Incorporating Memory and Learning Mechanisms Into Meta-RaPS

Due to the rapid increase of dimensions and complexity of real life problems, it has become more difficult to find optimal solutions using only exact mathematical methods. The need to find near-optimal solutions in an acceptable amount of time is a challenge when developing more sophisticated approaches. A proper answer to this challenge can be through the implementation of metaheuristic approaches. However, a more powerful answer might be reached by incorporating intelligence into metaheuristics. Meta-RaPS (Metaheuristic for Randomized Priority Search) is a metaheuristic that creates high quality solutions for discrete optimization problems. It is proposed that incorporating memory and learning mechanisms into Meta-RaPS, which is currently classified as a memoryless metaheuristic, can help the algorithm produce higher quality results. The proposed Meta-RaPS versions were created by taking different perspectives of learning. The first approach taken is Estimation of Distribution Algorithms (EDA), a stochastic learning technique that creates a probability distribution for each decision variable to generate new solutions. The second Meta-RaPS version was developed by utilizing a machine learning algorithm, Q Learning, which has been successfully applied to optimization problems whose output is a sequence of actions. In the third Meta-RaPS version, Path Relinking (PR) was implemented as a post-optimization method in which the new algorithm learns the good attributes by memorizing best solutions, and follows them to reach better solutions. The fourth proposed version of Meta-RaPS presented another form of learning with its ability to adaptively tune parameters. The efficiency of these approaches motivated us to redesign Meta-RaPS by removing the improvement phase and adding a more sophisticated Path Relinking method. The new Meta-RaPS could solve even the largest problems in much less time while keeping up the quality of its solutions. To evaluate their performance, all introduced versions were tested using the 0-1 Multidimensional Knapsack Problem (MKP). After comparing the proposed algorithms, Meta-RaPS PR and Meta-RaPS Q Learning appeared to be the algorithms with the best and worst performance, respectively. On the other hand, they could all show superior performance than other approaches to the 0-1 MKP in the literature

AN INVESTIGATION OF METAHEURISTICS USING PATH- RELINKING ON THE QUADRATIC ASSIGNMENT PROBLEM

The Quadratic Assignment Problem (QAP) is a widely researched, yet complex, combinatorial optimization problem that is applicable in modeling many real-world problems. Specifically, many optimization problems are formulated as QAPs. To resolve QAPs, the recent trends have been to use metaheuristics rather than exact or heuristic methods, and many researchers have found that the use of hybrid metaheuristics is actually more effective. A newly proposed hybrid metaheuristic is path relinking (PR), which is used to generate solutions by combining two or more reference solutions. In this dissertation, we investigated these diversification and intensification mechanisms using QAP. To satisfy the extensive demands of the computational resources, we utilized a High Throughput Computing (HTC) environment and test cases from the QAPLIB (QAP test case repository). This dissertation consists of three integrated studies that are built upon each other. The first phase explores the effects of the parameter tuning, metaheuristic design, and representation schemes (random keys and permutation solution encoding procedures) of two path-based metaheuristics (Tabu Search and Simulated Annealing) and two population-based metaheuristics (Genetic Algorithms and Artificial Immune Algorithms) using QAP as a testbed. In the second phase of the study, we examined eight tuned metaheuristics representing two representation schemes using problem characteristics. We use problem size, flow and distance dominance measures, sparsity (number of zero entries in the matrices), and the coefficient of correlation measures of the matrices to build search trajectories. The third phase of the dissertation focuses on intensification and diversification mechanisms using path-relinking (PR) procedures (the two variants of position-based path relinking) to enhance the performance of path-based and population-based metaheuristics. The current research in this field has explored the unusual effectiveness of PR algorithms in variety of applications and has emphasized the significance of future research incorporating more sophisticated strategies and frameworks. In addition to addressing these issues, we also examined the effects of solution representations on PR augmentation. For future research, we propose metaheuristic studies using fitness landscape analysis to investigate particular metaheuristics\u27 fitness landscapes and evolution through parameter tuning, solution representation, and PR augmentation. The main research contributions of this dissertation are to widen the knowledge domains of metaheuristic design, representation schemes, parameter tuning, PR mechanism viability, and search trajectory analysis of the fitness landscape using QAPs

Un modelo de optimización analítica para el diseño de centros de distribución baja políticas de alamacenamiento basadas en clases

