On scalarizing functions in multiobjective optimization

Scalarizing functions play an essential role in solving multiobjective optimization problems. Many different scalarizing functions have been suggested in the literature based on different approaches. Here we concentrate on classification and reference point-based functions. We present a collection of functions that have been used in interactive methods as well as some modifications. We compare their theoretical properties and numerical behaviour. In particular, we are interested in the relation between the information provided and the results obtained. Our aim is to select some of them to be used in our WWW-NIMBUS optimization system. Received: June 11, 2001 / Accepted: October 31, 2001     

Optimisation of beam directions in intensity modulated radiation therapy planning

Abstract. In this paper we consider the problem of selecting optimal beam directions as well as optimal intensity profiles for radiation therapy. Our multiobjective mixed integer programming problem is based on and extends a multiobjective LP formulation for intensity optimisation by Hamacher and Küfer. We use a weighted sum scalarisation to explore the benefits of beam direction optimisation. We propose exact and heuristic methods for solving the problem and present some numerical results. Correspondence to: M. Ehrgott     

A unified modeling and solution framework for combinatorial optimization problems

Combinatorial optimization problems are often too complex to be solved within reasonable time limits by exact methods, in spite of the theoretical guarantee that such methods will ultimately obtain an optimal solution. Instead, heuristic methods, which do not offer a convergence guarantee, but which have greater flexibility to take advantage of special properties of the search space, are commonly a preferred alternative. The standard procedure is to craft a heuristic method to suit the particular characteristics of the problem at hand, exploiting to the extent possible the structure available. Such tailored methods, however, typically have limited usefulness in other problems domains.An alternative to this problem specific solution approach is a more general methodology that recasts a given problem into a common modeling format, permitting solutions to be derived by a common, rather than tailor-made, heuristic method. Because such general purpose heuristic approaches forego the opportunity to capitalize on domain-specific knowledge, they are characteristically unable to provide the effectiveness or efficiency of special purpose approaches. Indeed, they are typically regarded to have little value except for dealing with small or simple problems.This paper reports on recent work that calls this commonly held view into question. We describe how a particular unified modeling framework, coupled with latest advances in heuristic search methods, makes it possible to solve problems from a wide range of important model classes.Correspondence to: Gary A. Kochenberger.This research was supported in part by ONR grants N000140010598 and N000140310621.     

A computational study of LP-based heuristic algorithms for two-dimensional guillotine cutting stock problems

In this paper we develop and compare several heuristic methods for solving the general two-dimensional cutting stock problem. We follow the Gilmore-Gomory column generation scheme in which at each iteration a new cutting pattern is obtained as the solution of a subproblem on one stock sheet. For solving this subproblem, in addition to classical dynamic programming, we have developed three heuristic procedures of increasing complexity, based on GRASP and Tabu Search techniques, producing solutions differing in quality and in time requirements. In order to obtain integer solutions from the fractional solutions of the Gilmore-Gomory process, we compare three rounding procedures, rounding up, truncated branch and bound and the solution of a residual problem. We have coded and tested all the combinations of algorithms and rounding procedures. The computational results obtained on a set of randomly generated test problems show their relative efficiency and allow the potential user to choose from among them, according to the available computing time. Rceived: January 9, 2001 / Accepted: December 10, 2001     

Modeling and optimization of the intermodal terminal Mega Hub

The convergence of European states can be expected to lead to an increase in the trading of goods within the next few years and thus to a growing demand for transport. Overland intermodal transport is an important development, because it combines the advantages of rail for long distance transportation with the effective area cover offered by road. Different terminal concepts and production forms have been developed to increase the flexibility of intermodal transport and to make it more attractive for the customer. The intermodal terminal concept investigated in this paper is called Mega Hub. The configuration and the control of the terminal is a complex and challenging task. Here, the terminal is modeled as a multi-stage transshipment problem. In this approach, sequence-dependent duration of empty moves, alternative assignments (of containers to cranes) and a sequence-dependent number of operations have to be handled. An optimization model based on Constraint Satisfaction is formulated and heuristics for the search procedure, especially value and variable ordering are developed. Received: May 2, 2000 / Accepted: July 4, 2001     

An integrated system solution for supply chain optimization in the chemical process industry

This paper considers a complex scheduling problem in the chemical process industry involving batch production. The application described comprises a network of production plants with interdependent production schedules, multi-stage production at multi-purpose facilities, and chain production. The paper addresses three distinct aspects: (i) a scheduling solution obtained from a genetic algorithm based optimizer, (ii) a mechanism for collaborative planning among the involved plants, and (iii) a tool for manual updates and schedule changes. The tailor made optimization algorithm simultaneously considers alternative production paths and facility selection as well as product and resource specific parameters such as batch sizes, and setup and cleanup times. The collaborative planning concept allows all the plants to work simultaneously as partners in a supply chain resulting in higher transparency, greater flexibility, and reduced response time as a whole. The user interface supports monitoring production schedules graphically and provides custom-built utilities for manual changes to the production schedule, investigation of various what-if scenarios, and marketing queries. RID="*" ID="*" The authors would like to thank Hans-Otto Günther and Roland Heilmann for helpful comments on draft versions of this paper.     

