Multi-objective multi-armed bandit (MOMAB) problems are crucial for complex decision-making scenarios where multiple conflicting objectives must be simultaneously optimized. However, most existing works are based on the linear assumption of the feedback rewards, which significantly constrains their applicability and efficacy in capturing the intricate dynamics of real-world environments. This paper explores a multi-objective neural bandit (MONB) framework, which integrates the universal approximators, neural networks, with the classical MOMABs. We adopt random scalarization to accommodate the special needs of a practitioner by setting an appropriate distribution on the regions of interest. Using the trade-off capabilities of upper confidence bound (UCB) and Thompson sampling (TS) strategies, we propose two novel algorithms, MONeural-UCB and MONeural-TS. Theoretical and empirical analysis demonstrate the superiority of our methods in multi-objective or multi-task bandit problems, which makes great improvement over the classical linear MOMABs.

Multi-objective optimization problems (MOPs) are prevalent in numerous real-world applications. Recently, Pareto Set Learning (PSL) has emerged as a powerful paradigm for solving MOPs. PSL can produce a neural network for modeling the set of all Pareto optimal solutions. However, applying PSL to black-box objectives, particularly those exhibiting non-separability, high dimensionality, and/or other complex properties, remains very challenging. To address this issue, we propose leveraging evolution strategies (ESs), a class of specialized black-box optimization algorithms, within the PSL paradigm. Traditional ESs capture the complex dimensional dependencies less efficiently, which can significantly hinder their performance in PSL. To tackle this issue, we suggest encapsulating the dependencies within a neural network, which is then trained using a novel gradient estimation method. The proposed method, termed Neural-ES, is evaluated using a bespoke benchmark suite for black-box PSL. Experimental comparisons with other methods demonstrate the efficiency of Neural-ES, underscoring its ability to learn the Pareto sets of challenging black-box MOPs.

Integrating non-elitist evolution strategies into MOEA/D is challenging because the former usually requires many samples for updates, which is costly for MOEAID. In contrast, we suggest using (1+ 1)-ES for three reasons: fewer samples needed for updates, lower computational overhead, and better flexibility for subproblem collaboration. To verify this, we introduce (1+1)-MOEA/D-CMA, where each subproblem is solved by a different (1+1)-ES solver, and the solvers collaborate through a novel solution injection scheme. Comprehensive experiments show that the proposed algorithm performs better than several widely used algorithms. More importantly, owing to the lightweight nature of (1+1)-CMA-ES, the algorithm is shown to run faster and scale better to large population sizes, than other MOEA/D variants based on (µ/µw, λ)-CMA-ES.

Genetic Programming (GP) is a powerful evolutionary algorithm that has a wide range of real-world applications. High-dimensional symbolic regression (HDSR) is an important yet challenging application of GP. In this paper, a comparative study is conducted to investigate and to discuss the effectiveness of dimensionality reduction (DR) techniques in assisting GP for HDSR problems. Three popular DR techniques, which are the Pearson Correlation Coefficient (PCC), the Principal Component Analysis (PCA), and the Maximal Information Coefficient (MIC), are selected for comparison and discussion. The experimental results showed that considering only correlation during DR is not effective enough to provide a suitable reduced set of problem dimensions, and that GP with DR may perform worse than its counterpart without DR. Meanwhile, we propose a novel two-phase DR method, considering both correlation and redundancy. The proposed method can give a more reasonable set of reduced dimensions, which can effectively improve the performance of GP on HDSR problems.

Test case prioritization (TCP) is a popular regression testing technique in software engineering field. The task of TCP is to schedule the execution order of test cases so that certain objective (e.g., code coverage) can be achieved quickly. In this article, we propose an efficient ant colony system framework for the TCP problem, with the aim of maximizing the code coverage as soon as possible. In the proposed framework, an effective heuristic function is proposed to guide the ants to construct solutions based on additional statement coverage among remaining test cases. Besides, a sorting-based local search mechanism is proposed to further accelerate the convergence speed of the algorithm. Experimental results on different benchmark problems, and a real-world application, have shown that the proposed framework can outperform several state-of-the-art methods, in terms of solution quality and search efficiency.