Previous theory work on multi-objective evolutionary algorithms considers mostly easy problems that are composed of unimodal objectives. This paper takes a first step towards a deeper understanding of how evolutionary algorithms solve multi-modal multi-objective problems. We propose the OneJumpZeroJump problem, a bi-objective problem whose single objectives are isomorphic to the classic jump functions benchmark. We prove that the simple evolutionary multi-objective optimizer (SEMO) cannot compute the full Pareto front. In contrast, for all problem sizes~$n$ and all jump sizes $k \in [4..\frac n2 - 1]$, the global SEMO (GSEMO) covers the Pareto front in $\Theta((n-2k)n^{k})$ iterations in expectation. To improve the performance, we combine the GSEMO with two approaches, a heavy-tailed mutation operator and a stagnation detection strategy, that showed advantages in single-objective multi-modal problems. Runtime improvements of asymptotic order at least $k^{\Omega(k)}$ are shown for both strategies. Our experiments verify the {substantial} runtime gains already for moderate problem sizes. Overall, these results show that the ideas recently developed for single-objective evolutionary algorithms can be effectively employed also in multi-objective optimization.

Genetic algorithms are among the most fascinating techniques for optimizing problems. They draw inspiration from Charles Darwin's theory of natural evolution. For this competition, individuals considered are potential boards at their initial state. To take full advantage of pytorch, the population is stored in a single boolean tensor with dimensions (number_of_individuals, N, N) where N is the dimension of a board; N 25 for this competition. Create a random initial population made of n_parents boards of size NxN.

In this paper, we propose a surrogate-assisted evolutionary algorithm (EA) for hyperparameter optimization of machine learning (ML) models. The proposed STEADE model initially estimates the objective function landscape using RadialBasis Function interpolation, and then transfers the knowledge to an EA technique called Differential Evolution that is used to evolve new solutions guided by a Bayesian optimization framework. We empirically evaluate our model on the hyperparameter optimization problems as a part of the black box optimization challenge at NeurIPS 2020 and demonstrate the improvement brought about by STEADE over the vanilla EA.

In this paper we consider a continuous description based on stochastic differential equations of the popular particle swarm optimization (PSO) process for solving global optimization problems and derive in the large particle limit the corresponding mean-field approximation based on Vlasov-Fokker-Planck-type equations. The disadvantage of memory effects induced by the need to store the local best position is overcome by the introduction of an additional differential equation describing the evolution of the local best. A regularization process for the global best permits to formally derive the respective mean-field description. Subsequently, in the small inertia limit, we compute the related macroscopic hydrodynamic equations that clarify the link with the recently introduced consensus based optimization (CBO) methods. Several numerical examples illustrate the mean field process, the small inertia limit and the potential of this general class of global optimization methods.

Quantum Computing is considered as the next frontier in computing, and it is attracting a lot of attention from the current scientific community. This kind of computation provides to researchers with a revolutionary paradigm for addressing complex optimization problems, offering a significant speed advantage and an efficient search ability. Anyway, despite hopes placed in this field are high, Quantum Computing is still in an incipient stage of development. For this reason, present architectures show certain limitations in terms of computational capabilities and performance. These limitations have motivated the carrying out of this paper. With this paper, we contribute to the field introducing a novel solving scheme coined as hybrid Quantum Computing - Tabu Search Algorithm. Main pillars of operation of the proposed method are a greater control over the access to quantum resources, and a considerable reduction of non-profitable accesses. For assessing the quality of our method, we have used the well-known TSP as benchmarking problem. Furthermore, the performance of QTA has been compared with QBSolv -- a state-of-the-art decomposing solver -- on a set of 7 different TSP instances. The obtained experimental outcomes support the preliminary conclusion that QTA is an approach which offers promising results for solving partitioning problems, while it drastically reduces the access to QC resources. Furthermore, we also contribute in this paper to the field of Transfer Optimization by developing and using a evolutionary multiform multitasking algorithm as initialization method for the introduced hybrid Quantum Computing - Tabu Search Algorithm. Concretely, the evolutionary multitasking algorithm implemented is a multiform variant of the recently published Coevolutionary Variable Neighborhood Search Algorithm for Discrete Multitasking.