A scheduling method for Berth and Quay cranes

This paper discusses a method for scheduling Berth and Quay cranes, which are critical resources in port container terminals. An integer programming model is formulated by considering various practical constraints. A two-phase solution procedure is suggested for solving the mathematical model. The first phase determines the Berthing position and time of each vessel as well as the number of cranes assigned to each vessel at each time segment. The subgradient optimization technique is applied to obtain a near-optimal solution of the first phase. In the second phase, a detailed schedule for each Quay crane is constructed based on the solution found from the first phase. The dynamic programming technique is applied to solve the problem of the second phase. A numerical experiment was conducted to test the performance of the suggested algorithms. RID="*" ID="*" This research has been supported in part by Brain Korea 21 Program (1999–2002). Correspondence to: Y.-M. Park     

Optimal tax depreciation lives and charges under regulatory constraints

Depreciation is not only a representation of the loss in asset-value over time. It is also a strategic tool for management and can be used to minimize tax payments. In this paper we derive the depreciation scheme that minimizes the expected value of the present value of future tax payments for two types of constraints on the depreciation method. We show how the optimal scheme depends on the discount factor and the cash flow distributions. Moreover, we find the somewhat surprising result that the way in which the optimum is affected by uncertainty depends crucially on the type of regulatory constraint. Received: January 9, 2001 / Accepted: Feburary 25, 2002     

Meta-heuristic based decision support for portfolio optimization with a case study on tracking error minimization in passive portfolio management

In this paper we describe the concept and design of a meta-heuristic based decision support system generator (DSS-generator) for portfolio optimization. We report extensively on experience with the application of a specific DSS that has been customized for controlling and optimizing passively managed stock funds. Here, the constraints from the law on investment trust companies as well as several fund specific guidelines prohibit that the benchmark can be identically reproduced. For measuring the performance of the portfolio a tracking error model with data stemming from a factor model is applied. Our results show that the system provides proposals for the fund manager in acceptable time which are feasible with respect to the guidelines and excellent in quality.     

A Theory of Complexity, Periodicity and the Design Axioms

One of the topics that has received the attention of mathematicians, scientists and engineers is the notion of complexity. The subject is still being debated, as it lacks a common definition of complexity, concrete theories that can predict complex phenomena, and the mathematical tools that can deal with problems involving complexity. In axiomatic design, complexity is defined only when specific functional requirements or the exact nature of the query are defined. Complexity is defined as a measure of uncertainty in achieving a set of specific functions or functional requirements. Complexity is related to information, which is defined in terms of the probability of success of achieving the Functional Requirements (FRs). There are two classes of complexity: time-dependent complexity and time-independent complexity. There are two orthogonal components of time-independent complexity, i.e., real complexity and imaginary complexity. The vector sum is called absolute complexity. Real complexity of coupled design is larger than that of uncoupled or decoupled designs. Imaginary complexity can be reduced when the design matrix is known. As an example of time-independent imaginary complexity, the design of a printing machine based on xerography is discussed. There are two kinds of time-dependent real complexity: time-dependent combinatorial complexity and time-dependent periodic complexity. Using a robot-scheduling problem as an example, it is shown that a coupled design with a combinatorial complexity can be reduced to a decoupled design with periodic complexity. The introduction of periodicity simplifies the design by making it deterministic, which requires much less information. Whenever a combinatorial complexity is converted to a periodic complexity, complexity and uncertainty is reduced and design simplified.     

A Study on Engineering History Base

During engineering processes, many kinds and amounts of information are used and produced. Such information is useful in successive cases, and thus its reuse is desired. In this paper, information on attributes of the products is referred to as ‘product information’, and information on the reasons for and/or history of a designer’s thought process is referred to as ‘process information’. According to this classification, process information can be used for obtaining an explanation of product information. The purpose of this work is to build a database, called an ‘engineering history base’, from which engineers can retrieve explanations to enable the reuse of product information. In this paper, explanation from the ‘process’ viewpoint is thought to be important in promoting the reuse of product information. There are two types of explanation for the process: teleological and causal. However, until now, little attention has been paid to the causal explanation for the process. Thus, in this paper, an information model which focuses on both types of explanation is proposed. The model is adopted for the engineering history base and a prototype system is developed. The appropriateness of this model is discussed by analyzing the actual data in the development of a color video printer.     

A Taxonomy for Design Requirements from Corporate Customers

We have developed a taxonomy that classifies those needs of a corporation that impact product design. We call these needs corporate requirements. In contrast to the consumer or end-user requirements, corporate requirements come from internal sources such as marketing, finance, manufacturing, and service. This taxonomy allows for an organized method of gathering, managing, and retrieving the requirements. The taxonomy also helps to facilitate a broader, clearer form of Quality Function Deployment. Generic in nature, this taxonomy provides a template with which to create taxonomies for a given product within a given company or industry. We include an industrial case study to demonstrate this concept.     

