Aspiration Level Methods in Interactive Multi-objecitve Programming and Their Engineering Applications

Prof. Hirotaka Nakayama, Konan University, Japan

One of the most important tasks in multi-objective optimization is "trade-off analysis" which aims to make the total balance among objective functions. The trade-off relation among alternatives can be shown as Pareto frontier. In cases with two or three objective functions, the set of Pareto optimal solutions in the objective function space (i.e., Pareto frontier) can be depicted relatively easily. Seeing Pareto frontiers, we can grasp the trade-off relation among objectives totally. Therefore, it would be the best way to depict Pareto frontiers in cases with two or three objectives. (It might be difficult to read the trade-off relation among objectives with three dimension, though). In cases with more than three objectives, however, it is impossible to depict Pareto frontier. There are some cases with a large number (e.g., a few hundreds) of objective functions in engineering applications such as erection management of cable stayed bridges and optical lens design. Under this circumstance, interactive methods can help decision makers (DMs) to make local trade-off analysis through interaction of DMs and computers by showing a Pareto solution nearest to their desire. Along this line, aspiration level methods were developed, and have been observed to be effective in many practical problems in various fields. Satisficing Trade-off Method proposed by the author is one of aspiration level methods, and has several devices for making trade-off analysis easily, i.e., automatic trade-off and exact trade-off. This paper discusses those methods for multi-objective optimization, in particular, from a viewpoint of engineering application.

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Improving the efficacy of multi-objective evolutionary algorithms for real-world applications

Dr. Kay Chen Tan, National University of Singapore

Multi-objective evolutionary algorithms (MOEAs) are a class of stochastic optimization techniques that simulate biological evolution to solve problems with multiple objectives. Multi-objective (MO) optimization is a challenging research topic because it involves the simultaneous optimization of several (and normally conflicting) objectives in the Pareto optimal sense. It requires researchers to address many issues that are unique to MO problems, such as fitness assignment, diversity preservation, balance between exploration and exploitation, elitism and archiving. In this talk, a few advanced features for handling large and computationally intensive real-world MO optimization problems will be presented. These include a distributed cooperative coevolutionary approach to handle large-scale problems via a divide-and-conquer strategy by harnessing technological advancements in parallel and distributed systems and a hybridization scheme with local search heuristics for combinatorial optimization with domain knowledge. The talk will also discuss the application of these techniques to various engineering problems including scheduling and system design, which often involve different competing specifications in a large and highly constrained search space.

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Decision Making in Evolutionary Optimization

Dr. Carlos M. Fonseca, Universidade do Algarve, Portugal

Current evolutionary multiobjective optimization (EMO) approaches tend to emphasize the approximation of the Pareto-optimal front as a whole, thereby dissociating the optimization process from the selection of the final compromise solution by a decision maker. This has the advantage of removing subjective preference information from the optimization problem formulation, but it also makes the resulting problem computationally more demanding. In order to concentrate the search effort on the regions of potential interest to the decision maker, techniques for the progressive articulation of preferences in EMO have been proposed, casting EMO as the interaction between an evolutionary search mechanism and a decision maker. It is worth noting that even the promotion of diversity across the Pareto-optimal front, which is generally regarded as an optimizer design issue, may be successfully addressed by the decision maker within this framework, as it has been proposed recently by others.

Regarding the evolutionary search mechanism, the main question at each iteration consists of determining the next candidate solution(s) to be evaluated, given the information acquired since the beginning of the run. This may be seen as another decision-making problem, but one with (very) incomplete attribute information, since objective values are generally not known for most potential alternatives. Alternatively, it may be seen as a control problem, where actions (new solutions) are to be selected based on the feedback provided by the decision maker. Either way, some model, however weak, of the underlying optimization problem must be assumed.

In this talk, both the evaluation of current solutions and the generation of new candidate solutions in EMO will be discussed from a decision making perspective. From the discussion, opportunities for incorporating more explicit decision making in EMO will be identified.

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MOEAs in the Design of Network Centric Systems

Prof. Gary B. Lamont, Air Force Institute of Technology, USA

Advances in information and communications technology are changing network design techniques quantitatively and qualitatively. This technology is supporting the design of large scale network centric systems which are required in many contemporary real-world situations. These high-level robust centric systems by definition must provide improved information sharing and collaboration between network entities. Such systems enhance the quality of information awareness, improving sustainability, and mission effectiveness and efficiency. The hierarchical development of network centric systems includes all dynamic information elements and is applied so as to maximize the desired decision and action impact. Associated network information flow problems can have as objectives costs, delays, robustness, vulnerability, and reliability with related constraints of network flow capacities, rates, and quantities of information. The optimization of coupled complex capacitated network flow problems is therefore an integral and basic element of network centric systems design. Thus, the focus of the discussion is on the efficacy of multiobjective evolutionary algorithms (MOEAs) to solve effectively and efficiency variations of associated network flow problems, given sophisticated mathematical models. Also to be addressed are dynamic network environments where various information channels become non-available, change their characteristics, or information priorities are modified. Discrimination between possible MOEA operators (recombination, mutation, selection) and associated MOEA parameter values is discussed as related to solving effectively variations of multiobjective network centric information flow problems including real-time behavior. Example network flow applications provide insight to choosing appropriate MOEA characteristics. Included is a discussion of opportunities for future MOEA research in this arena.

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