Deep reinforcement learning (DRL) algorithms and evolution strategies (ES) have been applied to various tasks, showing excellent performances. These have the opposite properties, with DRL having good sample efficiency and poor stability, while ES being vice versa. Recently, there have been attempts to combine these algorithms, but these methods fully rely on synchronous update scheme, making it not ideal to maximize the benefits of the parallelism in ES. To solve this challenge, asynchronous update scheme was introduced, which is capable of good time-efficiency and diverse policy exploration. In this paper, we introduce an Asynchronous Evolution Strategy-Reinforcement Learning (AES-RL) that maximizes the parallel efficiency of ES and integrates it with policy gradient methods. Specifically, we propose 1) a novel framework to merge ES and DRL asynchronously and 2) various asynchronous update methods that can take all advantages of asynchronism, ES, and DRL, which are exploration and time efficiency, stability, and sample efficiency, respectively. The proposed framework and update methods are evaluated in continuous control benchmark work, showing superior performance as well as time efficiency compared to the previous methods.

This paper introduces EvoCraft, a framework for Minecraft designed to study open-ended algorithms. We introduce an API that provides an open-source Python interface for communicating with Minecraft to place and track blocks. In contrast to previous work in Minecraft that focused on learning to play the game, the grand challenge we pose here is to automatically search for increasingly complex artifacts in an open-ended fashion. Compared to other environments used to study open-endedness, Minecraft allows the construction of almost any kind of structure, including actuated machines with circuits and mechanical components. We present initial baseline results in evolving simple Minecraft creations through both interactive and automated evolution. While evolution succeeds when tasked to grow a structure towards a specific target, it is unable to find a solution when rewarded for creating a simple machine that moves. Thus, EvoCraft offers a challenging new environment for automated search methods (such as evolution) to find complex artifacts that we hope will spur the development of more open-ended algorithms.

In this paper, the publicly available dataset of condition based maintenance of combined diesel-electric and gas (CODLAG) propulsion system for ships has been utilized to obtain symbolic expressions which could estimate gas turbine shaft torque and fuel flow using genetic programming (GP) algorithm. The entire dataset consists of 11934 samples that was divided into training and testing portions of dataset in an 80:20 ratio. The training dataset used to train the GP algorithm to obtain symbolic expressions for gas turbine shaft torque and fuel flow estimation consisted of 9548 samples. The best symbolic expressions obtained for gas turbine shaft torque and fuel flow estimation were obtained based on their $R^2$ score generated as a result of the application of the testing portion of the dataset on the aforementioned symbolic expressions. The testing portion of the dataset consisted of 2386 samples. The three best symbolic expressions obtained for gas turbine shaft torque estimation generated $R^2$ scores of 0.999201, 0.999296, and 0.999374, respectively. The three best symbolic expressions obtained for fuel flow estimation generated $R^2$ scores of 0.995495, 0.996465, and 0.996487, respectively.

A novel multi-agent evolutionary robotics (ER) based framework, inspired by competitive evolutionary environments in nature, is demonstrated for training Spiking Neural Networks (SNN). The weights of a population of SNNs along with morphological parameters of bots they control in the ER environment are treated as phenotypes. Rules of the framework select certain bots and their SNNs for reproduction and others for elimination based on their efficacy in capturing food in a competitive environment. While the bots and their SNNs are given no explicit reward to survive or reproduce via any loss function, these drives emerge implicitly as they evolve to hunt food and survive within these rules. Their efficiency in capturing food as a function of generations exhibit the evolutionary signature of punctuated equilibria. Two evolutionary inheritance algorithms on the phenotypes, Mutation and Crossover with Mutation, are demonstrated. Performances of these algorithms are compared using ensembles of 100 experiments for each algorithm. We find that Crossover with Mutation promotes 40% faster learning in the SNN than mere Mutation with a statistically significant margin.

By studying the underlying policies of decision-making agents, we can learn about their shortcomings and potentially improve them. Traditionally, this has been done either by examining the agent's implementation, its behaviour while it is being executed, its performance with a reward/fitness function or by visualizing the density of states the agent visits. However, these methods fail to describe the policy's behaviour in complex, high-dimensional environments or do not scale to thousands of policies, which is required when studying training algorithms. We propose policy supervectors for characterizing agents by the distribution of states they visit, adopting successful techniques from the area of speech technology. Policy supervectors can characterize policies regardless of their design philosophy (e.g. rule-based vs. neural networks) and scale to thousands of policies on a single workstation machine. We demonstrate method's applicability by studying the evolution of policies during reinforcement learning, evolutionary training and imitation learning, providing insight on e.g. how the search space of evolutionary algorithms is also reflected in agent's behaviour, not just in the parameters.