Hybrid Genetic-ALNS Framework

• The paper introduces AHGSLNS, a framework combining genetic algorithms with ALNS to evolve instance-specific parameters for improved solution robustness.
• AHGSLNS is a hybrid method that integrates global search and adaptive intensification via dynamic destroy/repair operator weights tailored for COPs such as MAVRP and OAS.
• The framework achieves enhanced convergence and performance using genetic operators like trip- and journey-crossover alongside adaptive acceptance criteria.

A Hybrid Genetic-ALNS (Adaptive Hybrid Genetic Search and Large Neighborhood Search, AHGSLNS) framework combines population-based genetic methods with the adaptive intensification mechanisms of Adaptive Large Neighborhood Search (ALNS) to solve complex combinatorial optimization problems (COPs) such as the Multi-Attribute Vehicle Routing Problem (MAVRP) and Order Acceptance and Scheduling (OAS) with sequence-dependent setups and time windows. AHGSLNS addresses the limitations of uniform ALNS parameterization by evolving instance-specific parameter sets, destroy/repair operator weights, and acceptance criteria in parallel, thereby improving solution quality, convergence, and robustness across heterogeneous instances (Liu et al., 2024, He et al., 2019).

1. Conceptual Foundations and Motivation

ALNS achieves high-quality solutions in COPs through repeated cycles of destroy and repair heuristics, guided by adaptively updated operator weights and one of several established acceptance criteria (hill-climbing, record-to-record, simulated annealing). Its main limitation is sensitivity to parameter settings, often yielding inconsistent performance if a static configuration is applied to diverse instance topologies.

Genetic Search (GS) brings global search and parameter adaptation via population dynamics, exploring multiple configurations simultaneously and enabling parallel intensification. The AHGSLNS design strategy is to utilize GS as an outer-level controller for evolving a population of individuals, each encapsulating a solution, ALNS operator weights, parameterizations, and acceptance rule. Each individual's short ALNS run (PALNS) then locally intensifies its solution under its bespoke configuration, while genetic operations and survival mechanisms propagate effective parameter–solution pairs through the population (Liu et al., 2024).

2. Algorithmic Architecture

2.1 Individual Representation

An individual in AHGSLNS consists of a tuple:

• $x_s^c$: Current solution (e.g., journey representation for MAVRP).
• $x_s^b$: Best solution found by the individual.
• $\rho_s^-$: Weights for destroy operators.
• $\rho_s^+$: Weights for repair operators.
• $\mathrm{DR}_s^{\text{set}}$: Real-valued ALNS parameters (e.g., destroy/repair severities).
• $\mathrm{accept}_s$: Acceptance rule and its internal parameters.

Fitness is calculated as $$\text{MSP}(x_s^b) = \max_{k \in K} \{\text{travel time of vehicle } k\}$$ for MAVRP.

2.2 Main Phases

AHGSLNS proceeds in two main phases:

• Adaptive Survival: All $N$ individuals undergo parallel PALNS runs. The $M$ worst are eliminated, preserving elites with effective configurations for the instance at hand.
• Cooperative Evolution: Over $g_{\max}$ generations, genetic operations (crossover, diversification) are periodically triggered based on progress epochs. Each surviving or newly generated individual is further intensified with PALNS.

Pseudocode (from (Liu et al., 2024)) illustrates these stages, with per-individual data structures continuously updated.

2.3 Genetic Operators

• Parent Selection: Binary tournament on fitness.
• Crossover: Two custom operators:
  • Trip-crossover: Exchange a subset of trips between parents, repairing to maintain feasibility.
  • Journey-crossover: Swap complete journeys of selected vehicles.
  • Offspring inherit a partition of ALNS parameters and acceptance rules from parents.
• Diversification: Injection of new random individuals when stagnation criteria are met.
• Population Management: Ensures $x_s^b$0, with re-injection of diversity and elitist replacement strategies as required.