Planning and scheduling in the process industry

Since there has been tremendous progress in planning and scheduling in the process industry during the last 20 years, it might be worthwhile to give an overview of the current state-of-the-art of planning and scheduling problems in the chemical process industry. This is the purpose of the current review which has the following structure: we start with some conceptional thoughts and some comments on special features of planning and scheduling problems in the process industry. In Section 2 the focus is on planning problems while in Section 3 different types of scheduling problems are discussed. Section 4 presents some solution approaches especially those applied to a benchmark problem which has received considerable interest during the last years. Section 5 allows a short view into the future of planning and scheduling. In the appendix we describe the Westenberger-Kallrath problem which has already been used extensively as a benchmark problem for planning and scheduling in the process industr y.     

Truncated branch-and-bound,schedule-construction,and schedule-improvement procedures for resource-constrained project scheduling

We present heuristic procedures for approximately solving large project scheduling problems with general temporal and resource constraints. In particular, we propose several truncated branch-and-bound techniques, priority-rule methods, and schedule-improvement procedures of types tabu search and genetic algorithm. A detailed experimental performance analysis compares the different heuristics devised and shows that large problem instances with up to 1000 activities and several resources can efficiently be solved with sufficient accuracy.

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Received: July 26, 2000 / Accepted: May 15, 2001     

On the location of antennas for treatment planning in hyperthermia

Abstract. In this paper we investigate how to determine optimal locations of the microwave antennas being circularly ordered in a hyperthermia device. The heated area containing the tumor should have minimal volume. Based on a simple geometric model for the two and three dimensional case we develop algorithms for the computation of these volumes and present numerical results for the optimal locations. Correspondence to: J. Jahn     

Coordination Approaches and Systems – Part I: A Strategic Perspective

This is the first part of a two-part paper presenting a fundamental review and summary of research of design coordination and cooperation technologies. The theme of this review is aimed at the research conducted within the decision management aspect of design coordination. The focus is therefore on the strategies involved in making decisions and how these strategies are used to satisfy design requirements. The paper reviews research within collaborative and coordinated design, project and workflow management, and, task and organization models. The research reviewed has attempted to identify fundamental coordination mechanisms from different domains, however it is concluded that domain independent mechanisms need to be augmented with domain specific mechanisms to facilitate coordination. Part II is a review of design coordination from an operational perspective.     

A-Design: An Agent-Based Approach to Conceptual Design in a Dynamic Environment

This paper provides an introduction to a new design methodology known as A-Design, which combines aspects of multi-objective optimization, multi-agent systems, and automated design synthesis. The A-Design theory is founded on the notion that engineering design occurs in interaction with an ever-changing environment, and therefore computer tools developed to aid in the design process should be adaptive to these changes. In this paper, A-Design is introduced along with some simple test problems to demonstrate the capabilities of different aspects of the theory. The theory of A-Design is then shown as the basis for a design tool that adaptively creates electro-mechanical configuration designs for changing user preferences.     

Evaluation of Product and Process Design Robustness

Critical design decisions are commonly made throughout the product development process assuming known material and process behavior. However, stochastic variation during manufacture can inadvertently result in inferior or unacceptable product performance and reduced production yields. Stochastic simulations have been developed to estimate the end-use performance distribution prior to the commitment of hard tooling. This article proposes a definition for integrated product and process robustness, and extends existing stochastic methods to model the important role of the manufacturing flexibility in elimination of defects and product optimization. The goal is to enable the designer to understand and account for not only the negative effects of manufacturing variation, but also the positive impact of manufacturing flexibility wherein instantaneous corrections in the manufacturing process can frequently improve the product quality and eliminate flaws in the product design. Then, a methodology is introduced and contrasted with conventional development methods in the evaluation of best practices for development of a molded plastic component.     

Developing Strategic Alliances: A Framework for Collaborative Negotiation in Design

This work applies a theory-based framework of collaborative negotiation to some of the disputes that regularly arise during group design. Although the framework was developed to provide general support for group work, this paper focuses on its use as a design tool. The framework, embodied in our system NegotiationLens, has four facets. It: 1. Provides a negotiation method intended to produce gain for all parties. 2. Provides an efficient process for conflict resolution. 3. Develops working alliances. 4. Lets parties decide quickly when they should go their separate ways. The framework produces the above results by: • Helping parties develop well-reasoned and clearly articulated points of view (Adelson and Jordan, 1991; Conklin and Yakemovic, 1991; Conklin and Begeman, 1988; MacLean et al ., 1991). • Creating a context of committment and respect. • Moving negotiating parties away from an adversarial stance and into a collaboration. • Allowing joint construction of solutions that are more beneficial than the unilateral solutions each party initially brought to the table. We present our framework for collaborative negotiation, describe NegotiationLens, and present two cases in which it was used. We present a third case, a large design project with recurrent design conflicts, and argue how NegotiationLens could have been of benefit there.