The aim of this paper study the impact of class-based storage policy based on the optimal configuration of U-flow single command warehouses using a on an ABC product classification. For that purpose, the authors propose a non linear optimization model to minimize the expected travel distance of the warehouse and use analytical methods to solve it. The most important contribution is to provide a mathematical proof that regardless of the storage policy (It does not matter the specifics of the turnover pattern of the products), the optimal warehouse has a width that is the double of its length, and the pick and deposit point should be located in the middle of the width of the warehouse. In addition, authors perform a sensitivity analysis that indicates that the optimal solution is robust, meaning that a certain deviation from the optimum layout does not impose a significant penalty on the expected travel distance of the warehouse.Este artículo estudia el impacto de las políticas de alamacenamiento basadas en clases en el diseño de centros de distribución . Se asume una operación con una sola entrada y salida para los montacargas, los montacargas pueden transportar una unidad de carga al tiempo, y la política de almacenamiento es basada en la clasificación ABC de los productos. Se presenta un modelo de optimización no lineal para minimizar el valor esperado de la distancia por viaje del montacargas — un estimativo del costo de manejo de materiales — y se resuelve utilizando métodos analíticos. La contribución mas revelevante de este artículo es una demonstración matemática de que no independiente de la curva de distribución de la rotación de inventario de los productos, el diseño óptimo del centro de distribución es el mismo. Finalmente, el análisis de sensibilidad muestra que pequeñas desviaciones del desiño óptimo no afecta significativamente el costo de manejo de materiales

An Integrated Strategy for a Production Planning and Warehouse Layout Problem: Modeling and Solution Approaches

We study a real-world production warehousing case, where the company always faces the challenge to find available space for their products and to manage the items in the warehouse. To resolve the problem, an integrated strategy that combines warehouse layout with the capacitated lot-sizing problem is presented, which have been traditionally treated separately in the existing literature. We develop a mixed integer linear programming model to formulate the integrated optimization problem with the objective of minimizing the total cost of production and warehouse operations. The problem with real data is a large-scale instance that is beyond the capability of optimization solvers. A novel Lagrangian relax-and-fix heuristic approach and its variants are proposed to solve the large-scale problem. The preliminary numerical results from the heuristic approaches are reported

An examination of heuristics for the shelf space allocation problem.

Wong, Mei Ting.Thesis (M.Phil.)--Chinese University of Hong Kong, 2010.Includes bibliographical references (p. 115-120).Abstracts in English and Chinese.Chapter 1. --- Introduction --- p.1Chapter 1.1 --- Background --- p.1Chapter 1.2 --- Our Contributions --- p.4Chapter 1.3 --- Framework of Shelf Space Allocation Problem --- p.4Chapter 1.4 --- Organization --- p.6Chapter 2. --- Literature Review --- p.7Chapter 2.1 --- Introduction --- p.7Chapter 2.2 --- Commercial Approaches --- p.7Chapter 2.3 --- Experimental Approaches --- p.8Chapter 2.4 --- Optimization Approaches --- p.11Chapter 2.4.1 --- Exact Approaches --- p.11Chapter 2.4.2 --- Heuristics Approaches --- p.16Chapter 2.5 --- Summary --- p.19Chapter 3. --- Overview of Shelf Space Allocation Problem --- p.21Chapter 3.1 --- Introduction --- p.21Chapter 3.2 --- Problem description --- p.22Chapter 3.2.1 --- Mathematical Model --- p.24Chapter 3.2.1.1 --- Notations --- p.25Chapter 3.2.1.2 --- Model --- p.25Chapter 3.2.1.3 --- Assumption --- p.26Chapter 3.2.1.4 --- Notations of final model --- p.27Chapter 3.2.1.5 --- Final model --- p.27Chapter 3.3 --- Original Heuristic --- p.28Chapter 3.3.1 --- Yang (2001) Method --- p.28Chapter 3.3.2 --- Remarks on Original Heuristic --- p.29Chapter 3.4 --- Original Heuristic with Yang's Adjustment --- p.30Chapter 3.4.1 --- Remarks on Yang's Adjustment --- p.32Chapter 3.5 --- New Neighborhood Movements --- p.33Chapter 3.5.1 --- New Adjustment Phase --- p.33Chapter 3.6 --- Network Flow Model --- p.35Chapter 3.6.1 --- ULSSAP --- p.35Chapter 3.6.2 --- Transforming shelf space allocation problem (SSAP) --- p.38Chapter 3.7 --- Tabu Search --- p.41Chapter 3.7.1 --- Tabu Search Algorithm --- p.42Chapter 3.7.1.1 --- Neighborhood search moves --- p.42Chapter 3.7.1.2 --- Candidate list strategy --- p.45Chapter 3.7.1.3 --- Tabu list --- p.46Chapter 3.7.1.4 --- Aspiration criteria.........................................: --- p.47Chapter 3.7.1.5 --- Intensification and Diversification --- p.48Chapter 3.7.1.6 --- Stopping criterion --- p.49Chapter 3.7.1.7 --- Probabilistic choice --- p.50Chapter 3.7.2 --- General Process of Tabu Search --- p.51Chapter 3.7.3 --- Application of Tabu Search to SSAP --- p.54Chapter 3.7.4 --- Analysis of Tabu Search --- p.58Chapter 4. --- Tabu Search with Path Relinking --- p.60Chapter 4.1 --- Introduction --- p.60Chapter 4.2 --- Foundations of path relinking --- p.62Chapter 4.3 --- Path Relinking Template --- p.65Chapter 4.4 --- Identification of Reference set --- p.69Chapter 4.5 --- Choosing initial and guiding solution --- p.73Chapter 4.6 --- Neighborhood structure --- p.74Chapter 4.7 --- Moving along paths --- p.81Chapter 4.8 --- Application of Tabu Search with Path Relinking --- p.87Chapter 4.9 --- Conclusion --- p.90Chapter 5. --- Computational Studies --- p.92Chapter 5.1 --- Introduction --- p.92Chapter 5.2 --- General Parameter Setting --- p.92Chapter 5.3 --- Parameter values for Tabu search --- p.94Chapter 5.4 --- Sensitivity test for Tabu search with Path Relinking --- p.95Chapter 5.4.1 --- Reference Set Strategies and Initial and Guiding Solution Criteria --- p.96Chapter 5.4.2 --- Frequency of Path Relinking --- p.99Chapter 5.4.3 --- Size of reference set --- p.101Chapter 5.4.4 --- Comparison with Tabu Search --- p.102Chapter 5.5 --- Comparison with other heuristics --- p.105Chapter 5.6 --- Conclusion --- p.109Chapter 6. --- Conclusion --- p.111Chapter 6.1 --- Summary of achievements --- p.112Chapter 6.2 --- Future Works --- p.113Bibliography --- p.11

