Luigi Barone

A review of multiobjective test problems and a scalable test problem toolkit

When attempting to better understand the strengths and weaknesses of an algorithm, it is important to have a strong understanding of the problem at hand. This is true for the field of multiobjective evolutionary algorithms (EAs) as it is for any other field. Many of the multiobjective test problems employed in the EA literature have not been rigorously analyzed, which makes it difficult to draw accurate conclusions about the strengths and weaknesses of the algorithms tested on them. In this paper, we systematically review and analyze many problems from the EA literature, each belonging to the important class of real-valued, unconstrained, multiobjective test problems. To support this, we first introduce a set of test problem criteria, which are in turn supported by a set of definitions. Our analysis of test problems highlights a number of areas requiring attention. Not only are many test problems poorly constructed but also the important class of nonseparable problems, particularly nonseparable multimodal problems, is poorly represented. Motivated by these findings, we present a flexible toolkit for constructing well-designed test problems. We also present empirical results demonstrating how the toolkit can be used to test an optimizer in ways that existing test suites do not

A faster algorithm for calculating hypervolume

We present an algorithm for calculating hypervolume exactly, the Hypervolume by Slicing Objectives (HSO) algorithm, that is faster than any that has previously been published. HSO processes objectives instead of points, an idea that has been considered before but that has never been properly evaluated in the literature. We show that both previously studied exact hypervolume algorithms are exponential in at least the number of objectives and that although HSO is also exponential in the number of objectives in the worst case, it runs in significantly less time, i.e., two to three orders of magnitude less for randomly generated and benchmark data in three to eight objectives. Thus, HSO increases the utility of hypervolume, both as a metric for general optimization algorithms and as a diversity mechanism for evolutionary algorithms.

A scalable multi-objective test problem toolkit

This paper presents a new toolkit for creating scalable multi-objective test problems. The WFG Toolkit is flexible, allowing characteristics such as bias, multi-modality, and non-separability to be incorporated and combined as desired. A wide variety of Pareto optimal geometries are also supported, including convex, concave, mixed convex/concave, linear, degenerate, and disconnected geometries. All problems created by the WFG Toolkit are well defined, are scalable with respect to both the number of objectives and the number of parameters, and have known Pareto optimal sets. Nine benchmark multi-objective problems are suggested, including one that is both multi-modal and non-separable, an important combination of characteristics that is lacking among existing (scalable) multi-objective problems.

A Fast Way of Calculating Exact Hypervolumes

We describe a new algorithm WFG for calculating hypervolume exactly. WFG is based on the recently-described observation that the exclusive hypervolume of a point p relative to a set S is equal to the difference between the inclusive hypervolume of p and the hypervolume of S with each point limited by the objective values in p. WFG applies this technique iteratively over a set to calculate its hypervolume. Experiments show that WFG is substantially faster (in five or more objectives) than all previously-described algorithms that calculate hypervolume exactly.

A Fast Incremental Hypervolume Algorithm

When hypervolume is used as part of the selection or archiving process in a multiobjective evolutionary algorithm, it is necessary to determine which solutions contribute the least hypervolume to a front. Little focus has been placed on algorithms that quickly determine these solutions and there are no fast algorithms designed specifically for this purpose. We describe an algorithm, IHSO, that quickly determines a solutions contribution. Furthermore, we describe and analyse heuristics that reorder objectives to minimize the work required for IHSO to calculate a solutions contribution. Lastly, we describe and analyze search techniques that reduce the amount of work required for solutions other than the least contributing one. Combined, these techniques allow multiobjective evolutionary algorithms to calculate hypervolume inline in increasingly complex and large fronts in many objectives.

An evolution strategy with probabilistic mutation for multi-objective optimisation

Evolutionary algorithms have been applied with great success to the difficult field of multiobjective optimisation. Nevertheless, the need for improvements in this field is still strong. We present a new evolutionary algorithm, ESP (the Evolution Strategy with Probabilistic mutation). ESP extends traditional evolution strategies in two principal ways: it applies mutation probabilistically in a GA-like fashion, and it uses a new hyper-volume based, parameterless, scaling independent measure for resolving ties during the selection process. ESP outperforms the state-of-the-art algorithms on a suite of benchmark multiobjective test functions using a range of popular metrics.

Heuristics for optimizing the calculation of hypervolume for multi-objective optimization problems

The fastest known algorithm for calculating the hypervolume of a set of solutions to a multi-objective optimization problem is the HSO algorithm (hypervolume by slicing objectives). However, the performance of HSO for a given front varies a lot depending on the order in which it processes the objectives in that front. We present and evaluate two alternative heuristics that each attempt to identify a good order for processing the objectives of a given front. We show that both heuristics make a substantial difference to the performance of HSO for randomly-generated and benchmark data in 5-9 objectives, and that they both enable HSO to reliably avoid the worst-case performance for those fronts. The enhanced HSO enable the use of hypervolume with larger populations in more objectives.

An adaptive learning model for simplified poker using evolutionary algorithms

Evolution is the process of adapting to a potentially dynamic environment. By utilising the implicit learning characteristic of evolution in our algorithms, we can create computer programs that learn, and evolve, in uncertain environments. We propose to use evolutionary algorithms to learn to play games of imperfect information-in particular, the game of poker. We describe a new adaptive learning model using evolutionary algorithms that is suitable for designing adaptive computer poker players. We identify several important principles of poker play and use these as the basis for a hypercube of evolving populations in our model. We report experiments using this model to learn a simplified version of poker; results indicate that our new approach demonstrates emergent adaptive behaviour in evolving computer poker players. In particular, we show that our evolving poker players develop different techniques to counteract the variety of strategies employed by their opponents in order to maximise winnings. We compare the strategies evolved by our evolved poker players with a competent static player to demonstrate the importance of adaptation to achieve this end. Comparison with our existing evolutionary poker model highlights the improved performance of this approach.

Nature-Inspired Techniques in the Context of Fraud Detection

Electronic fraud is highly lucrative, with estimates suggesting these crimes to be worth millions of dollars annually. Because of its complex nature, electronic fraud detection is typically impractical to solve without automation. However, the creation of automated systems to detect fraud is very difficult as adversaries readily adapt and change their fraudulent activities which are often lost in the magnitude of legitimate transactions. This study reviews the most popular types of electronic fraud and the existing nature-inspired detection methods that are used for them. The common characteristics of electronic fraud are examined in detail along with the difficulties and challenges that these present to computational intelligence systems. Finally, open questions and opportunities for further work, including a discussion of emerging types of electronic fraud, are presented to provide a context for ongoing research.

Maximising Hypervolume for Selection in Multi-objective Evolutionary Algorithms

When hypervolume is used as part of the selection or archiving process in a multi-objective evolutionary algorithm, the basic requirement is to choose a subset of the solutions in a non-dominated front such that the hypervolume of the subset is maximised. We describe and evaluate two algorithms to approximate this process: a greedy algorithm that assesses and eliminates solutions individually, and a local search algorithm that assesses entire subsets. We present empirical data which suggests that a hybrid approach is needed to get the best tradeoff between good results and computational cost.