Hybrid Whale Goshawk Algorithm Optimizes Uncertain Cloud Manufacturing Service Selection

A computational framework developed for cloud manufacturing environments successfully resolves complex service composition challenges by synthesizing two distinct nature-inspired search mechanisms into a unified metaheuristic architecture. The system, termed the Whale-Goshawk Optimization Algorithm, merges the explorative hunting strategies of the Whale Optimization Algorithm with the exploitative pursuit tactics of the Northern Goshawk Optimization Algorithm. Engineered specifically for Service Composition and Optimization Selection in industrial settings, this methodology incorporates a specialized similar integer encoding system that organizes candidate services according to mathematical proximity. Extensive numerical testing demonstrates that the integrated algorithm consistently identifies optimal combinations of distributed manufacturing services under varying levels of operational uncertainty, avoiding the local optima traps that typically hinder conventional heuristic algorithms and significantly outperforming standalone metaheuristic baselines across multi-dimensional task configurations.

The rapid shift toward consumer-centric manufacturing has elevated Cloud Manufacturing into a dominant industrial paradigm that centralizes heterogeneous distributed resources into accessible, reconfigurable services tailored to dynamic user demands. Within this architecture, large-scale industrial tasks are mapped onto physical assets and virtualized representations known as digital twins, decomposing complex procedures into chains of discrete functional tasks. Finding the single best combination of modular components from massive online catalogs to form a dependable composite service constitutes an NP-hard optimization challenge known as Service Composition and Optimization Selection. Because repositories contain vast numbers of providers capable of executing identical basic functions, non-functional attributes evaluated through Quality of Service metrics determine the overall performance, agility, and economic viability of the resulting composite system across its complete execution lifecycle.

Conventional methodologies applied to quality-driven service composition have encountered severe performance bottlenecks when operating in dynamic industrial environments characterized by fluctuating demand, unpredictable network conditions, and component service failures. Deterministic exact algorithms face exponential computational costs that render them unusable for large service repositories, while machine learning paradigms such as reinforcement learning and deep neural networks require costly model retraining whenever the underlying service repository experiences structural modifications. Metaheuristic algorithms, including particle swarm optimization, genetic algorithms, and ant colony optimization, offer flexible alternatives by identifying near-optimal configurations without exhaustive searches; however, modern metaheuristics remain primarily tailored for continuous variable spaces. Adapting these algorithms to discrete combinations through traditional integer encoding often strips away critical spatial and non-functional relationships, causing adjacent integer values in the encoding sequence to possess wildly divergent performance attributes.

To overcome the structural deficiencies of traditional integer representations, the newly developed framework introduces a cosine similarity-based encoding procedure that embeds spatial Quality of Service features directly into the algorithmic representation. In this scheme, candidate services possessing equivalent functional capabilities are evaluated by measuring the cosine angle between their multi-dimensional attribute vectors, grouping services with similar performance profiles into distinct subsets whenever their measured similarity exceeds an established mathematical threshold of 0.6. By arranging candidate services so that indices correspond to comparable non-functional capabilities, the integer encoding ensures that numerical neighborhood modifications during optimization correlate with smooth, gradual variations in solution quality. This prevents stochastic search operators from erratically jumping across disparate regions of the objective landscape and establishes a stable foundation for targeted local exploration.

The underlying manufacturing model formalizes service tasks as sequential workflows that consume explicit input parameter sets and produce designated output parameter sets. Candidate options within each task’s service pool consist of atomic Basic Component Services, which represent indivisible operational units, and modular Abstract Component Services, which encompass hierarchical digital twin structures organized into sequential, parallel, or choice topologies. The non-functional evaluation of each candidate composite workflow incorporates four critical Quality of Service attributes: execution time, monetary cost, operational uncertainty, and process maturity. The framework normalizes these properties and aggregates them into a comprehensive fitness objective using the Simple Additive Weighting technique, multiplying each normalized attribute by a designated user preference coefficient to ensure that minimizing negative attributes such as cost and latency aligns mathematically with maximizing positive attributes such as maturity and operational reliability.

The optimization phase executes through a coordinated two-stage behavioral model that alternates between broad landscape exploration and intensified regional refinement. In the first phase, mimicking the prey identification phase of the northern goshawk, the algorithm determines hunting targets across the discrete integer matrix by partitioning candidate positions into two complementary update mechanisms. A portion of the search population follows update rules derived from the Whale Optimization Algorithm, which randomly adjusts positions relative to other population members to rapidly discover promising, high-fitness zones across the global search space. Meanwhile, a stochastic selection factor derived from iteration counts prevents premature convergence by occasionally generating random prey positions, ensuring that the population retains diversity and evades premature stagnation in sub-optimal solution clusters.