Supply chain management: An opportunity for metaheuristics

In today’s highly competitive and global marketplace the pressure on organizations to find new ways to create and deliver value to customers grows ever stronger. In the last two decades, logistics and supply chain has moved to the center stage. There has been a growing recognition that it is through an effective management of the logistics function and the supply chain that the goal of cost reduction and service enhancement can be achieved. The key to success in Supply Chain Management (SCM) require heavy emphasis on integration of activities, cooperation, coordination and information sharing throughout the entire supply chain, from suppliers to customers. To be able to respond to the challenge of integration there is the need of sophisticated decision support systems based on powerful mathematical models and solution techniques, together with the advances in information and communication technologies. The industry and the academia have become increasingly interested in SCM to be able to respond to the problems and issues posed by the changes in the logistics and supply chain. We present a brief discussion on the important issues in SCM. We then argue that metaheuristics can play an important role in solving complex supply chain related problems derived by the importance of designing and managing the entire supply chain as a single entity. We will focus specially on the Iterated Local Search, Tabu Search and Scatter Search as the ones, but not limited to, with great potential to be used on solving the SCM related problems. We will present briefly some successful applications.Supply chain management, metaheuristics, iterated local search, tabu search and scatter search

Optimization of storage and picking systems in warehouses

La croissance du commerce électronique exige une hausse des performances des systèmes d'entreposage, qui sont maintenant repensés pour faire face à un volume massif de demandes à être satisfait le plus rapidement possible. Le système manuel et le système à robots mobile (SRM) sont parmi les plus utilisés pour ces activités. Le premier est un système centré sur l'humain pour réaliser des opérations complexes que les robots actuels ne peuvent pas effectuer. Cependant, les nouvelles générations de robots autonomes mènent à un remplacement progressif par le dernier pour augmenter la productivité. Quel que soit le système utilisé, plusieurs problèmes interdépendants doivent être résolus pour avoir des processus de stockage et de prélèvement efficaces. Les problèmes de stockage concernent les décisions d'où stocker les produits dans l'entrepôt. Les problèmes de prélèvement incluent le regroupement des commandes à exécuter ensemble et les itinéraires que les cueilleurs et les robots doivent suivre pour récupérer les produits demandés. Dans le système manuel, ces problèmes sont traditionnellement résolus à l'aide de politiques simples que les préparateurs peuvent facilement suivre. Malgré l'utilisation de robots, la même stratégie de solution est répliquée aux problèmes équivalents trouvés dans le SRM. Dans cette recherche, nous étudions les problèmes de stockage et de prélèvement rencontrés lors de la conception du système manuel et du SRM. Nous développons des outils d'optimisation pour aider à la prise de décision pour mettre en place leurs processus, en améliorant les mesures de performance typiques de ces systèmes. Certains problèmes traditionnels sont résolus avec des techniques améliorées, tandis que d'autres sont intégrés pour être résolus ensemble au lieu d'optimiser chaque sous-système de manière indépendante. Nous considérons d'abord un système manuel avec un ensemble connu de commandes et intégrons les décisions de stockage et de routage. Le problème intégré et certaines variantes tenant compte des politiques de routage communes sont modélisés mathématiquement. Une métaheuristique générale de recherche de voisinage variable est présentée pour traiter des instances de taille réelle. Des expériences attestent de l'efficience de la métaheuristique proposée par rapport aux modèles exacts et aux politiques de stockage communes. Lorsque les demandes futures sont incertaines, il est courant d'utiliser une stratégie de zonage qui divise la zone de stockage en zones et attribue les produits les plus demandés aux meilleures zones. Les tailles des zones sont à déterminer. Généralement, des dimensions arbitraires sont choisies, mais elles ignorent les caractéristiques de l'entrepôt et des demandes. Nous abordons le problème de dimensionnement des zones pour déterminer quels facteurs sont pertinents pour choisir de meilleures tailles de zone. Les données générées à partir de simulations exhaustives sont utilisées pour trainer quatre modèles de régression d'apprentissage automatique - moindres carrés ordinaire, arbre de régression, forêt aléatoire et perceptron multicouche - afin de prédire les dimensions optimales des zones en fonction de l'ensemble de facteurs pertinents identifiés. Nous montrons que tous les modèles entraînés suggèrent des dimensions sur mesure des zones qui performent meilleur que les dimensions arbitraires couramment utilisées. Une autre approche pour résoudre les problèmes de stockage pour le système manuel et pour le SRM considère les corrélations entre les produits. L'idée est que les produits régulièrement demandés ensemble doivent être stockés près pour réduire les coûts de routage. Cette politique de stockage peut être modélisée comme une variante du problème d'affectation quadratique (PAQ). Le PAQ est un problème combinatoire traditionnel et l'un des plus difficiles à résoudre. Nous examinons les variantes les plus connues du PAQ et développons une puissante métaheuristique itérative de recherche tabou mémétique en parallèle capable de les résoudre. La métaheuristique proposée s'avère être parmi les plus performantes pour le PAQ et surpasse considérablement l'état de l'art pour ses variantes. Les SRM permettent de repositionner facilement