Sigurdur Olafsson

Nested Partitions Method for Global Optimization

We propose a new randomized method for solving global optimization problems. This method, the Nested Partitions (NP) method, systematically partitions the feasible region and concentrates the search in regions that are the most promising. The most promising region is selected in each iteration based on information obtained from random sampling of the entire feasible region and local search. The method hence combines global and local search. We first develop the method for discrete problems and then show that the method can be extended to continuous global optimization. The method is shown to converge with probability one to a global optimum in finite time. In addition, we provide bounds on the expected number of iterations required for convergence, and we suggest two stopping criteria. Numerical examples are also presented to demonstrate the effectiveness of the method.

Operations research and data mining

With the rapid growth of databases in many modern enterprises data mining has become an increasingly important approach for data analysis. The operations research community has contributed significantly to this field, especially through the formulation and solution of numerous data mining problems as optimization problems, and several operations research applications can also be addressed using data mining methods. This paper provides a survey of the intersection of operations research and data mining. The primary goals of the paper are to illustrate the range of interactions between the two fields, present some detailed examples of important research work, and provide comprehensive references to other important work in the area. The paper thus looks at both the different optimization methods that can be used for data mining, as well as the data mining process itself and how operations research methods can be used in almost every step of this process. Promising directions for future research are also identified throughout the paper. Finally, the paper looks at some applications related to the area of management of electronic services, namely customer relationship management and personalization.

Discovering Dispatching Rules Using Data Mining

This paper introduces a novel methodology for generating scheduling rules using a data-driven approach. We show how to use data mining to discover previously unknown dispatching rules by applying the learning algorithms directly to production data. This approach involves preprocessing of historic scheduling data into an appropriate data file, discovery of key scheduling concepts, and representation of the data mining results in a way that enables its use for job scheduling. We also consider how by using this new approach unexpected knowledge and insights can be obtained, in a manner that would not be possible if an explicit model of the system or the basic scheduling rules had to be obtained beforehand. All of our results are illustrated via numerical examples and experiments on simulated data.

An Optimization Framework for Product Design

An important problem in the product design and development process is to use the part-worths preferences of potential customers to design a new product such that market share is maximized. The authors present a new optimization framework for this problem, the nested partitions (NP) method. This method is globally convergent and may utilize existing heuristic methods to speed its convergence. We incorporate several known heuristics into this framework and demonstrate through numerical experiments that using the NP method results in superior product designs. Our numerical results suggest that the new framework is particularly useful for designing complex products with many attributes.

New parallel randomized algorithms for the traveling salesman problem

Abstract We recently developed a new randomized optimization framework, the Nested Partitions (NP) method. This approach uses partitioning, global random sampling, and local search heuristics to create a Markov chain that has global optima as its absorbing states. This new method combines global and local search in a natural way and it is highly matched to emerging massively parallel processing capabilities. In this paper, we apply the NP method to the Travelling Salesman Problem . Preliminary numerical results show that the NP method generates high-quality solutions compared to well-known heuristic methods, and that it can be a very promising alternative for finding a solution to the TSP. Scope and purpose The traveling salesman problem involves finding the shortest route between a number of cities. This route must visit each of the cities exactly once and begin and finish in the same city. As easy as it is to describe, this problem is notoriously difficult to solve. It is widely believed that there is no efficient algorithm that can solve it accurately. On the other hand, this problem is very important since it has many applications in such areas as routing robots through automatic warehouses and drilling holes in printed circuit boards. We present a new method, the Nested Partitions method, for solving the traveling salesman problem. The method is very flexible in that it is capable of finding good solutions rapidly and given enough time will identify the optimal solution. This new method is also highly matched with parallel processing capabilities.

Joint order batching and order picking in warehouse operations

Traditional warehousing focuses on improving efficiency within the warehouse, and while this is certainly of great importance, it does not necessarily translate directly into better response to customers and supply chain partners. This paper reconsiders the traditional warehousing problems of batching and picking orders with respect not only to improving efficiency, as measured by low picking time and effective use of vehicles, but also to doing so in a way that optimizes customer response time. To this end, we formulate the batching and order picking problem jointly as a combinatorial optimization problem, evaluate the benefits of addressing the joint problem and propose simple but effective heuristics for its solution.

Optimization-based feature selection with adaptive instance sampling

Preprocessing the data to filter out redundant and irrelevant features is one of the most important steps in the data mining process. Careful feature selection may improve both the computational time of inducing subsequent models and the quality of those models. Using fewer features often leads to simpler and easier to interpret models, and selecting important feature can lead to important insights into the application. The feature selection problem is inherently a combinatorial optimization problem. This paper builds on a metaheuristic called the nested partitions method that has been shown to be particularly effective for the feature selection problem. Specifically, we focus on the scalability of the method and show that its performance is vastly improved by incorporating random sampling of instances. Furthermore, we develop an adaptive variant of the algorithm that dynamically determines the required sample rate. The adaptive algorithm is shown to perform very well when applied to a set of standard test problems.

An integrated framework for deterministic and stochastic optimization

optimization problem which takes the following form. In recent articles we presented a general methodology for finite optimization. The new method, the Nested Partitions (NP) method, combines partitioning, random sampling, a selection of a promising index, and backtracking to create a Markov chain that converges to a global optimum. In this paper we demonstrate, through examples, how the NP method can be applied to solve both deterministic and stochastic finite optimization problems in a unified framework.

A method for scheduling in parallel manufacturing systems with flexible resources

We address the Parallel-Machine Flexible-Resource Scheduling (PMFRS) problem of simultaneously allocating flexible resources, and sequencing jobs, in cellular manufacturing systems where the cells are configured in parallel. We present a new solution methodology for the PMFRS problem called the Nested Partitions (NP) method. This method combines global sampling of the feasible region and local search heuristics. To efficiently apply the NP method we reformulate the PMFRS problem, develop a new sampling algorithm that can be used to obtain good feasible schedules, and suggest a new improvement heuristic. Numerical examples are also presented to illustrate the new method.

Chapter 21 Metaheuristics

Abstract Metaheuristics have been established as one of the most practical approaches to simulation optimization. However, these methods are generally designed for combinatorial optimization, and their implementations do not always adequately account for the presence of simulation noise. Research in simulation optimization, on the other hand, has focused on convergent algorithms, giving rise to the impression of a gap between research and practice. This chapter surveys the use of metaheuristics for simulation optimization, focusing on work bridging the current gap between the practical use of such methods and research, and points out some promising directions for research in this area. The main emphasis is on two issues: accounting for simulation noise in the implementation of metaheuristics, and convergence analysis of metaheuristics that is both rigorous and of practical value. To illustrate the key points, three metaheuristics are discussed in some detail and used for examples throughout, namely genetic algorithms, tabu search, and the nested partitions method.