Knee Point Identification Based on Trade-Off Utility

Knee points, characterised as their smallest trade-off loss at all objectives, are attractive to decision makers in multi-criterion decision-making. In contrast, other Pareto-optimal solutions are less attractive since a small improvement on one objective can lead to a significant degradation on at least one of the other objectives. In this paper, we propose a simple and effective knee point identification method based on trade-off utility, dubbed KPITU, to help decision makers identify knee points from a given set of trade-off solutions. The basic idea of KPITU is to sequentially validate whether a solution is a knee point or not by comparing its trade-off utility with others within its neighbourhood. In particular, a solution is a knee point if and only if it has the best trade-off utility among its neighbours. Moreover, we implement a GPU version of KPITU that carries out the knee point identification in a parallel manner. This GPU version reduces the worst-case complexity from quadratic to linear. To validate the effectiveness of KPITU, we compare its performance with five state-of-the-art knee point identification methods on 134 test problem instances. Empirical results fully demonstrate the outstanding performance of KPITU especially on problems with many local knee points. At the end, we further validate the usefulness of KPITU for guiding EMO algorithms to search for knee points on the fly during the evolutionary process.

A Novel CNet-assisted Evolutionary Level Repairer and Its Applications to Super Mario Bros

Applying latent variable evolution to game level design has become more and more popular as little human expert knowledge is required. However, defective levels with illegal patterns may be generated due to the violation of constraints for level design. A traditional way of repairing the defective levels is programming specific rule-based repairers to patch the flaw. However, programming these constraints is sometimes complex and not straightforward. An autonomous level repairer which is capable of learning the constraints is needed. In this paper, we propose a novel approach, CNet, to learn the probability distribution of tiles giving its surrounding tiles on a set of real levels, and then detect the illegal tiles in generated new levels. Then, an evolutionary repairer is designed to search for optimal replacement schemes equipped with a novel search space being constructed with the help of CNet and a novel heuristic function. The proposed approaches are proved to be effective in our case study of repairing GAN-generated and artificially destroyed levels of Super Mario Bros. game. Our CNet-assisted evolutionary repairer can also be easily applied to other games of which the levels can be represented by a matrix of objects or tiles.

Analysis of Evolutionary Algorithms on Fitness Function with Time-linkage Property

In real-world applications, many optimization problems have the time-linkage property, that is, the objective function value relies on the current solution as well as the historical solutions. Although the rigorous theoretical analysis on evolutionary algorithms has rapidly developed in recent two decades, it remains an open problem to theoretically understand the behaviors of evolutionary algorithms on time-linkage problems. This paper takes the first step to rigorously analyze evolutionary algorithms for time-linkage functions. Based on the basic OneMax function, we propose a time-linkage function where the first bit value of the last time step is integrated but has a different preference from the current first bit. We prove that with probability $1-o(1)$, randomized local search and $(1+1)$ EA cannot find the optimum, and with probability $1-o(1)$, $(\mu+1)$ EA is able to reach the optimum.

How to Evaluate Solutions in Pareto-based Search-Based Software Engineering? A Critical Review and Methodological Guidance

With modern requirements, there is an increasing tendancy of considering multiple objectives/criteria simultaneously in many Software Engineering (SE) scenarios. Such a multi-objective optimization scenario comes with an important issue --- how to evaluate the outcome of optimization algorithms, which typically is a set of incomparable solutions (i.e., being Pareto non-dominated to each other). This issue can be challenging for the SE community, particularly for practitioners of Search-Based SE (SBSE). On one hand, multiobjective optimization may still be relatively new to SE/SBSE researchers, who may not be able to identify right evaluation methods for their problems. On the other hand, simply following the evaluation methods for general multiobjective optimisation problems may not be appropriate for specific SE problems, especially when the problem nature or decision maker's preferences are explicitly/implicitly available. This has been well echoed in the literature by various inappropriate/inadequate selection and inaccurate/misleading uses of evaluation methods. In this paper, we carry out a critical review of quality evaluation for multiobjective optimization in SBSE. We survey 717 papers published between 2009 and 2019 from 36 venues in 7 repositories, and select 97 prominent studies, through which we identify five important but overlooked issues in the area. We then conduct an in-depth analysis of quality evaluation indicators and general situations in SBSE, which, together with the identified issues, enables us to provide a methodological guidance to selecting and using evaluation methods in different SBSE scenarios.

Dynamic Multi-objective Optimization of the Travelling Thief Problem

Investigation of detailed and complex optimisation problem formulations that reflect realistic scenarios is a burgeoning field of research. A growing body of work exists for the Travelling Thief Problem, including multi-objective formulations and comparisons of exact and approximate methods to solve it. However, as many realistic scenarios are non-static in time, dynamic formulations have yet to be considered for the TTP. Definition of dynamics within three areas of the TTP problem are addressed; in the city locations, availability map and item values. Based on the elucidation of solution conservation between initial sets and obtained non-dominated sets, we define a range of initialisation mechanisms using solutions generated via solvers, greedily and randomly. These are then deployed to seed the population after a change and the performance in terms of hypervolume and spread is presented for comparison. Across a range of problems with varying TSP-component and KP-component sizes, we observe interesting trends in line with existing conclusions; there is little benefit to using randomisation as a strategy for initialisation of solution populations when the optimal TSP and KP component solutions can be exploited. Whilst these separate optima don't guarantee good TTP solutions, when combined, provide better initial performance and therefore in some examined instances, provides the best response to dynamic changes. A combined approach that mixes solution generation methods to provide a composite population in response to dynamic changes provides improved performance in some instances for the different dynamic TTP formulations. Potential for further development of a more cooperative combined method are realised to more cohesively exploit known information about the problems.

