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Automatic Component-Wise Design of Multi-Objective Evolutionary Algorithms Leonardo C

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Automatic Component-Wise Design of Multi-Objective Evolutionary Algorithms Leonardo C FINAL DRAFT ACCEPTED FOR IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 1 Automatic Component-wise Design of Multi-objective Evolutionary Algorithms Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle Abstract—Multi-objective evolutionary algorithms are typi- newly devised. Examples are the fitness and diversity compo- cally proposed, studied and applied as monolithic blocks with nents that appear in many MOEAs [11, 14]. This component- a few numerical parameters that need to be set. Few works have wise view has two main benefits. First, it allows algorithm studied how the algorithmic components of these evolutionary algorithms can be classified and combined to produce new algo- designers to identify the various options available for each rithmic designs. The motivation for studies of this latter type stem algorithmic component and whether a particular combination from the development of flexible software frameworks and the of components, i.e., an algorithm “design”, has already been usage of automatic algorithm configuration methods to find novel proposed. Second, it allows algorithm users to adapt the design algorithm designs. In this paper, we propose a multi-objective of MOEAs to their particular application scenario. evolutionary algorithm template and a new conceptual view of its components that surpasses existing frameworks in both the num- One motivation for this component-wise view of MOEAs ber of algorithms that can be instantiated from the template and is the development of software frameworks that help prac- the flexibility to produce novel algorithmic designs. We empiri- titioners apply and adapt MOEAs to their own application cally demonstrate the flexibility of our proposed framework by scenarios. Unfortunately, the design of most MOEA frame- automatically designing multi-objective evolutionary algorithms works focuses on applying existing MOEAs to new scenarios, for continuous and combinatorial optimization problems. The automatically designed algorithms are often able to outperform rather than on flexibly combining their components to produce six traditional multi-objective evolutionary algorithms from the new designs [15–17]. Even MOEA frameworks that allow literature, even after tuning their numerical parameters. the combination of algorithmic components from different Index Terms—Multiobjective optimization, evolutionary al- MOEAs [14] are limited to MOEAs that are structurally gorithms, permutation flowshop problem, automatic algorithm similar, for example, based on the traditional fitness and configuration. diversity components. More recent MOEAs that differ from this template, such as HypE [5] and SMS-EMOA [6], cannot be instantiated from algorithmic components through such I. INTRODUCTION frameworks. We see two reasons behind this lack of flexibility. ULTI-OBJECTIVE evolutionary algorithms (MOEAs) First, the analysis of MOEA components has relied on how the M are a central research topic in evolutionary computation algorithms were described by their original authors, and only as evidenced by the number of different proposals in the few works try to generalize functionally equivalent concepts literature [1–8]. The traditional study of MOEAs considers of MOEAs into broader concepts [11, 14, 18, 19]. Second, a these algorithms as monolithic units [9, 10] and only few arti- high degree of flexibility in a software framework may be cles have considered the contribution of individual algorithmic deemed undesired, since some configurations may produce components of MOEAs to performance [11–13]. These latter unreasonable algorithm designs or the number of possible empirical studies indicate that (i) performance improvements configurations may be too large for human designers. may be achieved by replacing the algorithmic components In this paper, we propose a new conceptual view of MOEA of well-established MOEAs by alternative options from other components that allows instantiating, from the same algorith- MOEAs and that (ii) the benefits of such changes become mic template, a larger number of MOEAs from the literature more important when applying MOEAs to scenarios different than existing MOEA frameworks. For example, we are able to from those for which they were originally designed. instantiate at least six well-known MOEAs from the literature: The component-wise view of MOEAs consists in identifying MOGA [1], NSGA-II [2], SPEA2 [3], IBEA [4], HypE [5], individual algorithmic components in different MOEAs that and SMS-EMOA [6]. More importantly, our framework allows have the same function and, thus, could be replaced by to produce a large number of novel MOEA designs that are, alternative procedures