true],
['tests_passing', true],
['documentation_complete', true]
]),
effects: new Map([['deployment_ready', true]])
}
];2. Action Graph Construction
// Build adjacency matrix for sublinear optimization
async function buildActionGraph(actions, worldState) {
const n = actions.length;
const adjacencyMatrix = Array(n).fill().map(() => Array(n).fill(0));
// Calculate action dependencies and transitions
for (let i = 0; i < n; i++) {
for (let j = 0; j < n; j++) {
if (canTransition(actions[i], actions[j], worldState)) {
adjacencyMatrix[i][j] = 1 / actions[j].cost; // Weight by inverse cost
}
}
}
// Analyze matrix properties for optimization
const analysis = await mcp__sublinear_time_solver__analyzeMatrix({
matrix: {
rows: n,
cols: n,
format: "dense",
data: adjacencyMatrix
},
checkDominance: true,
checkSymmetry: false,
estimateCondition: true
});
return { adjacencyMatrix, analysis };
}3. Goal Prioritization with PageRank
async function prioritizeGoals(actionGraph, goals) {
// Use PageRank to identify critical actions and goals
const pageRank = await mcp__sublinear_time_solver__pageRank({
adjacency: {
rows: actionGraph.length,
cols: actionGraph.length,
format: "dense",
data: actionGraph
},
damping: 0.85,
epsilon: 1e-6
});
// Sort goals by importance scores
const prioritizedGoals = goals.map((goal, index) => ({
goal,
priority: pageRank.ranks[index],
index
})).sort((a, b) => b.priority - a.priority);
return prioritizedGoals;
}4. Temporal Advantage Planning
async function planWithTemporalAdvantage(planningMatrix, constraints) {
// Predict optimal solutions before full problem manifestation
const prediction = await mcp__sublinear_time_solver__predictWithTemporalAdvantage({
matrix: planningMatrix,
vector: constraints,
distanceKm: 12000 // Global coordination distance
});
// Validate temporal feasibility
const validation = await mcp__sublinear_time_solver__validateTemporalAdvantage({
size: planningMatrix.rows,
distanceKm: 12000
});
if (validation.feasible) {
return {
solution: prediction.solution,
temporalAdvantage: prediction.temporalAdvantage,
confidence: prediction.confidence
};
}
return null;
}5. A* Search with Sublinear Optimization
async function findOptimalPath(startState, goalState, actions) {
const openSet = new PriorityQueue();
const closedSet = new Set();
const gScore = new Map();
const fScore = new Map();
const cameFrom = new Map();
openSet.enqueue(startState, 0);
gScore.set(stateKey(startState), 0);
fScore.set(stateKey(startState), heuristic(startState, goalState));
while (!openSet.isEmpty()) {
const current = openSet.dequeue();
const currentKey = stateKey(current);
if (statesEqual(current, goalState)) {
return reconstructPath(cameFrom, current);
}
closedSet.add(currentKey);
// Generate successor states using available actions
for (const action of getApplicableActions(current, actions)) {
const neighbor = applyAction(current, action);
const neighborKey = stateKey(neighbor);
if (closedSet.has(neighborKey)) continue;
const tentativeGScore = gScore.get(currentKey) + action.cost;
if (!gScore.has(neighborKey) || tentativeGScore < gScore.get(neighborKey)) {
cameFrom.set(neighborKey, { state: current, action });
gScore.set(neighborKey, tentativeGScore);
// Use sublinear solver for heuristic optimization
const heuristicValue = await optimizedHeuristic(neighbor, goalState);
fScore.set(neighborKey, tentativeGScore + heuristicValue);
if (!openSet.contains(neighbor)) {
openSet.enqueue(neighbor, fScore.get(neighborKey));
}
}
}
}
return null; // No path found
}🌐 Multi-Agent Coordination
Swarm-Based Planning
async function coordinateWithSwarm(complexGoal) {
// Initialize planning swarm
const swarm = await mcp__claude_flow__swarm_init({
topology: "hierarchical",
maxAgents: 8,
strategy: "adaptive"
});
// Spawn specialized planning agents
const coordinator = await mcp__claude_flow__agent_spawn({
type: "coordinator",
capabilities: ["goal_decomposition", "plan_synthesis"]
});
const analyst = await mcp__claude_flow__agent_spawn({
type: "analyst",
capabilities: ["constraint_analysis", "feasibility_assessment"]
});
const optimizer = await mcp__claude_flow__agent_spawn({
type: "optimizer",
capabilities: ["path_optimization", "resource_allocation"]
});
// Orchestrate distributed planning
const planningTask = await mcp__claude_flow__task_orchestrate({
task: `Plan execution for: ${complexGoal}`,
strategy: "parallel",
priority: "high"
});
return { swarm, planningTask };
}Consensus-Based Decision Making
async function achieveConsensus(agents, proposals) {
// Build consensus matrix
const consensusMatrix = buildConsensusMatrix(agents, proposals);
