Adaptive Grid Multi‑Objective Particle Swarm Optimization for Exhibition Slot Allocation with Shell Score Integration

Introduction The project aims to improve the selection of real‑estate agents displayed in the "exhibition slot" (a high‑visibility position on the Beike platform) by incorporating the Shell Score, a credit‑based trust metric, into the slot‑allocation strategy.

Exhibition Slot Overview When users browse a property, the slot shows the agent’s information, offering a key channel for generating business opportunities. The slot is assigned to the agent with the highest computed Q‑value based on familiarity and service capability factors.

Shell Score Integration Shell Score evaluates agents on multiple dimensions (e.g., transaction history, service ability). The project proposes to map the Shell Score to a "slot Shell Score" using a piecewise linear function with three parameters: full‑score, lower bound, and upper bound.

Problem Formulation Determining the optimal three parameters and evaluating their impact on business metrics (e.g., conversion rate, slot stability) constitutes a multi‑objective optimization problem with conflicting goals.

Algorithm Survey Several swarm‑intelligence algorithms were examined: Artificial Bee Colony (ABC), Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), and Multi‑Objective PSO (MOPSO). While PSO and MOPSO are well‑suited for continuous optimization, MOPSO suffers from density‑information loss, imbalance between global and local search, and high computational complexity.

Chosen Approach: AG‑MOPSO The Adaptive Grid Multi‑Objective PSO (AG‑MOPSO) addresses MOPSO’s shortcomings by using an adaptive grid to evaluate Pareto front density, prune low‑quality particles, and maintain diversity with modest computational cost.

Algorithm Structure AG‑MOPSO maintains two populations: a standard PSO swarm and an Archive of non‑dominated solutions. The adaptive grid partitions the objective space, guiding the selection of gBest particles based on density. The main steps are: 1. Initialization of swarm and Archive. 2. For each generation: adjust parameter bounds, generate new particles (FindgBest, UpdateParticle, Evaluate, UpdatepBest), update the Archive (AdaptiveGridArchive, PruneArchive), and output results.

Implementation Plan The project is divided into seven phases: 1) develop the AG‑MOPSO algorithm, 2) analyze Shell Score data to set parameter ranges, 3) prepare city‑level feature data (property role, viewings, transactions, conversion, Shell Score), 4) develop the calculation layer in Python (pandas) with Shell Score mapping, 5) define objective functions (slot stability, Shell Score proportion, newcomer slot share, etc.), 6) run parallel simulations for multiple cities, 7) collect and analyze results to select optimal parameter sets.

Results Simulation curves show convergence of objective values over iterations. Visualizations demonstrate that the algorithm can produce Pareto‑optimal parameter triples for each city, balancing slot stability, Shell Score coverage, and other business metrics. Selected solutions achieve higher target values while keeping observed indicators within acceptable ranges.

Conclusion AG‑MOPSO efficiently computes multi‑objective optimal parameters for the exhibition slot strategy across diverse cities. Key lessons include the importance of clear, measurable objectives, reasonable parameter bounds, and careful tuning of swarm size and iteration count to balance exploration, convergence speed, and resource consumption.