In the second stage of the optimization cycle, representing the rapid chase and escape behavior of the hunting goshawk, the algorithm executes fine-grained local searches to extract maximum quality from identified candidate regions. The pursuit behavior splits mathematically into two operational branches based on whether the current service instance possesses a populated similar service set. When the similar service set contains eligible candidates, the local search operates exclusively within this pre-filtered neighborhood, executing localized step modifications governed by a adaptive scale parameter directly proportional to the size of the similar service set and the remaining iteration budget. When no similar services meet the similarity threshold, the algorithm falls back to localized searching within the broader candidate service pool, utilizing controlled rounding functions to maintain strictly valid discrete integer assignments throughout the iterative process.

Validation experiments were conducted within a MATLAB simulation environment modeling five thousand discrete manufacturing services distributed across one hundred unique subtask classifications. Candidate pools maintained a three-to-two ratio between Basic Component Services and Abstract Component Services, with attributes randomly assigned within defined operational intervals: execution duration between zero and ten, monetary cost between zero and one, operational uncertainty between zero and ten, and maturity between zero and one. Algorithmic comparisons benchmarked the Whale-Goshawk Optimization Algorithm against standard metaheuristic baselines, including Genetic Algorithms, Particle Swarm Optimization, standalone Whale Optimization, standalone Northern Goshawk Optimization, and Golden Jackal Optimization. Each algorithm executed across fifty independent experimental runs consisting of one thousand iterations apiece to mitigate stochastic variance, evaluating mean optimization errors, standard deviations, and convergence velocity across five escalating task complexity tiers.

Quantitative benchmarking confirms that the Whale-Goshawk Optimization Algorithm achieved superior convergence stability and solution quality across every tested task complexity level, successfully converging within five hundred iterations. In comparative evaluations measuring average error reductions relative to the best known combinations, the proposed method improved solution performance by 25.8%, 17.2%, 17.6%, 10.5%, and 9.3% compared to standalone Whale Optimization across the five complexity levels, while surpassing standalone Northern Goshawk Optimization by 16.5%, 11.4%, 8.8%, 5.4%, and 5.5%. Additional dynamic tests subjected the algorithm to sudden structural perturbations by either halving the candidate service repository or introducing substantial volumes of newly available services at iteration five hundred. In both dynamic scenarios, the algorithm adapted autonomously without re-initialization, restabilizing fitness trajectories by iteration nine hundred and proving that its convergence rate remains fundamentally uncoupled from raw repository scale.

Rigorous efficiency testing further evaluated each algorithm’s capability to locate acceptable solutions meeting rigorous optimization accuracy thresholds of 0.85 and 0.90, defined as the ratio between the obtained solution fitness and the global optimum. While standard Particle Swarm Optimization and Genetic Algorithms failed entirely to find acceptable configurations at the 0.90 threshold across ten repeated trials, and standalone Whale Optimization and Golden Jackal Optimization attained only a fifty percent success rate, the Whale-Goshawk Optimization Algorithm achieved a consistent one hundred percent success rate with minimal iteration variance. Although the integration of similar service matrix calculations introduces higher per-iteration computational overhead, the overall wall-clock execution time remained highly competitive because the hybrid algorithm required significantly fewer total iterations. The researchers note that while the method narrows search scopes effectively, its memory and processing requirements remain demanding, highlighting hybrid integration with machine learning representations as a primary objective for future development.

Subject of Research: Heuristic optimization for cloud manufacturing service composition under uncertainty

Article Title: WGO: a similarly encoded whale-goshawk optimization algorithm for uncertain cloud manufacturing service composition

Article References: Chen, K., Wang, T., Zhuo, H., & Cheng, L. (2025). WGO: a similarly encoded whale-goshawk optimization algorithm for uncertain cloud manufacturing service composition. Autonomous Intelligent Systems, 5(1), Article 7. https://doi.org/10.1007/s43684-025-00089-x

Image Credits: AI Generated

DOI: 10.1007/s43684-025-00089-x

Keywords: cloud manufacturing, service composition, whale optimization algorithm, northern goshawk optimization, digital twin, quality of service, similar integer encoding, heuristic algorithms, combinatorial optimization, simple additive weighting, candidate service sets, cosine similarity, abstract component services, basic component services, dynamic environments, computational intelligence, manufacturing process modeling