// Solve for optimal consensus
const consensus = await mcp__sublinear_time_solver__solve({
matrix: consensusMatrix,
vector: generatePreferenceVector(agents),
method: "neumann",
epsilon: 1e-6
});
// Select proposal with highest consensus score
const optimalProposal = proposals[consensus.solution.indexOf(Math.max(...consensus.solution))];
return {
selectedProposal: optimalProposal,
consensusScore: Math.max(...consensus.solution),
convergenceTime: consensus.convergenceTime
};
}🎯 Advanced Planning Workflows
1. Hierarchical Goal Decomposition
async function decomposeGoal(complexGoal) {
// Create sandbox for goal simulation
const sandbox = await mcp__flow_nexus__sandbox_create({
template: "node",
name: "goal-decomposition",
env_vars: {
GOAL_CONTEXT: complexGoal.context,
CONSTRAINTS: JSON.stringify(complexGoal.constraints)
}
});
// Recursive goal breakdown
const subgoals = await recursiveDecompose(complexGoal, 0, 3); // Max depth 3
// Build dependency graph
const dependencyMatrix = buildDependencyMatrix(subgoals);
// Optimize execution order
const executionOrder = await mcp__sublinear_time_solver__pageRank({
adjacency: dependencyMatrix,
damping: 0.9
});
return {
subgoals: subgoals.sort((a, b) =>
executionOrder.ranks[b.id] - executionOrder.ranks[a.id]
),
dependencies: dependencyMatrix,
estimatedCompletion: calculateCompletionTime(subgoals, executionOrder)
};
}2. Dynamic Replanning
class DynamicPlanner {
constructor() {
this.currentPlan = null;
this.worldState = new Map();
this.monitoringActive = false;
}
async startMonitoring() {
this.monitoringActive = true;
while (this.monitoringActive) {
// OODA Loop Implementation
await this.observe();
await this.orient();
await this.decide();
await this.act();
await new Promise(resolve => setTimeout(resolve, 1000)); // 1s cycle
}
}
async observe() {
// Monitor world state changes
const stateChanges = await this.detectStateChanges();
this.updateWorldState(stateChanges);
}
async orient() {
// Analyze deviations from expected state
const deviations = this.analyzeDeviations();
if (deviations.significant) {
this.triggerReplanning(deviations);
}
}
async decide() {
if (this.needsReplanning()) {
await this.replan();
}
}
async act() {
if (this.currentPlan && this.currentPlan.nextAction) {
await this.executeAction(this.currentPlan.nextAction);
}
}
async replan() {
// Use temporal advantage for predictive replanning
const newPlan = await planWithTemporalAdvantage(
this.buildCurrentMatrix(),
this.getCurrentConstraints()
);
if (newPlan && newPlan.confidence > 0.8) {
this.currentPlan = newPlan;
// Store successful pattern
await mcp__claude_flow__memory_usage({
action: "store",
namespace: "goap-patterns",
key: `replan_${Date.now()}`,
value: JSON.stringify({
trigger: this.lastDeviation,
solution: newPlan,
worldState: Array.from(this.worldState.entries())
})
});
}
}
}3. Learning from Execution
class PlanningLearner {
async learnFromExecution(executedPlan, outcome) {
// Analyze plan effectiveness
const effectiveness = this.calculateEffectiveness(executedPlan, outcome);
if (effectiveness.success) {
// Store successful pattern
await this.storeSuccessPattern(executedPlan, effectiveness);
// Train neural network on successful patterns
await mcp__flow_nexus__neural_train({
config: {
architecture: {
type: "feedforward",
layers: [
{ type: "input", size: this.getStateSpaceSize() },
{ type: "hidden", size: 128, activation: "relu" },
{ type: "hidden", size: 64, activation: "relu" },
{ type: "output", size: this.getActionSpaceSize(), activation: "softmax" }
]
},
training: {
epochs: 50,
learning_rate: 0.001,
batch_size: 32
}
},
tier: "small"
});
} else {
// Analyze failure patterns
await this.analyzeFailure(executedPlan, outcome);
}
}
async retrieveSimilarPatterns(currentSituation) {
// Search for similar successful patterns
const patterns = await mcp__claude_flow__memory_search({
pattern: `situation:${this.encodeSituation(currentSituation)}`,
namespace: "goap-patterns",
limit: 10
});
// Rank by similarity and success rate
return patterns.results
.map(p => ({ ...p, similarity: this.calculateSimilarity(currentSituation, p.context) }))
.sort((a, b) => b.similarity * b.successRate - a.similarity * a.successRate);
}
}🎮 Gaming AI Integration
Behavior Tree Implementation
class GOAPBehaviorTree {
constructor() {
this.root = new SelectorNode([
new SequenceNode([
new ConditionNode(() => this.hasValidPlan()),
new ActionNode(() => this.executePlan())
]),
new SequenceNode([
new ActionNode(() => this.generatePlan()),
new ActionNode(() => this.executePlan())
]),
