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SMO Placement Algorithm

decide_placement Algorithm Summary

Purpose:
To determine the optimal cluster for each service in an application, considering resource capacities, service requirements, acceleration capabilities, and potentially the cost of changing an existing placement.

Core Methodology:
It formulates and solves a Mixed Integer Linear Programming (MILP) problem using the CVXPY modeling language and the HiGHS open-source solver.

Inputs (What it takes):

The function expects the following data, primarily as Python lists where the order/index corresponds to services or clusters:

  1. cluster_capacities: A list of numbers, where each number is the CPU capacity of a corresponding cluster.
    • Example: [10, 12] (Cluster 0 has 10 CPU units, Cluster 1 has 12).
  2. cluster_acceleration: A list of numbers (likely binary 0 or 1, or a feature level), where each number indicates the GPU/acceleration capability of a corresponding cluster.
    • Example: [0, 1] (Cluster 0 has no GPU, Cluster 1 has GPU).
  3. cpu_limits: A list of numbers, where each number is the CPU requirement of a corresponding service (per replica).
    • Example: [1, 2] (Service 0 needs 1 CPU unit, Service 1 needs 2).
  4. acceleration: A list of numbers (likely binary 0 or 1), where each number indicates the GPU/acceleration requirement of a corresponding service.
    • Example: [0, 1] (Service 0 needs no GPU, Service 1 needs GPU).
  5. replicas: A list of integers, where each number is the desired number of replicas for a corresponding service.
    • Example: [3, 2] (Service 0 has 3 replicas, Service 1 has 2).
  6. current_placement: A 2D list (matrix) of 0s and 1s, representing the existing placement of services on clusters. current_placement[service_idx][cluster_idx] = 1 if the service is currently on that cluster.
    • Example: [[1, 0], [0, 1]] (Service 0 on Cluster 0, Service 1 on Cluster 1).

Output (What it produces):

  • placement: A 2D list (matrix) of integers (0 or 1). placement[service_idx][cluster_idx] = 1 signifies that the algorithm has decided to place service_idx on cluster_idx. 0 means it’s not placed there.
    • Example: [[0, 1], [1, 0]] (Service 0 is now placed on Cluster 1, Service 1 on Cluster 0).

Internal Logic: Optimization Problem

The algorithm defines and solves an optimization problem characterized by:

1. Decision Variables:

  • x[s, e]: A binary variable (0 or 1). It’s 1 if service s is placed on cluster e, and 0 otherwise. This is what the algorithm tries to determine.

2. Objective Function (What it tries to optimize - Minimize):
The goal is to minimize a weighted sum of two costs:

  • Deployment Cost (Term 1): w_dep * sum_over_all_s_e(x[s, e])
    • w_dep is a weight.
    • This term, as written, tries to minimize the total number of active placement assignments. Given Constraint 1 (each service must be placed once), sum(x) will always be num_services. So, this term might be intended to represent something else (e.g., a fixed cost per service deployed, or a cost per cluster utilized) or is currently redundant.
  • Re-optimization Cost (Term 2): w_re * sum_over_all_s_e(current_placement[s,e] * (current_placement[s,e] - x[s,e]))
    • w_re is a weight.
    • This term penalizes removing a service from a cluster where it was previously (current_placement[s,e] = 1 and x[s,e] = 0). It does not directly penalize adding a service to a new cluster where it wasn’t. A more common re-optimization cost is sum(|x[s,e] - current_placement[s,e]|).

3. Constraints (Rules that the solution must satisfy):

  • C1: Each Service Placed Exactly Once:
    • For every service s, the sum of x[s, e] across all clusters e must be equal to 1.
    • Ensures every service gets a home.
  • C2: Cluster CPU Capacity Not Exceeded:
    • For every cluster e, the total CPU consumed by all services placed on it (sum(cpu_limit[s] * replicas[s] * x[s,e]) for all services s) must not exceed cluster_capacities[e].
    • Prevents overloading clusters.
  • C3: Acceleration Compatibility:
    • For every service s and every cluster e, if service s (requiring acceleration[s]) is placed on cluster e, then acceleration[s] must be less than or equal to cluster_acceleration[e].
    • Ensures services needing specific hardware (like GPUs) are placed on clusters that provide it.
    • (Note: The code applies this starting from service 1, implying service 0 might have special handling).
  • C4: “Dependency” Constraint (Problematic as written):
    • x[i, e] + x[i - 1, e] >= d[i - 1] for services i and i-1 on each cluster e. The meaning of d is unclear.
    • If d[i-1] is 1, it means at least one of service i or i-1 must be on each cluster e.
    • If d[i-1] is 2, it means both service i and i-1 must be on each cluster e (forced colocation on all clusters).
    • This constraint, in its current form, does not represent typical service dependencies (e.g., service A needs to communicate with B) and needs significant review and likely replacement based on how dependencies are defined in the “App Graph.” It might be an attempt at ensuring services in a chain are somewhat co-located or that capacity is available sequentially, but it’s not standard.