Synergizing Domain Expertise with Self-Awareness in Software Systems: A Patternized Architecture Guideline

Architectural patterns provide a reusable architectural solution for commonly recurring problems that can assist in designing software systems. In this regard, self-awareness architectural patterns are specialized patterns that leverage good engineering practices and experiences to help in designing self-awareness and self-adaptation of a software system. However, domain knowledge and engineers' expertise that is built over time are not explicitly linked to these patterns and the self-aware process. This linkage is important, as it can enrich the design patterns of these systems, which consequently leads to more effective and efficient self-aware and self-adaptive behaviours. This paper is an introductory work that highlights the importance of synergizing domain expertise into the self-awareness in software systems, relying on well-defined underlying approaches. In particular, we present a holistic framework that classifies widely known representations used to obtain and maintain the domain expertise, documenting their nature and specifics rules that permits different levels of synergies with self-awareness. Drawing on such, we describe mechanisms that can enrich existing patterns with engineers' expertise and knowledge of the domain. This, together with the framework, allow us to codify an intuitive step-by-step methodology that guides engineer in making design decisions when synergizing domain expertise into self-awareness and reveal their importances, in an attempt to keep 'engineers-in-the-loop'. Through three case studies, we demonstrate how the enriched patterns, the proposed framework and methodology can be applied in different domains, within which we quantitatively compare the actual benefits of incorporating engineers' expertise into self-awareness, at alternative levels of synergies.

Adaptive Initialization Method for K-means Algorithm

The K-means algorithm is a widely used clustering algorithm that offers simplicity and efficiency. However, the traditional K-means algorithm uses the random method to determine the initial cluster centers, which make clustering results prone to local optima and then result in worse clustering performance. Many initialization methods have been proposed, but none of them can dynamically adapt to datasets with various characteristics. In our previous research, an initialization method for K-means based on hybrid distance was proposed, and this algorithm can adapt to datasets with different characteristics. However, it has the following drawbacks: (a) When calculating density, the threshold cannot be uniquely determined, resulting in unstable results. (b) Heavily depending on adjusting the parameter, the parameter must be adjusted five times to obtain better clustering results. (c) The time complexity of the algorithm is quadratic, which is difficult to apply to large datasets. In the current paper, we proposed an adaptive initialization method for the K-means algorithm (AIMK) to improve our previous work. AIMK can not only adapt to datasets with various characteristics but also obtain better clustering results within two interactions. In addition, we then leverage random sampling in AIMK, which is named as AIMK-RS, to reduce the time complexity. AIMK-RS is easily applied to large and high-dimensional datasets. We compared AIMK and AIMK-RS with 10 different algorithms on 16 normal and six extra-large datasets. The experimental results show that AIMK and AIMK-RS outperform the current initialization methods and several well-known clustering algorithms. Furthermore, AIMK-RS can significantly reduce the complexity of applying it to extra-large datasets with high dimensions. The time complexity of AIMK-RS is O(n).

On Performance Estimation in Automatic Algorithm Configuration

Over the last decade, research on automated parameter tuning, often referred to as automatic algorithm configuration (AAC), has made significant progress. Although the usefulness of such tools has been widely recognized in real world applications, the theoretical foundations of AAC are still very weak. This paper addresses this gap by studying the performance estimation problem in AAC. More specifically, this paper first proves the universal best performance estimator in a practical setting, and then establishes theoretical bounds on the estimation error, i.e., the difference between the training performance and the true performance for a parameter configuration, considering finite and infinite configuration spaces respectively. These findings were verified in extensive experiments conducted on four algorithm configuration scenarios involving different problem domains. Moreover, insights for enhancing existing AAC methods are also identified.

Adversarial Feature Alignment: Avoid Catastrophic Forgetting in Incremental Task Lifelong Learning

Human beings are able to master a variety of knowledge and skills with ongoing learning. By contrast, dramatic performance degradation is observed when new tasks are added to an existing neural network model. This phenomenon, termed as \emph{Catastrophic Forgetting}, is one of the major roadblocks that prevent deep neural networks from achieving human-level artificial intelligence. Several research efforts, e.g. \emph{Lifelong} or \emph{Continual} learning algorithms, have been proposed to tackle this problem. However, they either suffer from an accumulating drop in performance as the task sequence grows longer, or require to store an excessive amount of model parameters for historical memory, or cannot obtain competitive performance on the new tasks. In this paper, we focus on the incremental multi-task image classification scenario. Inspired by the learning process of human students, where they usually decompose complex tasks into easier goals, we propose an adversarial feature alignment method to avoid catastrophic forgetting. In our design, both the low-level visual features and high-level semantic features serve as soft targets and guide the training process in multiple stages, which provide sufficient supervised information of the old tasks and help to reduce forgetting. Due to the knowledge distillation and regularization phenomenons, the proposed method gains even better performance than finetuning on the new tasks, which makes it stand out from other methods. Extensive experiments in several typical lifelong learning scenarios demonstrate that our method outperforms the state-of-the-art methods in both accuracies on new tasks and performance preservation on old tasks.

Federated Learning with Unbiased Gradient Aggregation and Controllable Meta Updating

Federated Averaging (FedAvg) serves as the fundamental framework in Federated Learning (FL) settings. However, we argue that 1) the multiple steps of local updating will result in gradient biases and 2) there is an inconsistency between the target distribution and the optimization objectives following the training paradigm in FedAvg. To tackle these problems, we first propose an unbiased gradient aggregation algorithm with the keep-trace gradient descent and gradient evaluation strategy. Then we introduce a meta updating procedure with a controllable meta training set to provide a clear and consistent optimization objective. Experimental results demonstrate that the proposed methods outperform compared ones with various network architectures in both the IID and non-IID FL settings.