new ActionNode(() => this.handlePlanningFailure())
]);
}
async tick() {
return await this.root.execute();
}
hasValidPlan() {
return this.currentPlan &&
this.currentPlan.isValid &&
!this.worldStateChanged();
}
async generatePlan() {
const startTime = performance.now();
// Use sublinear solver for rapid planning
const planMatrix = this.buildPlanningMatrix();
const constraints = this.extractConstraints();
const solution = await mcp__sublinear_time_solver__solve({
matrix: planMatrix,
vector: constraints,
method: "random-walk",
maxIterations: 1000
});
const endTime = performance.now();
this.currentPlan = {
actions: this.decodeSolution(solution.solution),
confidence: solution.residual < 1e-6 ? 0.95 : 0.7,
planningTime: endTime - startTime,
isValid: true
};
return this.currentPlan !== null;
}
}Utility-Based Action Selection
class UtilityPlanner {
constructor() {
this.utilityWeights = {
timeEfficiency: 0.3,
resourceCost: 0.25,
riskLevel: 0.2,
goalAlignment: 0.25
};
}
async selectOptimalAction(availableActions, currentState, goalState) {
const utilities = await Promise.all(
availableActions.map(action => this.calculateUtility(action, currentState, goalState))
);
// Use sublinear optimization for multi-objective selection
const utilityMatrix = this.buildUtilityMatrix(utilities);
const preferenceVector = Object.values(this.utilityWeights);
const optimal = await mcp__sublinear_time_solver__solve({
matrix: utilityMatrix,
vector: preferenceVector,
method: "neumann"
});
const bestActionIndex = optimal.solution.indexOf(Math.max(...optimal.solution));
return availableActions[bestActionIndex];
}
async calculateUtility(action, currentState, goalState) {
const timeUtility = await this.estimateTimeUtility(action);
const costUtility = this.calculateCostUtility(action);
const riskUtility = await this.assessRiskUtility(action, currentState);
const goalUtility = this.calculateGoalAlignment(action, currentState, goalState);
return {
action,
timeUtility,
costUtility,
riskUtility,
goalUtility,
totalUtility: (
timeUtility * this.utilityWeights.timeEfficiency +
costUtility * this.utilityWeights.resourceCost +
riskUtility * this.utilityWeights.riskLevel +
goalUtility * this.utilityWeights.goalAlignment
)
};
}
}Usage Examples
Example 1: Complex Project Planning
// Goal: Launch a new product feature
const productLaunchGoal = {
objective: "Launch authentication system",
constraints: ["2 week deadline", "high security", "user-friendly"],
resources: ["3 developers", "1 designer", "$10k budget"]
};
// Decompose into actionable sub-goals
const subGoals = [
"Design user interface",
"Implement backend authentication",
"Create security tests",
"Deploy to production",
"Monitor system performance"
];
// Build dependency matrix
const dependencyMatrix = buildDependencyMatrix(subGoals);
// Optimize execution order
const optimizedPlan = await mcp__sublinear_time_solver__solve({
matrix: dependencyMatrix,
vector: resourceConstraints,
method: "neumann"
});Example 2: Resource Allocation Optimization
// Multiple competing objectives
const objectives = [
{ name: "reduce_costs", weight: 0.3, urgency: 0.7 },
{ name: "improve_quality", weight: 0.4, urgency: 0.8 },
{ name: "increase_speed", weight: 0.3, urgency: 0.9 }
];
// Use PageRank for multi-objective prioritization
const objectivePriorities = await mcp__sublinear_time_solver__pageRank({
adjacency: buildObjectiveGraph(objectives),
personalized: objectives.map(o => o.urgency)
});
// Allocate resources based on priorities
const resourceAllocation = optimizeResourceAllocation(objectivePriorities);Example 3: Predictive Action Planning
// Predict market conditions before they change
const marketPrediction = await mcp__sublinear_time_solver__predictWithTemporalAdvantage({
matrix: marketTrendMatrix,
vector: currentMarketState,
distanceKm: 20000 // Global market data propagation
});
// Plan actions based on predictions
const strategicActions = generateStrategicActions(marketPrediction);
// Execute with temporal advantage
const results = await executeWithTemporalLead(strategicActions);Example 4: Multi-Agent Goal Coordination
// Initialize coordinated swarm
const coordinatedSwarm = await mcp__flow_nexus__swarm_init({
topology: "mesh",
maxAgents: 12,
strategy: "specialized"
});
// Spawn specialized agents for different goal aspects
const agents = await Promise.all([
mcp__flow_nexus__agent_spawn({ type: "researcher", capabilities: ["data_analysis"] }),
mcp__flow_nexus__agent_spawn({ type: "coder", capabilities: ["implementation"] }),
mcp__flow_nexus__agent_spawn({ type: "optimizer", capabilities: ["performance"] })
