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Title: Background and Theory of Constraint Programming
Abstract: This talk will review the principles and the historical roots of constraint programming (CP). Indeed, understanding the history behind this field helps understand the basic principles it is built on. CP can be traced back to a combination of Artificial Intelligence, Combinatorics (graph algorithms), and programming language design. It took two decades to unify these in a comprehensive and versatile framework shared by all modern CP tools and solvers. We'll review this framework and how it is implemented in recent tools. Last we will relate it and contrast it with mathematical programming.
Title: Practical Application of Constraint Programming Techniques
Abstract:
This talk will build on the previous one by presenting a number of
techniques that are typically used by CP practitioners to solve problems more
effectively. These techniques can be divided into two categories: those which
can be applied when modeling the problem, and those which relate to the
solving process. Both categories will be explored. Throughout the
presentation we will use IBM's constraint programming solver, CP Optimizer, to
illustrate how a user would either access or implement these techniques.
Title: Berth Allocation and Quay Crane Assignment using Constraint programming
Abstract:
In this talk we will tackle the berth and crane allocation problem arising in large container terminals and describe a constraint programming approach able to model many realistic operational constraints. The costs for berth allocation, crane allocation, time windows, breaks and transition times during gang movements are optimized simultaneously. The model is richer than the state of the art in the operations research community. Experiments show that the model produces solutions with a cost gap of 1/10 (7,8%) to 1/5 (18,8%) compared to an ideal operational setting where operational constraints are ignored.
Title: Introduction to Some Methods and Applications of Nonlinear Multiobjective Optimization - part 1 and 2
Abstract:
In multiobjective optimization, the goal is to find the best possible solution in the presence of several, conflicting objectives. Multiobjective optimization is important because most real-life problems contain more than one objective and they should be considered simultaneously.
Using mathematical tools we can define a set of nondominated or Pareto optimal solutions where none of the objective values can be improved without impairing at least one of the other objective values. Because vectors cannot be ordered completely, we need some some additional preference information from an expert, a decision maker, to find the most preferred Pareto optimal solution as the final solution to be implemented.
Multiobjective optimization methods can be classified according to the role of the decision maker in the solution process. We review different types of methods and summarize their strengths and weaknesses. We pay most attention to interactive methods, where the decision maker takes actively part in the solution process and directs the search for the final solution according to her/his desires and hopes. This enables the decision maker to gain insight about the interdependencies of the conflicting objectives and learn about one's own preferences. Among the methods to be discussed are the classification-based NIMBUS method, the Nautilus method which enables decision making without trading-off and Pareto Navigator for computationally expensive problems.
Finally, we study some complex real-life problems that have been successively solved by applying multiobjective optimization software and demonstrate how useful it is to consider several objectives simultaneously.
The problems are related, for example, to chemical engineering processes, optimal shape design and wastewater treatment. To conclude, we collect some experiences.
Keywords:
Multiple objective optimization, nonlinear optimization, MCDM, decision support, interactive methods, NIMBUS, Nautilus, Pareto Navigator, software
Title: Peculiarities of the Radiation Treatment Planning Optimization Problem: multiple objectives, user/algorithm interaction and feasibility
Abstract:
Radiation therapy is a main cancer treatment modality that exploits ionizing radiation to deliver a therapeutic dose to tumorous tissues in order to sterilize the proliferation of clonogenic cells.
Advanced high-precision conformal radiation therapy techniques like intensity-modulated radiotherapy (IMRT) offer technical solutions to deposit a sufficiently high dose to the tumor and simultaneously spare surrounding healthy tissues as much as possible. The inherent technical complexity of IMRT requires an inverse treatment planning approach, which relies on mathematical optimization techniques to search for an optimal treatment plan that satisfies the clinical goals. The problem is that these goals are mutually dependent and contradictory, and therefore a single best solution does not exist in general. Instead, the large number of degrees of freedom of IMRT to shape the dose distribution has opened the possibility to generate multiple solutions and to allow physician/patient specific trade-offs between achieving local tumor control and causing severe side effects in surrounding normal tissues. Therefore, there is a need for methods to find best-possible plans and assist in (interactive) balancing of patient- and physician-specific preferences.
This lecture will address methods from the field of Operations Research to deal with the multi-objective optimization problem of IMRT planning. Finding the best-possible compromise solutions requires user interaction and guidance from the search algorithm. Different methods to articulate preference information in inverse treatment planning will be reviewed. A priori preference methods use weighting factors to capture the relative importance of the objectives, but generally require several trial and error iterations to find an acceptable plan, because the relationship between the goals is unknown beforehand. Furthermore, the plain weighting factors do not reflect clinical importance, and the sensitivity to changes in the weighting factors is unknown. Therefore, in clinical practice the potential of IMRT cannot be fully exploited. To overcome the time-consuming human iteration loop, a posteriori preference methods for off-line generation of best-compromise solutions have been applied and explored. First, the set of Pareto solutions is identified for which improving one objective cannot be improved by deteriorating at least one other objective, and then the best solution is selected from a graphical representation of this set (Pareto front) according to individual preferences. In this way the treatment planner/physician can experience the sensitivity to changes in the goals and decide for the clinically optimal compromise.
The huge number of best-possible compromises requires: 1) efficient algorithms to approximate the Pareto front and 2) support tools for systematic interactive decision-making. Examples of these will be discussed and practical aspects relating to the use of these algorithms and tools will be elucidated. The feasibility of using Pareto fronts to quantitatively compare treatment plans between different treatment planning systems and treatment techniques has recently been described and will be addressed in this lecture.