Two-Layer Planning Model and Optimization Algorithm for Recycling Bin Layout and Scheduling in Urban Residential Areas

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Two-Layer Planning Model and Optimization Algorithm for Recycling Bin Layout and Scheduling in Urban Residential Areas

Introduction

With the rapid development of society and changes in residents’ lifestyles, the amount of waste generated continues to rise, making the recycling of renewable resources a global challenge. According to the 2020 China Renewable Resource Recycling Industry Development Report, China’s total renewable resource recovery reached 354 million tons, with a total recycling value of approximately 900.38 billion yuan. To promote the development of recycling logistics systems, the State Council issued the Action Plan for Promoting Large-Scale Equipment Updates and Replacement of Old Consumer Goods on March 13, 2024, emphasizing the need to further improve the renewable resource recycling network. Residential areas, as a core component of urban recycling networks, play a crucial role in the effective management of recyclable materials. However, current recycling bin placement, quantity, and collection routes in urban residential areas are often inefficient, leading to reduced recycling efficiency, lower resident satisfaction, and decreased profitability for recycling enterprises. Therefore, optimizing the layout of recycling bins and collection routes in urban residential areas can enhance recycling efficiency, improve resident satisfaction, and increase corporate profits, contributing to the development of smart urban recycling logistics networks.

Existing research on recycling bin layout planning and vehicle routing optimization has primarily focused on traditional waste collection scenarios, with limited studies specifically addressing recycling bins. Most studies either examine facility location or vehicle routing separately, while integrated models considering both aspects are scarce. Additionally, few studies have developed models tailored to urban residential areas, and most rely on conventional optimization algorithms such as genetic algorithms and particle swarm optimization, with limited exploration of newer metaheuristic approaches. To address these gaps, this study proposes a bi-level optimization model for recycling bin layout and vehicle routing in urban residential areas, incorporating population, recycling frequency, and recycling thresholds to determine optimal bin quantities. A hybrid human learning optimization (HHLO) algorithm is designed to solve this NP-hard problem, integrating adaptive learning strategies and a nested tabu search (TS) algorithm for improved performance.

Problem Description and Model Formulation

Problem Overview

The recycling network considered in this study consists of a recycling center and multiple residential demand points. Residents deposit recyclable materials into recycling bins located at designated collection points, and the recycling center is responsible for transporting these materials. The current challenge lies in the suboptimal placement and quantity of recycling bins, which fail to meet residents’ needs, leading to inefficiencies and financial losses for recycling enterprises. To address this, the study develops a strategy to determine the appropriate number of recycling bins for each residential area based on population, recycling frequency, and recycling thresholds. The goal is to maximize the total profit of the recycling center while minimizing transportation costs under resource constraints.

Model Assumptions

The bi-level optimization model is constructed under the following assumptions:

  1. The locations of residential demand points are known, and recycling bins are placed at these points without considering internal bin distribution within residential areas.
  2. The number of recycling bins in a residential area is linearly related to population, recycling frequency, and recycling thresholds.
  3. When a recycling bin reaches full capacity, it sends a collection request to the recycling center.
  4. The model does not differentiate between types of recyclable materials, and collection vehicles retrieve all materials upon arrival.
  5. The study considers a single service cycle, ignoring multiple collection frequencies within a planning period.

Key Parameters and Variables

The model incorporates several parameters and decision variables, including:
• Sets and Indices: Residential demand points, recycling vehicles, and their respective collections.

• Cost Parameters: Fixed and maintenance costs of recycling bins, transportation costs, and penalty costs for violating time windows.

• Operational Parameters: Recycling bin capacity, vehicle load limits, and time windows for collection.

• Decision Variables: Number of recycling bins at each demand point, vehicle routing decisions, and service schedules.

Bi-Level Optimization Model

The upper-level model focuses on maximizing the total profit of the recycling center, which includes revenue from recycled materials, government subsidies, and costs associated with bin installation, maintenance, and transportation. The objective function is formulated as:

The lower-level model optimizes vehicle routing to minimize transportation-related costs, including distance-based costs, fixed vehicle costs, and penalties for early or late arrivals. Constraints ensure that each demand point is served by only one vehicle, vehicle capacities are not exceeded, and sub-tours are eliminated.

