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In the last few years, the formulation of real-world optimization problems and their efficient solution via metaheuristic algorithms has been a catalyst for a myriad of research studies. In spite of decades of historical advancements on the design and use of metaheuristics, large difficulties still remain in regards to the understandability, algorithmic design uprightness, and performance verifiability of new technical achievements. A clear example stems from the scarce replicability of works dealing with metaheuristics used for optimization, which is often infeasible due to ambiguity and lack of detail in the presentation of the methods to be reproduced. Additionally, in many cases, there is a questionable statistical significance of their reported results. This work aims at providing the audience with a proposal of good practices which should be embraced when conducting studies about metaheuristics methods used for optimization in order to provide scientific rigor, value and transparency. To this end, we introduce a step by step methodology covering every research phase that should be followed when addressing this scientific field. Specifically, frequently overlooked yet crucial aspects and useful recommendations will be discussed in regards to the formulation of the problem, solution encoding, implementation of search operators, evaluation metrics, design of experiments, and considerations for real-world performance, among others. Finally, we will outline important considerations, challenges, and research directions for the success of newly developed optimization metaheuristics in their deployment and operation over real-world application environments.

Transfer Optimization has gained a remarkable attention from the Swarm and Evolutionary Computation community in the recent years. It is undeniable that the concepts underlying Transfer Optimization are formulated on solid grounds. However, evidences observed in recent contributions confirm that there are critical aspects that are not properly addressed to date. This short communication aims to engage the readership around a reflection on these issues, and to provide rationale why they remain unsolved. Specifically, we emphasize on three critical points of Evolutionary Multitasking Optimization: i) the plausibility and practical applicability of this paradigm; ii) the novelty of some proposed multitasking methods; and iii) the methodologies used for evaluating newly proposed multitasking algorithms. As a result of this research, we conclude that some important efforts should be directed by the community in order to keep the future of this promising field on the right track. Our ultimate purpose is to unveil gaps in the current literature, so that prospective works can attempt to fix these gaps, avoiding to stumble on the same stones and eventually achieve valuable advances in the area., Comment: 17 pages, 3 figures. This papers has been accepted and published in Swarm and Evolutionary Computation under this DOI: 10.1016/j.swevo.2022.101203

In this work we consider multitasking in the context of solving multiple optimization problems simultaneously by conducting a single search process. The principal goal when dealing with this scenario is to dynamically exploit the existing complementarities among the problems (tasks) being optimized, helping each other through the exchange of valuable knowledge. Additionally, the emerging paradigm of Evolutionary Multitasking tackles multitask optimization scenarios by using as inspiration concepts drawn from Evolutionary Computation. The main purpose of this survey is to collect, organize and critically examine the abundant literature published so far in Evolutionary Multitasking, with an emphasis on the methodological patterns followed when designing new algorithmic proposals in this area (namely, multifactorial optimization and multipopulation-based multitasking). We complement our critical analysis with an identification of challenges that remain open to date, along with promising research directions that can stimulate future efforts in this topic. Our discussions held throughout this manuscript are offered to the audience as a reference of the general trajectory followed by the community working in this field in recent times, as well as a self-contained entry point for newcomers and researchers interested to join this exciting research avenue., Comment: 35 pages, 4 figures, under review for its consideration

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, Quantum Computing is still in an incipient stage of development. For this reason, present architectures show certain limitations, which have motivated the carrying out of this paper. In this paper, we introduce 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. To assess the quality of our method, we have used 7 different Traveling Salesman Problem instances as benchmarking set. The obtained outcomes support the preliminary conclusion that our algorithm is an approach which offers promising results for solving partitioning problems while it drastically reduces the access to quantum computing resources. We also contribute to the field of Transfer Optimization by developing an evolutionary multiform multitasking algorithm as initialization method., Comment: 8 pages, 4 figures, paper accepted in IEEE Congress on Evolutionary Computation 2021

