Chapter 4

Task Allocation and Planning

弘益人間 (홍익인간) · Benefit All Humanity

Effective task allocation ensures that work is distributed fairly and efficiently among agents, maximizing collective productivity while respecting individual capabilities. Like a well-organized community where each member contributes according to their strengths, multi-agent systems achieve optimal outcomes through intelligent task distribution.

The Task Allocation Problem

Task allocation is the process of assigning tasks to agents in a way that optimizes system performance while satisfying constraints. This is one of the most fundamental problems in multi-agent systems.

Definition: Task allocation determines which agent should execute which task to optimize overall system utility while respecting agent capabilities, resource constraints, and temporal dependencies.

Key considerations in task allocation include:

Allocation Strategies

Round Robin Allocation

Tasks are distributed cyclically among agents. Simple but doesn't account for agent capabilities or current workload.

class RoundRobinAllocator {
    constructor(agents) {
        this.agents = agents;
        this.currentIndex = 0;
    }

    allocate(task) {
        const agent = this.agents[this.currentIndex];
        this.currentIndex = (this.currentIndex + 1) % this.agents.length;

        return {
            task: task,
            assignedAgent: agent.id,
            timestamp: Date.now()
        };
    }

    allocateBatch(tasks) {
        return tasks.map(task => this.allocate(task));
    }
}

// Simple but may not balance workload effectively
// 弘益人間: Equal distribution for fairness

Capability-Based Allocation

Tasks are assigned to agents with the best matching capabilities and skills.

class CapabilityBasedAllocator {
    constructor(agents) {
        this.agents = agents;
        this.capabilityMatrix = this.buildCapabilityMatrix();
    }

    buildCapabilityMatrix() {
        const matrix = new Map();

        for (const agent of this.agents) {
            matrix.set(agent.id, {
                skills: agent.getSkills(),
                performance: agent.getPerformanceMetrics(),
                availability: agent.isAvailable()
            });
        }

        return matrix;
    }

    allocate(task) {
        let bestAgent = null;
        let bestScore = -Infinity;

        for (const agent of this.agents) {
            const capabilities = this.capabilityMatrix.get(agent.id);

            if (!capabilities.availability) continue;

            const score = this.calculateMatchScore(task, capabilities);

            if (score > bestScore) {
                bestScore = score;
                bestAgent = agent;
            }
        }

        return {
            task: task,
            assignedAgent: bestAgent?.id || null,
            matchScore: bestScore,
            timestamp: Date.now()
        };
    }

    calculateMatchScore(task, capabilities) {
        const requiredSkills = task.requiredSkills || [];
        const agentSkills = capabilities.skills;

        // Calculate skill match percentage
        const matchedSkills = requiredSkills.filter(
            skill => agentSkills.includes(skill)
        ).length;

        const skillScore = matchedSkills / requiredSkills.length;

        // Factor in agent performance
        const performanceScore = capabilities.performance.averageQuality;

        // Weighted combination
        return skillScore * 0.7 + performanceScore * 0.3;
    }
}

// 弘益人間: Matching tasks to expertise for optimal outcomes

Load-Balanced Allocation

Tasks are assigned to minimize imbalance in agent workloads.

class LoadBalancedAllocator {
    constructor(agents) {
        this.agents = agents;
        this.workload = new Map();

        // Initialize workload tracking
        agents.forEach(agent => this.workload.set(agent.id, 0));
    }

    allocate(task) {
        // Find agent with least current workload
        let minWorkload = Infinity;
        let leastLoadedAgent = null;

        for (const agent of this.agents) {
            const currentLoad = this.workload.get(agent.id);

            if (agent.canPerform(task) && currentLoad < minWorkload) {
                minWorkload = currentLoad;
                leastLoadedAgent = agent;
            }
        }

        if (leastLoadedAgent) {
            // Update workload
            const estimatedEffort = task.estimatedDuration || 1;
            this.workload.set(
                leastLoadedAgent.id,
                this.workload.get(leastLoadedAgent.id) + estimatedEffort
            );
        }

        return {
            task: task,
            assignedAgent: leastLoadedAgent?.id || null,
            currentWorkload: minWorkload,
            timestamp: Date.now()
        };
    }