Summary:

decide_placement tries to find the “cheapest” way to assign each service to exactly one cluster, respecting CPU and acceleration limits, while potentially trying to minimize changes from a previous deployment. The definition of “cheapest” and how dependencies are handled are the parts most needing clarification and alignment with the actual “App Graph” semantics and desired optimization goals (like energy efficiency for H3NI).

More Detailed Discussion of the placement.py Module

Overall Module Purpose

This module is responsible for determining where each service (or “node”) of an application graph should be deployed across a set of available clusters. It provides:

  1. decide_placement: The core function that uses an optimization model (CVXPY with HiGHS solver) to make placement decisions based on various constraints and objectives.
  2. calculate_naive_placement: A simpler, heuristic-based (first-fit) placement algorithm. This could be a fallback or an alternative strategy.
  3. Helper functions (swap_placement, convert_placement): Utilities to transform the placement data format.

Analysis of decide_placement in Light of Dimitris’s Comments

Dimitris emphasized:

  • Placement is #1 priority.
  • Input: “App graph.”
  • Output: “Configurations that effectively direct Helm chart deployment” (via Karmada).
  • Logic can be anything, as long as I/O aligns.

Let’s see how the provided decide_placement function aligns and where it might need adaptation or clarification for the H3NI project and SMO integration.

Inputs to decide_placement

  1. cluster_capacities: List of CPU capacity for each cluster.
    • Alignment: This is a fundamental input for any resource-aware placement.
    • H3NI Context: For energy-aware placement, a similar list/dict of cluster_energy_efficiency or cluster_renewable_source_availability would be needed.
  2. cluster_acceleration: List of GPU acceleration feature for each cluster.
    • Alignment: Good for matching service needs to cluster capabilities.
  3. cpu_limits: List of CPU limits for each service.
    • Alignment: Standard input.
  4. acceleration: List of GPU acceleration feature for each service.
    • Alignment: Standard input.
  5. replicas: List of number of replicas for each service.
    • Alignment: Crucial for calculating total resource demand of a service.
  6. current_placement: 2D list of current placement.
    • Alignment: Used in the objective function to potentially penalize re-optimization (moving services).

Output of decide_placement

  • placement: A 2D list (matrix) where placement[s][e] == 1 means service s is placed on cluster e.
    • Alignment with “Output = Helm chart config”: This output format is a direct representation of the placement decision. The SMO (or an intermediate layer) would take this matrix and:
      • Use convert_placement to get a {'service_id': 'cluster_id'} mapping.
      • Use this mapping to populate the clustersAffinity list in the valuesOverwrite section of the Helm chart for each service (as seen in the Brussels Demo’s image-compression-vo). This, in turn, configures the Karmada PropagationPolicy.
      • It might also inform serviceImportClusters if cross-cluster communication is determined by placement.

Internal Logic of decide_placement (CVXPY Model)

  • Decision Variables (x): A binary matrix x[s, e] representing if service s is on cluster e. This is standard.

  • Objective Function:
    python objective = cp.Minimize( w_dep * cp.sum(x) + # Deployment cost (sum of all placed instances - seems a bit odd, maybe cost per placement?) w_re * cp.sum(cp.multiply(y, (y - x))) # Re-optimization cost (penalizes changing from current_placement y) )

    • w_dep * cp.sum(x): This term aims to minimize the total number of “placements.” If each service must be placed once (as per Constraint 1), then cp.sum(x) will always be num_nodes. This part of the objective might be redundant or intended to represent a cost per active placement variable, which usually isn’t the goal. Often, deployment cost is associated with using a cluster or a cost per service type. This needs clarification. If the goal is just to find a feasible placement, this term might not be necessary or could be rephrased.
    • w_re * cp.sum(cp.multiply(y, (y - x))): This term correctly penalizes changes from the current_placement. y - x will be 1 if y=1, x=0 (service removed), -1 if y=0, x=1 (service added), and 0 if no change. y * (y-x) will be 1 if y=1, x=0 (cost for removing), 0 otherwise. This only penalizes removing a service from a cluster where it was. It doesn’t directly penalize adding it to a new one if it wasn’t there, other than through the w_dep term. A more common re-optimization cost is sum(|x - y|), penalizing any change.

  • Constraints:

    1. Each service placed once: cp.sum(x[s, :]) == 1. Standard and correct.
    2. Cluster capacity:
      python cp.sum( cp.multiply(x[:, e], [cpu_limits[s] * replicas[s] for s in range(num_nodes)]) ) <= cluster_capacities[e]
      This correctly ensures that the sum of CPU requirements of services placed on cluster e does not exceed its capacity.
    3. Acceleration feature:
      python x[s, e] * acceleration[s] <= cluster_acceleration[e]
      This means if service s (which requires acceleration[s]) is placed on cluster e (so x[s,e]=1), then its acceleration requirement must be less than or equal to what the cluster provides. If acceleration[s] is 0 (no GPU needed), this constraint is trivially satisfied. If acceleration[s] is 1 (GPU needed) and cluster_acceleration[e] is 0 (no GPU), then x[s,e] must be 0. This is correct.
      • The loop range(1, num_nodes) assumes service s0 has no acceleration constraint or is handled differently. This is a common pattern if s0 is a fixed entry point or gateway.
    4. Dependency Constraint:
      python d = [0, 0] # What does d represent? Usually inter-service communication cost or colocation/anti-colocation. for i in range(1, num_nodes): for e in range(num_clusters): constraints.append(x[i, e] + x[i - 1, e] >= d[i - 1]) # This is NOT a standard dependency constraint.
      • This constraint is problematic or needs significant clarification. As written, if d[i-1] is, for example, 1, this constraint x[i, e] + x[i-1, e] >= 1 means that for each cluster e, at least one of service i or service i-1 must be on that cluster. This is highly unusual for a dependency.
      • If d[i-1] is 2, it means both service i and service i-1 must be on cluster e. This would enforce colocation of i and i-1 on every single cluster, which is also not typical.
      • If d is meant to represent communication links (e.g., d[i-1]=1 means s_i depends on s_{i-1}), then a more typical constraint would be related to placing them on the same cluster to minimize latency, e.g., x[i,e] == x[i-1,e] if they must be colocated, or an objective term to minimize inter-cluster communication if they are on different clusters.
      • This part of the model needs to be reviewed based on the actual dependency requirements of the “App Graph”. The current form doesn’t look like a standard way to model “service A needs to talk to service B.”

  • Solver: problem.solve(solver=cp.HIGHS) uses the HiGHS solver, which is a good open-source option.

Alignment with H3NI Requirements

  • Input Data: The current decide_placement expects lists of numerical data. The “App Graph” (hdag.yaml) is more structured (dictionaries, nested objects). An Adaptation Layer will be needed within SMO (or as part of the H3NI plugin for SMO) to:

    1. Parse the “App Graph.”
    2. Extract relevant service IDs, their CPU/acceleration needs, replica counts (these might come from the graph’s intent or default values).
    3. Fetch or look up current cluster capacities and acceleration features (SMO needs to maintain this state or have a way to query it).
    4. Fetch current_placement from SMO’s database (if re-optimization is a goal).
    5. Transform all this data into the flat list format expected by decide_placement.
    6. Similarly, the output matrix needs to be converted back into a service-to-cluster mapping that can update the database and drive Helm value overrides.

  • Flexibility for H3NI Logic (“Logic can be anything we want”):

    • Yes, H3NI can replace the entire CVXPY model within decide_placement with its own logic (e.g., different optimization model, heuristics, ML-based decision engine).
    • Energy-Awareness: To make it energy-aware, H3NI’s new logic would require new inputs (cluster energy profiles, service energy consumption estimates) to be passed through the adaptation layer. The objective function and/or constraints would then incorporate energy.
    • Open-Source Solvers: The current use of cp.HIGHS is already open-source. If other solvers are desired, CVXPY supports many, or the model could be rewritten in Pyomo for broader solver compatibility.

Key Areas for H3NI to Address for decide_placement

  1. Clarify/Redesign the Dependency Constraint (Constraint 4): This is the most suspect part of the current model. The “App Graph” likely has explicit connectionPoints or dependencies between services. These need to be correctly modeled, e.g.:
    • To minimize latency (encourage colocation of communicating services in the objective).
    • To ensure dependent services can reach each other (handled by Karmada ServiceImport/Export, which are configured based on placement).
  2. Review the Objective Function: Ensure w_dep * cp.sum(x) actually models what’s intended for “deployment cost.” Refine the “re-optimization cost” if needed. Add energy costs/savings for H3NI’s energy-aware placement.
  3. Develop the Adaptation Layer: This is crucial for bridging the structured “App Graph” and cluster state data with the flat list inputs expected by a numerical optimization function like this one.
  4. Integrate Energy Data: Determine how energy-related parameters (for clusters and potentially services) will be sourced by SMO and passed to H3NI’s placement logic.

The calculate_naive_placement function

  • This is a greedy first-fit algorithm. It iterates through services and tries to place them on the first cluster that has capacity and meets acceleration requirements.
  • Usefulness:
    • Good as a quick, simple baseline.
    • Could be a fallback if the optimization model fails or takes too long.
    • Could be one of the “different algorithms” Dimitris mentioned that SMO could switch to.
  • Limitations: Greedy algorithms are often suboptimal. They don’t consider global objectives like minimizing re-optimization or balancing load perfectly.

In Conclusion

The provided placement.py offers a starting point with an optimization-based approach. For H3NI to effectively integrate and enhance it:

  • The input/output data flow (App Graph -> numerical lists -> decide_placement -> placement matrix -> Helm/Karmada config) needs to be clearly defined and implemented by SMO, with H3NI focusing on the decide_placement logic itself.
  • The dependency modeling within decide_placement needs a critical review and likely a redesign to match actual application graph semantics.
  • The objective function might need refinement.
  • H3NI can then replace or augment the CVXPY model with its advanced logic (energy-aware, potentially ML-influenced in the future if applicable to static placement).

Page last modified: 2025-06-03 13:46:37