Transfer Optimization is an incipient research area dedicated to solving multiple optimization tasks simultaneously. Among the different approaches that can address this problem effectively, Evolutionary Multitasking resorts to concepts from Evolutionary Computation to solve multiple problems within a single search process. In this paper we introduce a novel adaptive metaheuristic algorithm to deal with Evolutionary Multitasking environments coined as Adaptive Transfer-guided Multifactorial Cellular Genetic Algorithm (AT-MFCGA). AT-MFCGA relies on cellular automata to implement mechanisms in order to exchange knowledge among the optimization problems under consideration. Furthermore, our approach is able to explain by itself the synergies among tasks that were encountered and exploited during the search, which helps us to understand interactions between related optimization tasks. A comprehensive experimental setup is designed to assess and compare the performance of AT-MFCGA to that of other renowned evolutionary multitasking alternatives (MFEA and MFEA-II). Experiments comprise 11 multitasking scenarios composed of 20 instances of 4 combinatorial optimization problems, yielding the largest discrete multitasking environment solved to date. Results are conclusive in regard to the superior quality of solutions provided by AT-MFCGA with respect to the rest of the methods, which are complemented by a quantitative examination of the genetic transferability among tasks throughout the search process., Comment: 31 pages, 4 figures, paper accepted for being published in Information Sciences journal

The main goal of the multitasking optimization paradigm is to solve multiple and concurrent optimization tasks in a simultaneous way through a single search process. For attaining promising results, potential complementarities and synergies between tasks are properly exploited, helping each other by virtue of the exchange of genetic material. This paper is focused on Evolutionary Multitasking, which is a perspective for dealing with multitasking optimization scenarios by embracing concepts from Evolutionary Computation. This work contributes to this field by presenting a new multitasking approach named as Coevolutionary Variable Neighborhood Search Algorithm, which finds its inspiration on both the Variable Neighborhood Search metaheuristic and coevolutionary strategies. The second contribution of this paper is the application field, which is the optimal partitioning of graph instances whose connections among nodes are directed and weighted. This paper pioneers on the simultaneous solving of this kind of tasks. Two different multitasking scenarios are considered, each comprising 11 graph instances. Results obtained by our method are compared to those issued by a parallel Variable Neighborhood Search and independent executions of the basic Variable Neighborhood Search. The discussion on such results support our hypothesis that the proposed method is a promising scheme for simultaneous solving community detection problems over graphs., Comment: 7 pages, paper accepted for presentation in the 2020 IEEE Symposium Series on Computational Intelligence (IEEE SSCI)

Much has been said about the fusion of bio-inspired optimization algorithms and Deep Learning models for several purposes: from the discovery of network topologies and hyper-parametric configurations with improved performance for a given task, to the optimization of the model's parameters as a replacement for gradient-based solvers. Indeed, the literature is rich in proposals showcasing the application of assorted nature-inspired approaches for these tasks. In this work we comprehensively review and critically examine contributions made so far based on three axes, each addressing a fundamental question in this research avenue: a) optimization and taxonomy (Why?), including a historical perspective, definitions of optimization problems in Deep Learning, and a taxonomy associated with an in-depth analysis of the literature, b) critical methodological analysis (How?), which together with two case studies, allows us to address learned lessons and recommendations for good practices following the analysis of the literature, and c) challenges and new directions of research (What can be done, and what for?). In summary, three axes - optimization and taxonomy, critical analysis, and challenges - which outline a complete vision of a merger of two technologies drawing up an exciting future for this area of fusion research., Comment: 64 pages, 18 figures, under review for its consideration in Information Fusion journal

Multitasking optimization is a recently introduced paradigm, focused on the simultaneous solving of multiple optimization problem instances (tasks). The goal of multitasking environments is to dynamically exploit existing complementarities and synergies among tasks, helping each other through the transfer of genetic material. More concretely, Evolutionary Multitasking (EM) regards to the resolution of multitasking scenarios using concepts inherited from Evolutionary Computation. EM approaches such as the well-known Multifactorial Evolutionary Algorithm (MFEA) are lately gaining a notable research momentum when facing with multiple optimization problems. This work is focused on the application of the recently proposed Multifactorial Cellular Genetic Algorithm (MFCGA) to the well-known Capacitated Vehicle Routing Problem (CVRP). In overall, 11 different multitasking setups have been built using 12 datasets. The contribution of this research is twofold. On the one hand, it is the first application of the MFCGA to the Vehicle Routing Problem family of problems. On the other hand, equally interesting is the second contribution, which is focused on the quantitative analysis of the positive genetic transferability among the problem instances. To do that, we provide an empirical demonstration of the synergies arisen between the different optimization tasks., Comment: 8 pages, 1 figure, paper accepted for presentation in the 23rd IEEE International Conference on Intelligent Transportation Systems 2020 (IEEE ITSC 2020)