    // Called when agent completes a task
    taskCompleted(agentId, task) {
        const currentLoad = this.workload.get(agentId);
        const effort = task.actualDuration || task.estimatedDuration || 1;
        this.workload.set(agentId, Math.max(0, currentLoad - effort));
    }

    getWorkloadBalance() {
        const loads = Array.from(this.workload.values());
        const avg = loads.reduce((sum, load) => sum + load, 0) / loads.length;
        const variance = loads.reduce(
            (sum, load) => sum + Math.pow(load - avg, 2),
            0
        ) / loads.length;

        return {
            average: avg,
            variance: variance,
            standardDeviation: Math.sqrt(variance)
        };
    }
}

// 弘益人間: Fair workload distribution benefiting all agents

Coalition Formation

Some tasks require multiple agents working together. Coalition formation determines which agents should form teams to complete complex tasks.

class CoalitionFormation {
    constructor(agents, tasks) {
        this.agents = agents;
        this.tasks = tasks;
    }

    // Form coalitions for tasks requiring multiple agents
    formCoalitions() {
        const coalitions = [];

        for (const task of this.tasks) {
            if (task.requiredAgents > 1) {
                const coalition = this.findBestCoalition(task);
                if (coalition) {
                    coalitions.push({
                        task: task,
                        members: coalition.members,
                        value: coalition.value
                    });
                }
            } else {
                // Single agent task
                const agent = this.findBestAgent(task);
                if (agent) {
                    coalitions.push({
                        task: task,
                        members: [agent],
                        value: this.calculateValue(task, [agent])
                    });
                }
            }
        }

        return coalitions;
    }

    findBestCoalition(task) {
        const requiredSize = task.requiredAgents;
        const candidates = this.generateCombinations(this.agents, requiredSize);

        let bestCoalition = null;
        let bestValue = -Infinity;

        for (const coalition of candidates) {
            // Check if coalition can perform task
            if (!this.canPerformTask(coalition, task)) continue;

            const value = this.calculateCoalitionValue(coalition, task);

            if (value > bestValue) {
                bestValue = value;
                bestCoalition = coalition;
            }
        }

        return bestCoalition ? {
            members: bestCoalition,
            value: bestValue
        } : null;
    }

    canPerformTask(coalition, task) {
        const combinedSkills = new Set();
        coalition.forEach(agent => {
            agent.getSkills().forEach(skill => combinedSkills.add(skill));
        });

        return task.requiredSkills.every(skill => combinedSkills.has(skill));
    }

    calculateCoalitionValue(coalition, task) {
        // Value = task reward - coalition cost
        const reward = task.reward || 100;
        const cost = coalition.reduce(
            (sum, agent) => sum + agent.getCost(task),
            0
        );

        // Bonus for complementary skills
        const synergyBonus = this.calculateSynergy(coalition, task);

        return reward - cost + synergyBonus;
    }

    calculateSynergy(coalition, task) {
        // Agents with complementary skills work better together
        const skillCoverage = new Set();
        coalition.forEach(agent => {
            agent.getSkills().forEach(skill => skillCoverage.add(skill));
        });

        const coverageRatio = skillCoverage.size / coalition.length;
        return coverageRatio * 20; // Synergy bonus
    }
}

// 弘益人間: Collaborative teams for complex challenges

Dynamic Task Allocation

In dynamic environments, new tasks arrive continuously and agents' states change. Allocation must adapt in real-time.

class DynamicTaskAllocator {
    constructor(agents) {
        this.agents = agents;
        this.taskQueue = [];
        this.allocations = new Map();
        this.running = false;
    }

    start() {
        this.running = true;
        this.allocationLoop();
    }

    stop() {
        this.running = false;
    }

    addTask(task) {
        task.arrivalTime = Date.now();
        task.priority = task.priority || 0;

        // Insert in priority order
        const index = this.taskQueue.findIndex(t => t.priority < task.priority);
        if (index === -1) {
            this.taskQueue.push(task);
        } else {
            this.taskQueue.splice(index, 0, task);
        }
    }

    async allocationLoop() {
        while (this.running) {
            if (this.taskQueue.length > 0) {
                const task = this.taskQueue.shift();
                await this.allocateTask(task);
            }