]);
// Coordinate goal achievement
const coordinatedExecution = await mcp__flow_nexus__task_orchestrate({
task: "Build and optimize recommendation system",
strategy: "adaptive",
maxAgents: 3
});Example 5: Adaptive Replanning
// Monitor execution progress
const executionStatus = await mcp__flow_nexus__task_status({
taskId: currentExecutionId,
detailed: true
});
// Detect deviations from plan
if (executionStatus.deviation > threshold) {
// Analyze new constraints
const updatedMatrix = updateConstraintMatrix(executionStatus.changes);
// Generate new optimal plan
const revisedPlan = await mcp__sublinear_time_solver__solve({
matrix: updatedMatrix,
vector: updatedObjectives,
method: "adaptive"
});
// Implement revised plan
await implementRevisedPlan(revisedPlan);
}Best Practices
When to Use GOAP
- Complex Multi-Step Objectives: When goals require multiple interconnected actions
- Resource Constraints: When optimization of time, cost, or personnel is critical
- Dynamic Environments: When conditions change and plans need adaptation
- Predictive Scenarios: When temporal advantage can provide competitive benefits
- Multi-Agent Coordination: When multiple agents need to work toward shared goals
Goal Structure Optimization
// Well-structured goal definition
const optimizedGoal = {
objective: "Clear and measurable outcome",
preconditions: ["List of required starting states"],
postconditions: ["List of desired end states"],
constraints: ["Time, resource, and quality constraints"],
metrics: ["Quantifiable success measures"],
dependencies: ["Relationships with other goals"]
};Integration with Other Agents
- Coordinate with swarm agents for distributed execution
- Use neural agents for learning from past planning success
- Integrate with workflow agents for repeatable patterns
- Leverage sandbox agents for safe plan testing
Performance Optimization
- Matrix Sparsity: Use sparse representations for large goal networks
- Incremental Updates: Update existing plans rather than rebuilding
- Caching: Store successful plan patterns for similar goals
- Parallel Processing: Execute independent sub-goals simultaneously
Error Handling & Resilience
// Robust plan execution with fallbacks
try {
const result = await executePlan(optimizedPlan);
return result;
} catch (error) {
// Generate contingency plan
const contingencyPlan = await generateContingencyPlan(error, originalGoal);
return await executePlan(contingencyPlan);
}Monitoring & Adaptation
- Real-time Progress Tracking: Monitor action completion and resource usage
- Deviation Detection: Identify when actual progress differs from predictions
- Automatic Replanning: Trigger plan updates when thresholds are exceeded
- Learning Integration: Incorporate execution results into future planning
🔧 Advanced Configuration
Customizing Planning Parameters
const plannerConfig = {
searchAlgorithm: "a_star", // a_star, dijkstra, greedy
heuristicFunction: "manhattan", // manhattan, euclidean, custom
maxSearchDepth: 20,
planningTimeout: 30000, // 30 seconds
convergenceEpsilon: 1e-6,
temporalAdvantageThreshold: 0.8,
utilityWeights: {
time: 0.3,
cost: 0.3,
risk: 0.2,
quality: 0.2
}
};Error Handling and Recovery
class RobustPlanner extends GOAPAgent {
async handlePlanningFailure(error, context) {
switch (error.type) {
case 'MATRIX_SINGULAR':
return await this.regularizeMatrix(context.matrix);
case 'NO_CONVERGENCE':
return await this.relaxConstraints(context.constraints);
case 'TIMEOUT':
return await this.useApproximateSolution(context);
default:
return await this.fallbackToSimplePlanning(context);
}
}
}Advanced Features
Temporal Computational Advantage
Leverage light-speed delays for predictive planning:
- Plan actions before market data arrives from distant sources
- Optimize resource allocation with future information
- Coordinate global operations with temporal precision
Matrix-Based Goal Modeling
- Model goals as constraint satisfaction problems
- Use graph theory for dependency analysis
- Apply linear algebra for optimization
- Implement feedback loops for continuous improvement
Creative Solution Discovery
- Generate novel action combinations through matrix operations
- Explore solution spaces beyond obvious approaches
- Identify emergent opportunities from goal interactions
- Optimize for multiple success criteria simultaneously
This goal-planner agent represents the cutting edge of AI-driven objective achievement, combining mathematical rigor with practical execution capabilities through the powerful sublinear-time-solver toolkit and Claude Flow ecosystem.