Bio-inspired optimization (including Evolutionary Computation and Swarm Intelligence) is a growing research topic with many competitive bio-inspired algorithms being proposed every year. In such an active area, preparing a successful proposal of a new bio-inspired algorithm is not an easy task. Given the maturity of this research field, proposing a new optimization technique with innovative elements is no longer enough. Apart from the novelty, results reported by the authors should be proven to achieve a significant advance over previous outcomes from the state of the art. Unfortunately, not all new proposals deal with this requirement properly. Some of them fail to select appropriate benchmarks or reference algorithms to compare with. In other cases, the validation process carried out is not defined in a principled way (or is even not done at all). Consequently, the significance of the results presented in such studies cannot be guaranteed. In this work we review several recommendations in the literature and propose methodological guidelines to prepare a successful proposal, taking all these issues into account. We expect these guidelines to be useful not only for authors, but also for reviewers and editors along their assessment of new contributions to the field., Comment: 81 pages, 4 figures

In short-term traffic forecasting, the goal is to accurately predict future values of a traffic parameter of interest occurring shortly after the prediction is queried. The activity reported in this long-standing research field has been lately dominated by different Deep Learning approaches, yielding overly complex forecasting models that in general achieve accuracy gains of questionable practical utility. In this work we elaborate on the performance of Deep Echo State Networks for this particular task. The efficient learning algorithm and simpler parametric configuration of these alternative modeling approaches make them emerge as a competitive traffic forecasting method for real ITS applications deployed in devices and systems with stringently limited computational resources. An extensive comparison benchmark is designed with real traffic data captured over the city of Madrid (Spain), amounting to more than 130 automatic Traffic Readers (ATRs) and several shallow learning, ensembles and Deep Learning models. Results from this comparison benchmark and the analysis of the statistical significance of the reported performance gaps are decisive: Deep Echo State Networks achieve more accurate traffic forecasts than the rest of considered modeling counterparts., Comment: 6 pages, 4 figures

The emerging research paradigm coined as multitasking optimization aims to solve multiple optimization tasks concurrently by means of a single search process. For this purpose, the exploitation of complementarities among the tasks to be solved is crucial, which is often achieved via the transfer of genetic material, thereby forging the Transfer Optimization field. In this context, Evolutionary Multitasking addresses this paradigm by resorting to concepts from Evolutionary Computation. Within this specific branch, approaches such as the Multifactorial Evolutionary Algorithm (MFEA) has lately gained a notable momentum when tackling multiple optimization tasks. This work contributes to this trend by proposing the first adaptation of the recently introduced Multifactorial Evolutionary Algorithm II (MFEA-II) to permutation-based discrete optimization environments. For modeling this adaptation, some concepts cannot be directly applied to discrete search spaces, such as parent-centric interactions. In this paper we entirely reformulate such concepts, making them suited to deal with permutation-based search spaces without loosing the inherent benefits of MFEA-II. The performance of the proposed solver has been assessed over 5 different multitasking setups, composed by 8 datasets of the well-known Traveling Salesman (TSP) and Capacitated Vehicle Routing Problems (CVRP). The obtained results and their comparison to those by the discrete version of the MFEA confirm the good performance of the developed dMFEA-II, and concur with the insights drawn in previous studies for continuous optimization., Comment: 7 pages, 0 figures, Camera-ready version of the paper accepted for presentation in The Genetic and Evolutionary Computation Conference 2020 (GECCO 2020)

Multitasking optimization is an emerging research field which has attracted lot of attention in the scientific community. The main purpose of this paradigm is how to solve multiple optimization problems or tasks simultaneously by conducting a single search process. The main catalyst for reaching this objective is to exploit possible synergies and complementarities among the tasks to be optimized, helping each other by virtue of the transfer of knowledge among them (thereby being referred to as Transfer Optimization). In this context, Evolutionary Multitasking addresses Transfer Optimization problems by resorting to concepts from Evolutionary Computation for simultaneous solving the tasks at hand. This work contributes to this trend by proposing a novel algorithmic scheme for dealing with multitasking environments. The proposed approach, coined as Coevolutionary Bat Algorithm, finds its inspiration in concepts from both co-evolutionary strategies and the metaheuristic Bat Algorithm. We compare the performance of our proposed method with that of its Multifactorial Evolutionary Algorithm counterpart over 15 different multitasking setups, composed by eight reference instances of the discrete Traveling Salesman Problem. The experimentation and results stemming therefrom support the main hypothesis of this study: the proposed Coevolutionary Bat Algorithm is a promising meta-heuristic for solving Evolutionary Multitasking scenarios., Comment: 13 pages, 0 figures, paper submitted and accepted in the 11th workshop Computational Optimization, Modelling and Simulation (COMS 2020), part of the International Conference on Computational Science (ICCS 2020)

