Heni Widayani
Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia

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Evaluating Hierarchical Pathfinding A* (HPA*) for Multi‑Order Routing in a Small Warehouse Layout Ig. Prasetya Dwi Wibawa; Meta Kallista; Ramdhan Nugraha; Heni Widayani; Harish Chandra Bhandari; Angga Rusdinar
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.39659

Abstract

Hierarchical Pathfinding A* (HPA*) is a hierarchical search framework that partitions grid‑based environments into clusters to reduce computational time while preserving a near-optimal path. The warehouse layout features cross-aisle connectivity, and multi-order optimization is performed using the HPA* algorithm, which integrates travel times with multi-rack picking times to the objective cost function. We simulate by assigning 30 random orders, with a total of 10641 items stored in the warehouse and 10 item types. The travel time is calculated assuming a picker has a constant speed of 1.2 m/s along edges, the picking time is proportional to the number of items picked per rack, and a small warehouse layout. Estimated cycle times of the orders (travel plus picking time) range from 114.4 to 349.9 seconds using the HPA* optimization, with a mean of 232.0 seconds. From the optimization results, orders require an average of 5.2 rack visits, ensuring that the picker travels more than two racks per order. The HPA* reduces the original low‑level graph (50 nodes and 61 edges, including base and stage station) to a graph with 22 nodes and 17 edges, enabling faster route computation while preserving observed cycle‑time patterns when combined with picking-time durations. Compared to A*, given the layout and orders, HPA* demonstrates an efficient warehouse path‑planning method that reduces search computation while maintaining near‑optimal routing performance.
Comparative Evaluation of Hyperparameter Optimization Strategies for k-Nearest Neighbors over Mixed Domain Search Spaces Meta Kallista; Ig. Prasetya Dwi Wibawa; Heni Widayani
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.42295

Abstract

k-Nearest Neighbors (KNN) remains a strong baseline due to its simplicity, interpretability, and non-parametric structure; however, its predictive performance is highly sensitive to interacting hyperparameters. This paper studies search-constrained hyperparameter optimization for KNN over a mixed search space comprising an integer neighborhood size, a categorical distance metric, and a continuous Minkowski exponent. Seven tuning strategies are compared under a unified nested validation protocol with standardized preprocessing: grid search, random search, Bayesian optimization, genetic algorithm, surrogate optimization, particle swarm optimization, and grey wolf optimizer. Experiments on diverse public classification datasets from UCI, OpenML, and Kaggle evaluate predictive performance (accuracy, macro-AUC, cross-entropy), validation loss, and runtime. The results indicate that adaptive optimizers generally provide more favorable performancecost trade-offs than exhaustive grids under limited evaluations, while no single method is uniformly best across all datasets. Rank-based statistical comparisons using non-parametric tests further support the observed differences and motivate practical recommendations for selecting tuning strategies as a function of evaluation search and mixed-domain search-space characteristics.