Borg: An Auto-Adaptive Many-Objective Evolutionary Computing Framework

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Abstract

This study introduces the Borg multi-objective evolutionary algorithm (MOEA) for many-objective, multimodal optimization. The Borg MOEA combines ε-dominance, a measure of convergence speed named ε-progress, randomized restarts, and auto-adaptive multioperator recombination into a unified optimization framework. A comparative study on 33 instances of 18 test problems from the DTLZ, WFG, and CEC 2009 test suites demonstrates Borg meets or exceeds six state of the art MOEAs on the majority of the tested problems. The performance for each test problem is evaluated using a 1,000 point Latin hypercube sampling of each algorithm's feasible parameterization space. The statistical performance of every sampled MOEA parameterization is evaluated using 50 replicate random seed trials. The Borg MOEA is not a single algorithm; instead it represents a class of algorithms whose operators are adaptively selected based on the problem. The adaptive discovery of key operators is of particular importance for benchmarking how variation operators enhance search for complex many-objective problems.

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Approximating the nondominated front using the Pareto Archived Evolution Strategy.

J. Knowles, D W Corne (2000)

We introduce a simple evolution scheme for multiobjective optimization problems, called the Pareto Archived Evolution Strategy (PAES). We argue that PAES may represent the simplest possible nontrivial algorithm capable of generating diverse solutions in the Pareto optimal set. The algorithm, in its simplest form, is a (1 + 1) evolution strategy employing local search but using a reference archive of previously found solutions in order to identify the approximate dominance ranking of the current and candidate solution vectors. (1 + 1)-PAES is intended to be a baseline approach against which more involved methods may be compared. It may also serve well in some real-world applications when local search seems superior to or competitive with population-based methods. We introduce (1 + lambda) and (mu + lambda) variants of PAES as extensions to the basic algorithm. Six variants of PAES are compared to variants of the Niched Pareto Genetic Algorithm and the Nondominated Sorting Genetic Algorithm over a diverse suite of six test functions. Results are analyzed and presented using techniques that reduce the attainment surfaces generated from several optimization runs into a set of univariate distributions. This allows standard statistical analysis to be carried out for comparative purposes. Our results provide strong evidence that PAES performs consistently well on a range of multiobjective optimization tasks.

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Combining convergence and diversity in evolutionary multiobjective optimization.

Marco Laumanns, Lothar Thiele, Kalyanmoy Deb … (2002)

Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to find a number of Pareto-optimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms can progress towards the Pareto-optimal set with a widely spread distribution of solutions. However, none of the multiobjective evolutionary algorithms (MOEAs) has a proof of convergence to the true Pareto-optimal solutions with a wide diversity among the solutions. In this paper, we discuss why a number of earlier MOEAs do not have such properties. Based on the concept of epsilon-dominance, new archiving strategies are proposed that overcome this fundamental problem and provably lead to MOEAs that have both the desired convergence and distribution properties. A number of modifications to the baseline algorithm are also suggested. The concept of epsilon-dominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.