taken either from different MOEAs or in principle, reasonable from a human designer point of view. This is achieved by reformulating the traditional distinction L. C. T. Bezerra, M. López-Ibáñez, and T. Stützle are with the IRIDIA between fitness and diversity components [11, 14] as pref- laboratory at CoDE, Université Libre de Bruxelles, 1050, Belgium. erences composed by set-partitioning, quality and diversity email: {lteonaci,manuel.lopez-ibanez,stuetzle}@ulb.ac.be metrics [19]. In addition, different preferences may be used for This is the final draft version accepted by IEEE Transactions on Evolutionary Computation on 14 August, 2015. DOI: 10.1109/TEVC.2015.2474158 mating and environmental selection. Our proposal also formal- This research has received funding from the COMEX project (P7/36) within izes the distinction between internal and external populations the Interuniversity Attraction Poles Programme of the Belgian Science Policy and archives, which allows us to describe, using alternative Office. L. C. T. Bezerra, M. López-Ibáñez, and T. Stützle acknowledge support from the Belgian F.R.S.-FNRS, of which they are a FRIA fellow, a post- options for the same components, algorithms as different as doctoral researcher, and a senior research associate, respectively. SPEA2 and SMS-EMOA. Our proposal is implemented in a 2 FINAL DRAFT ACCEPTED FOR IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION software framework from which novel MOEA designs can be Algorithm 1 AutoMOEA template proposed in this work. instantiated by properly selecting the values of the various 1: pop Initialization () 2: if type (pop ) != none algorithmic components and numerical parameters. ext 3: popext pop Following previous work on automatic design [20], we 4: repeat apply an offline automatic configuration method, irace [21], to 5: pool BuildMatingPool (pop) our proposed framework, considering the various algorithmic 6: popnew Variation (pool) 7: popnew Evaluation (popnew) components as categorical parameters to be set. In this sense, 8: pop Replacement (pop, popnew) the configuration space searched by irace is actually a design 9: if type (popext) = bounded then space, where different MOEA components can be combined 10: popext ReplacementExt (popext, popnew) 11: else if type (popext) = unbounded then to generate unique and possibly novel MOEA designs. 12: popext popext [ pop We automatically design several MOEAs, called here Auto- 13: until termination criteria met MOEAs, for several application scenarios. Our scenarios were 14: if type (popext) = none 15: return pop selected to provide insights on several questions about MOEA 16: else design. The first question is whether the benchmark that guides 17: return popext the design process has a strong influence in the performance of the resulting design. Thus, we consider continuous optimiza- tion problems, in particular, two benchmark sets, DTLZ [10] functionally-equivalent algorithmic components and describes and WFG [22], with two, three, and five objectives, since the available design choices. A final objective is to investigate MOEAs have been primarily designed for these problems. Our which design choices (instead of which monolithic MOEAs) results indicate that the best MOEA design depends strongly are more appropriate for the various scenarios described above. on which benchmark is used for the automatic design. The remainder of this paper is structured as follows. A second question in MOEA design is the trade-off between SectionII presents in detail our component-wise MOEA computationally expensive components and the quality of the framework. We present empirical results and discussion for results. Thus, we consider two different stopping criteria for continuous and combinatorial problems in Sections III andIV, the MOEAs: maximum number of function evaluations (FEs) respectively, and conclude in SectionV. and maximum runtime. By using these two setups, we are able to represent problems with computationally demanding func- II. A TEMPLATE FOR DESIGNING MOEAS tion evaluations as well as problems where the computational The AutoMOEA template we propose for instantiating and overhead of MOEA components is relevant. Although the designing MOEAs is shown in Algorithm1. As we will former is the typical setup considered in the MOEA literature, explain below, from this template we can not only instantiate the conclusions obtained may not apply to the latter setup. This many well-known MOEAs, but also many new ones that is demonstrated by the fact that the AutoMOEAs produced have never been explored so far. The proposed template is for each setup show remarkable differences. In most cases, based on the view that MOEAs can be seen as extensions of for both setups, the AutoMOEAs are able to match, and often traditional single-objective EAs such as genetic algorithms [1– significantly surpass, the results obtained
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