Raymond R. Hill

The distributor's three-dimensional pallet-packing problem: a human intelligence-based heuristic approach

The distributors pallet-packing problem requires the loading of a pallet or container that has a fixed length, width and height with the objective to maximise utilisation of the pallets volume. We develop a new heuristic algorithm using novel heuristic rules and a dynamic data structure to mimic human intelligence, thus providing a new solution approach to 3-D pallet packing. Comprehensive empirical testing, to include new methods for generating problems with known optimal solutions, demonstrate that our algorithm achieves pallet volume utilisations comparable or better than the best-known solutions, while finding these solutions very quickly. Computer-independent complexity results are provided.

Problem reduction heuristic for the 0-1 multidimensional knapsack problem

This paper introduces new problem-size reduction heuristics for the multidimensional knapsack problem. These heuristics are based on solving a relaxed version of the problem, using the dual variables to formulate a Lagrangian relaxation of the original problem, and then solving an estimated core problem to achieve a heuristic solution to the original problem. We demonstrate the performance of these heuristics as compared to legacy heuristics and two other problem reduction heuristics for the multi-dimensional knapsack problem. We discuss problems with existing test problems and discuss the use of an improved test problem generation approach. We use a competitive test to highlight the performance of our heuristics versus the legacy heuristic approaches. We also introduce the concept of computational versus competitive problem test data sets as a means to focus the empirical analysis of heuristic performance.

A tabu search with vocabulary building approach for the vehicle routing problem with split demands

In the vehicle routing problem (VRP) a fleet of vehicles with limited capacity is utilised to supply the demand of a set of customers located around a unique depot while minimising the total travelled distance. All customer demands are supplied and customers are visited by exactly one vehicle. In the split delivery vehicle routing problem (SDVRP), customers can be visited by more than one vehicle meaning their demands can be split among multiple vehicles. This paper presents a learning procedure, called tabu search with vocabulary building approach (TSVBA) for solving the SDVRP. TSVBA is a population-based search approach that uses a set of solutions to find attractive solution attributes with which to construct new solutions. As the search progresses, the solution set evolves; better solutions move into the set while bad solutions are removed. The proposed learning procedure was tested on benchmark instances and performed well when its solutions are compared to those reported in the literature. New best solutions are obtained on some benchmark problems available.

A Monte-Carlo study of genetic algorithm initial population generation methods

Briefly describes genetic algorithms (GAs) and focuses attention on initial population generation methods for 2D knapsack problems. Based on work describing the probability that a random solution vector is feasible for 0-1 knapsack problems, we propose a simple heuristic for randomly generating good initial populations for GA applications to 2D knapsack problems. We report on an experiment comparing a current population generation technique with our proposed approach and find our proposed approach does a very good job of generating good initial populations.

Managing business complexity: discovering strategic solutions with agent-based modelling and simulation

This book, Managing Business Complexity by Michael North and Charles Macal, is not your typical agent-based modelling text. To date, it seems, most agent-based modelling texts fall into two broad categories: a collection of readings (such as from a conference), or a specific how-to text (for a specific methodology or software platform). Although serving a valued purpose, such works fail to provide that text targeted at that new technically savvy audience of readers interested in the agent-based modelling paradigm that require a relatively complete exposition based on a broadly defined view of agents and agent-based models. While the landmark text by Epstein and Axtell (1996) remains a necessary initial reference for anyone commencing their studies into agents and agent-based modelling, this text by North and Macal should be reserved as a key reference text. As noted in an earlier review of this book (Van Dyke Parunak, 2007), the 15 chapters in the book fall into three categories; a categorization that works for this review as well. Chapters 1–5 really provide foundational information about what are agents and what is agent-based modelling. Chapters 6–10 provide a series of ‘how to’ chapters pertaining to different components of the agent-based modelling paradigm. Finally, Chapters 11–14 cover topics related to modelling and simulation in general but tailored to agent-based modelling specifically. Chapter 15 is a concluding chapter. The authors take a much broader definition of agentbased than might be found in any other book on agents and agent-based modelling. As such they cover a greater breadth of topics as compared to these other texts. Their target audience is not the accomplished agent-based modeller, even though there is a wealth of worthwhile information in the book for that modeller. As stated, the target audience is ‘managers, analysts, and software developers in business and government’. To this, one should add, ‘or anyone interested in learning about agents or to those just getting started in research using agent models’. The caveat to this is that the book has sufficient technical depth to require some level of technical competence to comprehend the coverage and exploit the knowledge the book imparts. The first five chapters introduce the reader to agents and how agent-based models apply. This coverage includes defining the agent-based model paradigm (Chapter 2), defining agents (Chapter 3), providing some history of agent modelling (Chapter 4) and where agent-based modelling fits (Chapter 5). While overall they present quite a complete background, the Chapter 5 coverage gets overly ambitious in that it tries to lay out the complete spectrum of modelling approaches. Although not really in line with the focus of the book, this full-spectrum coverage does help the newcomer to agent-based modelling better distinguish among modelling approaches. Further, this broad review of modelling approaches provides useful background information for the remainder of the book. Chapters 6–10 provide the ‘how-to’ portion of the book. Chapter 6 is one of the best chapters in the text and a wonderful addition to the agent-based modelling literature. While capturing agent behaviours, and their interactions, is a crucial part of the agent-based modelling methodology, rarely do texts provide a how-to associated with this knowledge engineering component. North and Macal correct Journal of Simulation (2010) 4, 211–212 r 2010 Operational Research Society Ltd. All rights reserved. 1747-7778/10