Multitasking optimization is an incipient research area which is lately gaining a notable research momentum. Unlike traditional optimization paradigm that focuses on solving a single task at a time, multitasking addresses how multiple optimization problems can be tackled simultaneously by performing a single search process. The main objective to achieve this goal efficiently is to exploit synergies between the problems (tasks) to be optimized, helping each other via knowledge transfer (thereby being referred to as Transfer Optimization). Furthermore, the equally recent concept of Evolutionary Multitasking (EM) refers to multitasking environments adopting concepts from Evolutionary Computation as their inspiration for the simultaneous solving of the problems under consideration. As such, EM approaches such as the Multifactorial Evolutionary Algorithm (MFEA) has shown a remarkable success when dealing with multiple discrete, continuous, single-, and/or multi-objective optimization problems. In this work we propose a novel algorithmic scheme for Multifactorial Optimization scenarios - the Multifactorial Cellular Genetic Algorithm (MFCGA) - that hinges on concepts from Cellular Automata to implement mechanisms for exchanging knowledge among problems. We conduct an extensive performance analysis of the proposed MFCGA and compare it to the canonical MFEA under the same algorithmic conditions and over 15 different multitasking setups (encompassing different reference instances of the discrete Traveling Salesman Problem). A further contribution of this analysis beyond performance benchmarking is a quantitative examination of the genetic transferability among the problem instances, eliciting an empirical demonstration of the synergies emerged between the different optimization tasks along the MFCGA search process., Comment: Accepted for its presentation at WCCI 2020

In recent years, Multifactorial Optimization (MFO) has gained a notable momentum in the research community. MFO is known for its inherent capability to efficiently address multiple optimization tasks at the same time, while transferring information among such tasks to improve their convergence speed. On the other hand, the quantum leap made by Deep Q Learning (DQL) in the Machine Learning field has allowed facing Reinforcement Learning (RL) problems of unprecedented complexity. Unfortunately, complex DQL models usually find it difficult to converge to optimal policies due to the lack of exploration or sparse rewards. In order to overcome these drawbacks, pre-trained models are widely harnessed via Transfer Learning, extrapolating knowledge acquired in a source task to the target task. Besides, meta-heuristic optimization has been shown to reduce the lack of exploration of DQL models. This work proposes a MFO framework capable of simultaneously evolving several DQL models towards solving interrelated RL tasks. Specifically, our proposed framework blends together the benefits of meta-heuristic optimization, Transfer Learning and DQL to automate the process of knowledge transfer and policy learning of distributed RL agents. A thorough experimentation is presented and discussed so as to assess the performance of the framework, its comparison to the traditional methodology for Transfer Learning in terms of convergence, speed and policy quality , and the intertask relationships found and exploited over the search process., Comment: 8 pages, 5 figures, submitted to IEEE Conference on Evolutionary Computation 2020 (IEEE CEC)

Bat algorithm is a population metaheuristic proposed in 2010 which is based on the echolocation or bio-sonar characteristics of microbats. Since its first implementation, the bat algorithm has been used in a wide range of fields. In this paper, we present a discrete version of the bat algorithm to solve the well-known symmetric and asymmetric traveling salesman problems. In addition, we propose an improvement in the basic structure of the classic bat algorithm. To prove that our proposal is a promising approximation method, we have compared its performance in 37 instances with the results obtained by five different techniques: evolutionary simulated annealing, genetic algorithm, an island based distributed genetic algorithm, a discrete firefly algorithm and an imperialist competitive algorithm. In order to obtain fair and rigorous comparisons, we have conducted three different statistical tests along the paper: the Student's $t$-test, the Holm's test, and the Friedman test. We have also compared the convergence behaviour shown by our proposal with the ones shown by the evolutionary simulated annealing, and the discrete firefly algorithm. The experimentation carried out in this study has shown that the presented improved bat algorithm outperforms significantly all the other alternatives in most of the cases., Comment: 1 figure, 8 tables