les pods d'inventaire pendant les opérations, ce qui peut conduire à un processus de prélèvement plus économe en énergie. Nous intégrons les décisions de repositionnement des pods à l'attribution des commandes et à la sélection des pods à l'aide d'une stratégie de prélèvement par vague. Les pods sont réorganisés en tenant compte du moment et de l'endroit où ils devraient être demandés au futur. Nous résolvons ce problème en utilisant la programmation stochastique en tenant compte de l'incertitude sur les demandes futures et suggérons une matheuristique de recherche locale pour résoudre des instances de taille réelle. Nous montrons que notre schéma d'approximation moyenne de l'échantillon est efficace pour simuler les demandes futures puisque nos méthodes améliorent les solutions trouvées lorsque les vagues sont planifiées sans tenir compte de l'avenir. Cette thèse est structurée comme suit. Après un chapitre d'introduction, nous présentons une revue de la littérature sur le système manuel et le SRM, et les décisions communes prises pour mettre en place leurs processus de stockage et de prélèvement. Les quatre chapitres suivants détaillent les études pour le problème de stockage et de routage intégré, le problème de dimensionnement des zones, le PAQ et le problème de repositionnement de pod. Nos conclusions sont résumées dans le dernier chapitre.The rising of e-commerce is demanding an increase in the performance of warehousing systems, which are being redesigned to deal with a mass volume of demands to be fulfilled as fast as possible. The manual system and the robotic mobile fulfillment system (RMFS) are among the most commonly used for these activities. The former is a human-centered system that handles complex operations that current robots cannot perform. However, newer generations of autonomous robots are leading to a gradual replacement by the latter to increase productivity. Regardless of the system used, several interdependent problems have to be solved to have efficient storage and picking processes. Storage problems concern decisions on where to store products within the warehouse. Picking problems include the batching of orders to be fulfilled together and the routes the pickers and robots should follow to retrieve the products demanded. In the manual system, these problems are traditionally solved using simple policies that pickers can easily follow. Despite using robots, the same solution strategy is being replicated to the equivalent problems found in the RMFS. In this research, we investigate storage and picking problems faced when designing manual and RMFS warehouses. We develop optimization tools to help in the decision-making process to set up their processes and improve typical performance measures considered in these systems. Some classic problems are solved with improved techniques, while others are integrated to be solved together instead of optimizing each subsystem sequentially. We first consider a manual system with a known set of orders and integrate storage and routing decisions. The integrated problem and some variants considering common routing policies are modeled mathematically. A general variable neighborhood search metaheuristic is presented to deal with real-size instances. Computational experiments attest to the effectiveness of the metaheuristic proposed compared to the exact models and common storage policies. When future demands are uncertain, it is common to use a zoning strategy to divide the storage area into zones and assign the most-demanded products to the best zones. Zone sizes are to be determined. Commonly, arbitrary sizes are chosen, which ignore the characteristics of the warehouse and the demands. We approach the zone sizing problem to determine which factors are relevant to choosing better zone sizes. Data generated from exhaustive simulations are used to train four machine learning regression models - ordinary least squares, regression tree, random forest, and multilayer perceptron - to predict the optimal zone sizes given the set of relevant factors identified. We show that all trained models suggest tailor-made zone sizes with better picking performance than the arbitrary ones commonly used. Another approach to solving storage problems, both in the manual and RMFS, considers the correlations between products. The idea is that products constantly demanded together should be stored closer to reduce routing costs. This storage policy can be modeled as a quadratic assignment problem (QAP) variant. The QAP is a traditional combinatorial problem and one of the hardest to solve. We survey the most traditional QAP variants and develop a powerful parallel memetic iterated tabu search metaheuristic capable of solving them. The proposed metaheuristic is shown to be among the best performing ones for the QAP and significantly outperforms the state-of-the-art for its variants. The RMFS allows easy repositioning of inventory pods during operations that can lead to a more energy-efficient picking process. We integrate pod repositioning decisions with order assignment and pod selection using a wave picking strategy such that pods are parked after being requested considering when and where they are expected to be requested next. We solve this integrated problem using stochastic programming considering the uncertainty about future demands and suggest a local search matheuristic to solve real-size instances. We show that our sample average approximation scheme is effective to simulate future demands since our methods improve solutions found when waves are planned without considering the future demands. This thesis is structured as follows. After an introductory chapter, we present a literature review on the manual and RMFS, and common decisions made to set up their storage and picking processes. The next four chapters detail the studies for the integrated storage and routing problem, the zone sizing problem, the QAP, and the pod repositioning problem. Our findings are summarized in the last chapter