            // Check for task completions and reallocation needs
            await this.checkCompletions();
            await this.considerReallocation();

            await this.sleep(100); // Check every 100ms
        }
    }

    async allocateTask(task) {
        // Find best available agent
        const availableAgents = this.agents.filter(a => a.isIdle());

        if (availableAgents.length === 0) {
            // No agents available, put back in queue
            this.taskQueue.unshift(task);
            return;
        }

        const bestAgent = this.selectBestAgent(availableAgents, task);

        // Assign task
        this.allocations.set(task.id, {
            task: task,
            agent: bestAgent,
            startTime: Date.now(),
            status: 'in-progress'
        });

        await bestAgent.executeTask(task);
    }

    async considerReallocation() {
        // Consider reallocating tasks if better options become available
        for (const [taskId, allocation] of this.allocations) {
            if (allocation.status !== 'in-progress') continue;

            const currentAgent = allocation.agent;
            const idleAgents = this.agents.filter(
                a => a.isIdle() && a.id !== currentAgent.id
            );

            for (const agent of idleAgents) {
                if (this.shouldReallocate(allocation, agent)) {
                    await this.reallocate(allocation, agent);
                    break;
                }
            }
        }
    }

    shouldReallocate(allocation, newAgent) {
        const task = allocation.task;
        const currentAgent = allocation.agent;

        // Only reallocate if significant benefit
        const currentScore = this.scoreAssignment(currentAgent, task);
        const newScore = this.scoreAssignment(newAgent, task);

        return newScore > currentScore * 1.5; // 50% improvement threshold
    }

    async reallocate(allocation, newAgent) {
        const task = allocation.task;
        const oldAgent = allocation.agent;

        // Preempt current execution
        await oldAgent.cancelTask(task);

        // Reassign to new agent
        allocation.agent = newAgent;
        allocation.startTime = Date.now();

        await newAgent.executeTask(task);
    }
}

// 弘益人間: Adaptive allocation for changing conditions

Multi-Agent Planning

Planning involves determining sequences of actions that achieve goals. In multi-agent systems, agents must coordinate their plans.

Centralized Planning

A central planner creates a joint plan for all agents.

class CentralizedPlanner {
    constructor(agents, goals) {
        this.agents = agents;
        this.goals = goals;
    }

    createPlan() {
        // Generate global plan for all agents
        const plan = {
            agents: new Map(),
            schedule: [],
            dependencies: []
        };

        // Decompose goals into tasks
        const tasks = this.decomposeGoals(this.goals);

        // Allocate tasks to agents
        for (const task of tasks) {
            const agent = this.selectAgent(task);
            if (!plan.agents.has(agent.id)) {
                plan.agents.set(agent.id, []);
            }
            plan.agents.get(agent.id).push(task);
        }

        // Create schedule respecting dependencies
        plan.schedule = this.createSchedule(tasks);

        return plan;
    }

    decomposeGoals(goals) {
        const tasks = [];

        for (const goal of goals) {
            const subtasks = this.decomposeGoal(goal);
            tasks.push(...subtasks);
        }

        return tasks;
    }

    decomposeGoal(goal) {
        // Hierarchical task decomposition
        if (goal.isPrimitive) {
            return [goal];
        }

        const subtasks = [];
        for (const method of goal.methods) {
            if (this.isApplicable(method, goal)) {
                subtasks.push(...method.subtasks);
                break;
            }
        }

        // Recursively decompose
        return subtasks.flatMap(task =>
            task.isPrimitive ? [task] : this.decomposeGoal(task)
        );
    }

    createSchedule(tasks) {
        // Topological sort respecting dependencies
        const schedule = [];
        const completed = new Set();
        const remaining = [...tasks];

        while (remaining.length > 0) {
            const ready = remaining.filter(task =>
                task.dependencies.every(dep => completed.has(dep))
            );

            if (ready.length === 0) {
                throw new Error('Circular dependencies detected');
            }

            // Schedule ready tasks
            for (const task of ready) {
                schedule.push({
                    task: task,
                    earliestStart: this.calculateEarliestStart(task, schedule)
                });
                completed.add(task.id);
            }