Hybrid Human Learning Optimization Algorithm

Overview of the HHLO Algorithm

Given the NP-hard nature of the problem, traditional exact methods are impractical. Instead, a hybrid human learning optimization (HHLO) algorithm is proposed, combining an improved human learning optimization (HLO) algorithm with a nested tabu search (TS) algorithm. The HLO algorithm mimics human learning behaviors—random learning, individual learning, group learning, and social learning—to explore and exploit the solution space effectively. The TS algorithm refines vehicle routing solutions based on the bin layout determined by the HLO algorithm.

Encoding and Initialization

Each solution is encoded as a vector representing the number of recycling bins at each residential demand point. Initial solutions are generated randomly within predefined limits to ensure diversity in the population.

Learning Operators

  1. Random Learning Operator: Introduces randomness to explore new solutions, helping escape local optima.
  2. Individual Learning Operator: Leverages personal experience stored in an individual knowledge base to refine solutions.
  3. Group Learning Operator: Enhances global search by sharing knowledge within subgroups of the population.
  4. Social Learning Operator: Utilizes collective knowledge from the entire population to guide solution improvements.

An adaptive selection strategy dynamically adjusts the probabilities of applying these operators, balancing exploration and exploitation throughout the optimization process.

Tabu Search for Vehicle Routing

The TS algorithm is employed to optimize vehicle routes for a given bin layout. It begins with an initial solution generated using the nearest neighbor algorithm and iteratively explores neighboring solutions while maintaining a tabu list to avoid cycling. The algorithm terminates after a maximum number of iterations, returning the best-found routing solution.

Algorithm Workflow

  1. The HLO algorithm generates bin layout solutions and passes them to the TS algorithm.
  2. The TS algorithm computes optimal vehicle routes and returns transportation costs to the HLO algorithm.
  3. The HLO algorithm evaluates the overall solution fitness and updates the population.
  4. The process repeats until termination criteria are met, yielding the best bin layout and routing plan.

Computational Experiments

Algorithm Comparison

To validate the performance of the HHLO algorithm, computational experiments were conducted using 30 test instances of varying sizes (small, medium, and large). The HHLO algorithm was compared against four benchmark algorithms: basic HLO, genetic algorithm (GA), adaptive particle swarm optimization (APSO), and red-billed blue magpie optimization (RBMO). Key findings include:
• Small and Medium Instances: HHLO showed marginal improvements over benchmarks but consistently achieved higher resident satisfaction and recycling profits.

• Large Instances: HHLO outperformed other algorithms significantly, with profit increases of up to 50% compared to GA and HLO, and 30% compared to APSO and RBMO.

Case Study: Shanghai Yangpu District

A real-world case study was conducted in Shanghai’s Yangpu District, involving 31 residential demand points. The HHLO algorithm determined an optimal layout of 75 recycling bins and a routing plan requiring four collection vehicles. The solution achieved a resident satisfaction score of 0.77 and a net profit of 1,231.51 yuan per collection cycle.

Sensitivity Analysis

  1. Recycling Bin Capacity: Increasing bin capacity from 22 kg to 26 kg improved resident satisfaction from 0.62 to 0.91 and increased profits by 452%.
  2. Zonal Pricing Strategy: Implementing differentiated pricing based on recycling volume (e.g., 0.6 yuan for high-volume areas and 1.0 yuan for low-volume areas) increased profits by 28% and satisfaction by 15% compared to uniform pricing.
  3. Time-Based Pricing: Adjusting prices during peak (0.6 yuan) and off-peak (1.0 yuan) hours improved profits by 27% and satisfaction by 4%.

Conclusion

This study addresses the integrated problem of recycling bin layout and vehicle routing in urban residential areas by developing a bi-level optimization model. The proposed HHLO algorithm, incorporating adaptive learning strategies and a nested TS algorithm, demonstrates superior performance in solving large-scale instances. Practical insights from the Shanghai case study highlight the benefits of optimizing bin capacity and pricing strategies to enhance both profitability and resident satisfaction. Future research could extend this framework to include dynamic recycling demands and collaborative logistics models for large-item recycling.

doi.org/10.19734/j.issn.1001-3695.2024.06.0203

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