Solving Real-Life Hydroinformatics Problems with Operations Research and Artificial Intelligence

Many real life problems in the hydraulic engineering literature can be modelled as constrained optimisation problems. Often, they are addressed in the literature through genetic algorithms, although other techniques have been proposed. In this thesis, we address two of these real life problems through a variety of techniques taken from the Artificial Intelligence and Operations Research areas, such as mixed-integer linear programming, logic programming, genetic algorithms and path relinking, together with hybridization amongst these technologies and with hydraulic simulators. For the first time, an Answer Set Programming formulation of hydroinformatics problems is proposed. The two real life problems addressed hereby are the optimisation of the response in case of contamination events, and the optimisation of the positioning of the isolation valves. The constraints of the former describe the feasible region of the Multiple Travelling Salesman Problem, while the objective function is computed by a hydraulic simulator. A simulation–optimisation approach based on Genetic Algorithms, mathematical programming, and Path Relinking, and a thorough experimental analysis are discussed hereby. The constraints of the latter problem describe a graph partitioning enriched with a maximum flow, and it is a new variant of the common graph partitioning. A new mathematical model plus a new formalization in logic programming are discussed in this work. In particular, the technologies adopted are mixed-integer linear programming and Answer Set Programming. Addressing these two real applications in hydraulic engineering as constrained optimisation problems has allowed for i) computing applicable solutions to the real case, ii) computing better solutions than the ones proposed in the hydraulic literature, iii) exploiting graph theory for modellization and solving purposes, iv) solving the problems by well suited technologies in Operations Research and Artificial Intelligence, and v) designing new integrated and hybrid architectures for a more effective solving