            // Remove from remaining
            remaining.splice(0, remaining.length,
                ...remaining.filter(t => !completed.has(t.id))
            );
        }

        return schedule;
    }
}

// 弘益人間: Coordinated planning for shared goals

Distributed Planning

Each agent creates its own plan and coordinates with others to resolve conflicts and dependencies.

class DistributedPlanningAgent {
    constructor(id, goals) {
        this.id = id;
        this.goals = goals;
        this.plan = [];
        this.commitments = [];
    }

    async createPlan() {
        // Each agent plans independently
        this.plan = this.generateLocalPlan(this.goals);

        // Share plan with neighbors
        await this.sharePlan();

        // Coordinate and resolve conflicts
        await this.coordinatePlans();

        return this.plan;
    }

    generateLocalPlan(goals) {
        // Use A* or similar planner
        const plan = [];

        for (const goal of goals) {
            const actions = this.planForGoal(goal);
            plan.push(...actions);
        }

        return this.optimizePlan(plan);
    }

    async sharePlan() {
        for (const neighbor of this.neighbors) {
            await neighbor.receivePlan({
                agentId: this.id,
                plan: this.plan,
                resources: this.getRequiredResources()
            });
        }
    }

    async coordinatePlans() {
        // Iteratively refine plan through negotiation
        let conflicts = await this.detectConflicts();

        while (conflicts.length > 0) {
            for (const conflict of conflicts) {
                await this.resolveConflict(conflict);
            }

            conflicts = await this.detectConflicts();
        }
    }

    async resolveConflict(conflict) {
        if (conflict.type === 'resource') {
            // Negotiate resource usage time
            await this.negotiateResourceSchedule(conflict);
        } else if (conflict.type === 'ordering') {
            // Determine action ordering
            await this.negotiateOrdering(conflict);
        }
    }
}

// 弘益人間: Distributed planning empowering autonomous agents

Task Scheduling

Scheduling determines when tasks should be executed, considering deadlines, priorities, and resource availability.

class TaskScheduler {
    constructor() {
        this.schedule = [];
        this.resources = new Map();
    }

    // Earliest Deadline First (EDF) scheduling
    scheduleEDF(tasks) {
        const sorted = tasks.sort((a, b) => a.deadline - b.deadline);

        for (const task of sorted) {
            const slot = this.findEarliestSlot(task);
            if (slot) {
                this.schedule.push({
                    task: task,
                    startTime: slot.start,
                    endTime: slot.end
                });
            }
        }

        return this.schedule;
    }

    // Priority-based scheduling
    schedulePriority(tasks) {
        const sorted = tasks.sort((a, b) => b.priority - a.priority);

        for (const task of sorted) {
            const slot = this.findEarliestSlot(task);
            if (slot) {
                this.schedule.push({
                    task: task,
                    startTime: slot.start,
                    endTime: slot.end
                });
            }
        }

        return this.schedule;
    }

    findEarliestSlot(task) {
        const duration = task.duration;
        let currentTime = Date.now();

        while (currentTime < task.deadline) {
            if (this.isSlotAvailable(currentTime, duration, task.resources)) {
                return {
                    start: currentTime,
                    end: currentTime + duration
                };
            }
            currentTime += 1000; // Check every second
        }

        return null; // No slot found before deadline
    }

    isSlotAvailable(startTime, duration, requiredResources) {
        const endTime = startTime + duration;

        // Check if required resources are available
        for (const [resource, amount] of Object.entries(requiredResources)) {
            if (!this.checkResourceAvailability(resource, amount, startTime, endTime)) {
                return false;
            }
        }

        return true;
    }
}

// 弘益人間: Efficient scheduling maximizing collective productivity

Chapter Summary

Review Questions

  1. What factors should be considered in task allocation decisions?
  2. Compare round robin, capability-based, and load-balanced allocation strategies.
  3. When is coalition formation necessary? How are coalitions formed?
  4. Explain the difference between static and dynamic task allocation.
  5. What are the trade-offs between centralized and distributed planning?
  6. Describe hierarchical task decomposition in multi-agent planning.
  7. How does EDF (Earliest Deadline First) scheduling work?
  8. What is task reallocation and when should it be considered?
  9. How do you calculate coalition value considering synergy effects?
  10. How does effective task allocation support the 弘익人간 principle?

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