Using agent-based simulation to empirically examine search theory using a historical case study

Threats to a nations resources and forces are becoming increasingly lethal and mobile. Therefore, the ability to locate and interdict these threats is more important than ever. Search theory was developed during World War II (WWII), but remains an analytical tool vital to locating and countering the increasing threat. This paper presents results that demonstrate how simulation can be used to extend the analytical results of classic Search Theory. This paper presents a multi-agent simulation, built in the Java object-oriented programming language, and based on the Allied search for U-boats in the Bay of Biscay during WWII. Key components of the model are validated against historical data using statistical methods. The model is then used to empirically examine the utility of various modern search patterns particularly when rigid Search Theory assumptions are relaxed.

New greedy heuristics for the Multiple-choice Multi-dimensional Knapsack Problem

This paper examines the Multiple-choice Multi-dimensional Knapsack Problem (MMKP) – a more complex variant of the classic knapsack problem (KP). We survey existing algorithms for the variants of the KP and critically examine existing test problems for the MMKP. We present an empirical study of sample legacy solution approaches compared to two new systematically-developed greedy heuristics for the MMKP. We extend our testing to include a new systematically-generated test problem set. Characteristics of all the problem sets are compared and used to explain the empirical performance results obtained and demonstrate the superiority of our greedy heuristic approach.

Composition for multivariate random variables

We show how to find mixing probabilities, or weights, for composite probability mass functions (pmfs) for k-variate discrete random variables with specified marginal pmfs and a specified, feasible population correlation structure. We characterize a joint pmf that is a composition, or mixture, of 2/sup k-1/ extreme correlation joint pmfs and the joint pmf under independence. Our composition method is also valid for multivariate continuous random variables. We consider the cases where all of the marginal distributions are discrete uniform, negative exponential, or continuous uniform.

Some insights into the emergence of agent-based modelling

Agent-based modelling (ABM) has become a popular simulation analysis tool and has been used to examine systems from myriad domains. This article re-examines some of the scientific developments in computers, complexity, and systems thinking that helped lead to the emergence of ABM by shedding new light onto some old theories and connecting them to several key ABM principles of today. As it is often the case, examining history can lead to insightful views about the past, present, and the future. Thus, themes from cellular automata and complexity, cybernetics and chaos, and complex adaptive systems are examined and placed in historical context to better establish the application, capabilities, understanding, and future of ABM.

Devising a quick-running heuristic for an unmanned aerial vehicle (UAV) routing system

UAVs provide reconnaissance support for the US military and often need operational routes immediately; current practice involves manual route calculation that can involve hundreds of targets and a complex set of operational restrictions. Our research focused on providing an operational UAV routing system. This system required development of a reasonably effective, quick running routing heuristic. We present the statistical methodology used to devise a quick-running routing heuristic that provides reasonable solutions. We consider three candidate local search heuristic approaches, conduct an empirical analysis to parameterize each heuristic, competitively test each candidate heuristic, and provide statistical analysis on the performance of each candidate heuristic to include comparison of the results of the best candidate heuristic against a compilation of the best-known solutions for standard test problems. Our heuristic is a component of the final UAV routing system and provides the UAV operators a tool to perform their route development tasks quickly and efficiently.