Catálogo de publicaciones - libros

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.

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.

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.

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.

This work proposes a method to control the dominance area of solutions in order to induce appropriate ranking of solutions for the problem at hand, enhance selection, and improve the performance of MOEAs on combinatorial optimization problems. The proposed method can control the degree of expansion or contraction of the dominance area of solutions using a user-defined parameter . Modifying the dominance area of solutions changes their dominance relation inducing a ranking of solutions that is different to conventional dominance. In this work we use 0/1 multiobjective knapsack problems to analyze the effects on solutions ranking caused by contracting and expanding the dominance area of solutions and its impact on the search performance of a multi-objective optimizer when the number of objectives, the size of the search space, and the complexity of the problems vary. We show that either convergence or diversity can be emphasized by contracting or expanding the dominance area. Also, we show that the optimal value of the area of dominance depends strongly on all factors analyzed here: number of objectives, size of the search space, and complexity of the problems.

In this paper, we propose a new conceptual method for the design, investigation, and evaluation of multi-objective variation operators for evolutionary multi-objective algorithms. To this end, we apply a modified predator-prey model that allows an independent analysis of different operators. Using this model problem specific operators can be combined to more complex operators. Additionally, we review the simplex recombination, a new rotation-independent recombination scheme, and examine its impact concerning our design method. We show exemplarily as a first attempt the advantageous combination of several standard variation operators that lead to better results for selected test functions.

Recent works in evolutionary multiobjective optimization suggest to shift the focus from solely evaluating optimization success in the objective space to also taking the decision space into account. They indicate that this may be a) necessary to express the users requirements of obtaining distinct solutions (distinct Pareto set parts or subsets) of similar quality (comparable locations on the Pareto front) in real-world applications, and b) a demanding task for the currently most commonly used algorithms. We investigate if standard EMOA are able to detect and preserve equivalent Pareto subsets and develop an own special purpose EMOA that meets these requirements reliably.

This paper proposes an idea of using evolutionary multiobjective optimization (EMO) to optimize scalarizing functions. We assume that a scalarizing function to be optimized has already been generated from an original multiobjective problem. Our task is to optimize the given scalarizing function. In order to efficiently search for its optimal solution without getting stuck in local optima, we generate a new multiobjective problem to which an EMO algorithm is applied. The point is to specify multiple objectives, which are similar to but different from the scalarizing function, so that the location of the optimal solution is near the center of the Pareto front of the generated multiobjective problem. The use of EMO algorithms helps escape from local optima. It also helps find a number of alternative solutions around the optimal solution. Difficulties of Pareto ranking-based EMO algorithms in the handling of many objectives are avoided by the use of similar objectives. In this paper, we first demonstrate that the performance of EMO algorithms as single-objective optimizers of scalarizing functions highly depends on the choice of multiple objectives. Based on this observation, we propose a specification method of multiple objectives for the optimization of a weighted sum fitness function. Experimental results show that our approach works very well in the search for not only a single optimal solution but also a number of good alternative solutions around the optimal solution. Next we evaluate the performance of our approach in comparison with a hybrid EMO algorithm where a single-objective fitness evaluation scheme is probabilistically used in an EMO algorithm. Then we show that our approach can be also used to optimize other scalarizing functions (e.g., those based on constraint conditions and reference solutions). Finally we show that our approach is applicable not only to scalarizing functions but also other single-objective optimization problems.

Uncertainties in design variables and problem parameters are inevitable and must be considered in an optimization task including multi-objective optimization, if reliable optimal solutions are to be found. Sampling techniques become computationally expensive if a large reliability is desired. In this paper, first we present a brief review of statistical reliability-based optimization procedures. Thereafter, for the first time, we extend and apply multi-objective evolutionary algorithms for solving two different reliability-based optimization problems for which evolutionary approaches have a clear niche in finding a set of reliable, instead of optimal, solutions. The use of an additional objective of maximizing the reliability index in a multi-objective evolutionary optimization procedure allows a number of trade-off solutions to be found, thereby allowing the designers to find solutions corresponding to different reliability requirements. Next, the concept of single-objective reliability-based optimization is extended to multi-objective optimization of finding a reliable frontier, instead of an optimal frontier. These optimization tasks are illustrated by solving test problems and a well-studied engineering design problem. The results should encourage the use of evolutionary optimization methods to more such reliability-based optimization problems.

Spatially structured populations have been used in evolutionary computation for many years. Somewhat surprisingly, in the multiobjective optimization domain, very few spatial models have been proposed. In this paper, we introduce a new multiobjective evolutionary algorithm on complex networks. Here, the individuals in the evolving population are mapped onto the nodes of alternative complex networks – regular, small-world, scale-free and random. A selection regime based on a non-dominance rating and a crowding mechanism guides the evolutionary trajectory. Our model can be seen as an extension of the standard cellular evolutionary algorithm. However, the dynamical behaviour of the evolving population is constrained by the particular network architecture. An important contribution of this paper is the detailed analysis of the impact that the structural properties of the network – node degree distribution, characteristic path length and clustering coefficient – have on the behaviour of the evolutionary algorithm using benchmark bi-objective problems.