Learning in Multiobjective Optimization (Dagstuhl Seminar 12041)}}

Natural Computing, 2018

In almost no other field of computer science, the idea of using bio-inspired search paradigms has been so useful as in solving multiobjective optimization problems. The idea of using a population of search agents that collectively approximate the Pareto front resonates well with processes in natural evolution, immune systems, and swarm intelligence. Methods such as NSGA-II, SPEA2, SMS-EMOA, MOPSO, and MOEA/D became standard solvers when it comes to solving multiobjective optimization problems. This tutorial will review some of the most important fundamentals in multiobjective optimization and then introduce representative algorithms, illustrate their working principles, and discuss their application scope. In addition, the tutorial will discuss statistical performance assessment. Finally, it highlights recent important trends and closely related research fields. The tutorial is intended for readers, who want to acquire basic knowledge on the mathematical foundations of multiobjective optimization and state-of-the-art methods in evolutionary multiobjective optimization. The aim is to provide a starting point for researching in this active area, and it should also help the advanced reader to identify open research topics.

Complex & Intelligent Systems, 2019

Evolutionary multiobjective optimization has been a research area since the mid-1980s, and has experienced a very significant activity in the last 20 years. However, and in spite of the maturity of this field, there are still several important challenges lying ahead. This paper provides a short description of some of them, with a particular focus on open research areas, rather than on specific research topics or problems. The main aim of this paper is to motivate researchers and students to develop research in these areas, as this will contribute to maintaining this discipline active during the next few years.

Proceedings of the 9th annual conference on Genetic and evolutionary computation - GECCO '07, 2007

The research area of evolutionary multiobjective optimization (EMO) is reaching better understandings of the properties and capabilities of EMO algorithms, and accumulating much evidence of their worth in practical scenarios. An urgent emerging issue is that the favoured EMO algorithms scale poorly when problems have 'many' (e.g. five or more) objectives. One of the chief reasons for this is believed to be that, in many-objective EMO search, populations are likely to be largely composed of nondominated solutions. In turn, this means that the commonly-used algorithms cannot distinguish between these for selective purposes. However, there are methods that can be used validly to rank points in a nondominated set, and may therefore usefully underpin selection in EMO search. Here we discuss and compare several such methods. Our main finding is that simple variants of the often-overlooked 'Average Ranking' strategy usually outperform other methods tested, covering problems with 5-20 objectives and differing amounts of inter-objective correlation.

Advanced Information and Knowledge Processing, 2005

In this chapter we present a brief analysis of the current research performed on evolutionary multiobjective optimization. After analyzing first and second generation multiobjective evolutionary algorithms, we address two important issues: the role of elitism in evolutionary multiobjective optimization and the way in which concepts from multiobjective optimization can be applied to constraint-handling techniques. We conclude with a discussion of some of the most promising research trends in the years to come.

Evolutionary Computation, 2000

In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Pareto-optimal front (e.g., multimodality and deception). By investigating these different problem features separately, it is possible to predict the kind of problems to which a certain technique is or is not well suited. However, in contrast to what was suspected beforehand, the experimental results indicate a hierarchy of the algorithms under consideration. Furthermore, the emerging effects are evidence that the suggested test functions provide sufficient complexity to compare multiobjective optimizers. Finally, elitism is shown to be an important factor for improving evolutionary multiobjective search.

Lecture Notes in Computer Science, 2001

2005

In this paper, we demonstrate advantages and disadvantages of an evolutionary multiobjective optimization (EMO) approach in comparison with a reference solution-based single-objective approach through computational experiments on multiobjective 0/1 knapsack problems. The main characteristic feature of the EMO approach is that no a priori information about the decision maker's preference is assumed. The EMO approach tries to find well-distributed trade-off solutions with a wide range of objective values as many as possible. A final solution is supposed to be chosen from the obtained trade-off solutions by the decision maker. On the other hand, the reference solution-based approach utilizes the information about the decision maker's preference in the form of a reference solution. We examine whether the EMO approach can find good trade-off solutions close to an arbitrarily given reference solution. Experimental results show that good solutions are not always obtained by the EMO approach. We also examine where the reference solution-based approach can find many trade-off solutions around the given reference solution. Experimental results show that many trade-off solutions can not be obtained even when an archive population of non-dominated solutions is stored in the reference solution-based approach. Based on these observations, we suggest a hybrid approach.

2001

The paper describes a new preference method and its use in multiobjective optimization. These preferences are developed with a goal to reduce the cognitive overload associated with the relative importance of a certain criterion within a multiobjective design environment involving large numbers of objectives. Their successful integration with several genetic-algorithm-based design search and optimization techniques (weighted sums, weighted Pareto, weighted coevolutionary methods, and weighted scenarios) are described and theoretical results relating to complexity and sensitivity of the algorithm are presented and discussed. Its usefulness has been demonstrated in a real-world project of conceptual airframe design (a joint project with British Aerospace Systems).

International Journal of Bio-Inspired Computation, 2019

Research in the field of multi-objective optimisation problem (MOP) has garnered ample interest in the last two decades. Majority of methods developed for solving the problem belong to the class of evolutionary algorithms (EA) which are population-based evolution search strategies involving exploration and exploitation in general. Multi-criteria decision making (MCDM) is another aspect of MOP which involves finding methods to help a decision maker (DM) in making most optimal decisions in a conflicting scenario. In this paper, we present a brief review of the methods and techniques developed in the last 15 years which try to solve the MOP and MCDM problems. The strengths and weaknesses of methods have been discussed to present a holistic view. This paper covers challenges associated with MOEAs, different solution approaches such as Pareto-based methods and non-Pareto methods, indicator-based methods, aggregation methods, decomposition-based methods, methods using reference sets, MOEAs involving DM, a priori, interactive and a posteriori preference incorporation methods. It also discusses most of the quality metrics and performance indicators proposed in the literature along with benchmark problems. In addition, some future research issues and directions are also presented.

IEEE Transactions on Evolutionary Computation, 2010

This paper describes the use of decision maker preferences in terms of the relative importance of objectives in evolutionary multiobjective optimization. A mathematical model of the relative importance of objectives and an elicitation algorithm are proposed, and three methods of incorporating explicated preference information are described and applied to standard test problems in an empirical study. The axiomatic model proposed here formalizes the notion of relative importance of objectives as a partial order that supports strict preference, equality of importance, and incomparability between objective pairs. Unlike most approaches, the proposed model does not encode relative importance as a set of real-valued parameters. Instead, the approach provides a functional correspondence between a coherent overall preference with a subset of the Pareto-optimal front. An elicitation algorithm is also provided to assist a human decision maker in constructing a coherent overall preference. Besides elicitation of a priori preference, an interactive facility is also furnished to enable modification of overall preference while the search progresses. Three techniques of integrating explicated preference information into the wellknown Non-dominated Sorting Genetic Algorithm (NSGA)-II are also described and validated in a set of empirical investigation. The approach allows a focus on a subset of the Pareto-front. Validations on test problems demonstrate that the preferencebased algorithm gained better convergence as the dimensionality of the problems increased.