LCS & GBML Central

This article concerns the study of mixed Pareto-lexicographic multiobjective optimization problems where the objectives must be partitioned in multiple priority levels (PLs). A PL is a group of objectives having the same importance in terms of optimization and subsequent decision making, while between PLs a lexicographic ordering exists. A naive approach would be to define a multilevel dominance relationship and apply a standard EMO/EMaO algorithm, but the concept does not conform to a stable optimization process as the resulting dominance relationship violates the transitive property needed to achieve consistent comparisons. To overcome this, we present a novel approach that merges a custom nondominance relation with the Grossone methodology, a mathematical framework to handle infinite and infinitesimal quantities. The proposed method is implemented on a popular multiobjective optimization algorithm (NSGA-II), deriving a generalization of it called by us PL-NSGA-II. We also demonstrate the usability of our strategy by quantitatively comparing the results obtained by PL-NSGA-II against other priority and nonpriority-based approaches. Among the test cases, we include two real-world applications: one 10-objective aircraft design problem and one 3-objective crash safety vehicle design task. The obtained results show that PL-NSGA-II is more suited to solve lexicographical many-objective problems than the general purpose EMaO algorithms.

Various studies have shown that immune system-inspired hypermutation operators can allow artificial immune systems (AIS) to be very efficient at escaping local optima of multimodal optimization problems. However, this efficiency comes at the expense of considerably slower runtimes during the exploitation phase compared to the standard evolutionary algorithms. We propose modifications to the traditional hypermutations with mutation potential (HMP) that allow them to be efficient at exploitation, as well as maintaining their effective explorative characteristics. Rather than deterministically evaluating fitness after each bit-flip of a hypermutation, we sample the fitness function stochastically with a “parabolic” distribution. This allows the stop at the first constructive mutation (FCM) variant of HMP to reduce the linear amount of wasted function evaluations when no improvement is found to a constant. The stochastic distribution also allows the removal of the FCM mechanism altogether as originally desired in the design of the HMP operators. We rigorously prove the effectiveness of the proposed operators for all the benchmark functions, where the performance of HMP is rigorously understood in the literature. We validate the gained insights to show linear speed-ups for the identification of high-quality approximate solutions to classical NP-Hard problems from combinatorial optimization. We then show the superiority of the HMP operators to the traditional ones in an analysis of the complete standard Opt-IA AIS, where the stochastic evaluation scheme allows HMP and aging operators to work in harmony. Through a comparative performance study of other “fast mutation” operators from the literature, we conclude that a power-law distribution for the parabolic evaluation scheme is the best compromise in black-box scenarios, where little problem knowledge is available.

Generative adversarial networks (GANs) have been a popular deep generative model for real-world applications. Despite many recent efforts on GANs that have been contributed, mode collapse and instability of GANs are still open problems caused by their adversarial optimization difficulties. In this article, motivated by the cooperative co-evolutionary algorithm, we propose a cooperative dual evolution-based GAN (CDE-GAN) to circumvent these drawbacks. In essence, CDE-GAN incorporates dual evolution with respect to the generator(s) and discriminators into a unified evolutionary adversarial framework to conduct effective adversarial multiobjective optimization. Thus, it exploits the complementary properties and injects dual mutation diversity into the training, to steadily diversify the estimated density in capturing multimodes and improve generative performance. Specifically, CDE-GAN decomposes the complex adversarial optimization problem into two subproblems (generation and discrimination), and each subproblem is solved with a separated subpopulation (E-Generators and E-Discriminators), evolved by its own evolutionary algorithm. Additionally, we further propose a Soft Mechanism to balance the tradeoff between E-Generators and E-Discriminators to conduct steady training for CDE-GAN. Extensive experiments on one synthetic dataset and three real-world benchmark image datasets demonstrate that the proposed CDE-GAN achieves a competitive and superior performance in generating good quality and diverse samples over baselines. The code and more generated results are available at our project homepage https://shiming-chen.github.io/CDE-GAN-website/CDE-GAN.html.

The third issue of Volume 22 of Genetic Programming and Evolvable Machines is now available for download.

It contains:

Feature extraction by grammatical evolution for one-class time series classification
by Stefano Mauceri, James Sweeney, Miguel Nicolau, James McDermott

Genetic programming-based regression for temporal data
by Cry Kuranga, Nelishia Pillay

Tag-based regulation of modules in genetic programming improves context-dependent problem solving
by Alexander Lalejini, Matthew Andres Moreno, Charles Ofria

LETTER
Symbolic-regression boosting
by Moshe Sipper, Jason H. Moore

SOFTWARE REVIEW
Software review: Pony GE2
by Tuong Manh Vu

BOOK REVIEW
Introducing Design Automation for Quantum Computing, Alwin Zulehner and Robert Wille. ISBN 978-3-030-41753-6, 2020, Springer International Publishing. 222 Pages, 51 b/w illustrations, 14 illustrations in colour
by Robin Harper

2021 Humies Winners

Evolutionary algorithms via decomposition, namely, DEAs, decompose the original challenging problem and evolve a number of subproblems/subspaces concurrently in a cooperative fashion. Adaptive computational resource allocation (CRA) strategy is able to identify the efficiency of different subspaces and invest search effort on them accordingly in an online manner. A crucial issue for CRA is to measure the efficiency of subspaces. Unfortunately, existing approaches for efficiency measurement are either fitness improvement oriented or contribution oriented, which struggle to capture the potentials of subspaces accurately. To mitigate such drawback, we present an ensemble method for CRA, based on the recent fitness contribution rates (FCRs) and fitness improvement rates (FIRs) of subspaces simultaneously. In order to dynamically track the potential of each subregion, we adopt two memory matrices to record FIR and FCR for multiple subspaces over recent generations, respectively. Afterward, an aptitude vector indicating the potentials of subspaces is defined by exploiting FCR and FIR with memory and decaying scheme. On the basis of above strategies, an ensemble CRA (ECRA) scheme is designed, which is then embedded into an adaptive objective space partition-based DEA, termed ECRA-DEA, for solving the multi/many-objective optimization. Extensive experimental studies for ECRA-DEA on various types of challenging problems have been carried out and the results confirm that ECRA is effective. Besides, the competence of ECRA-DEA is empirically validated in comparison with state-of-the-art designs. The proposed ECRA paves a new way to leverage the capability of DEAs on handling complex problems.

Many real-world optimization problems are dynamic. The field of dynamic optimization deals with such problems where the search space changes over time. In this two-part article, we present a comprehensive survey of the research in evolutionary dynamic optimization for single-objective unconstrained continuous problems over the last two decades. In Part A of this survey, we propose a new taxonomy for the components of dynamic optimization algorithms (DOAs), namely, convergence detection, change detection, explicit archiving, diversity control, and population division and management. In comparison to the existing taxonomies, the proposed taxonomy covers some additional important components, such as convergence detection and computational resource allocation. Moreover, we significantly expand and improve the classifications of diversity control and multipopulation methods, which are underrepresented in the existing taxonomies. We then provide detailed technical descriptions and analysis of different components according to the suggested taxonomy. Part B of this survey provides an in-depth analysis of the most commonly used benchmark problems, performance analysis methods, static optimization algorithms used as the optimization components in the DOAs, and dynamic real-world applications. Finally, several opportunities for future work are pointed out.