Eneko Osaba

Sebastián V. Romero, Eneko Osaba, Esther Villar-Rodriguez et al.

Efficient packing of items into bins is a common daily task. Known as Bin Packing Problem, it has been intensively studied in the field of artificial intelligence, thanks to the wide interest from industry and logistics. Since decades, many variants have been proposed, with the three-dimensional Bin Packing Problem as the closest one to real-world use cases. We introduce a hybrid quantum-classical framework for solving real-world three-dimensional Bin Packing Problems (Q4RealBPP), considering different realistic characteristics, such as: i) package and bin dimensions, ii) overweight restrictions, iii) affinities among item categories and iv) preferences for item ordering. Q4RealBPP permits the solving of real-world oriented instances of 3dBPP, contemplating restrictions well appreciated by industrial and logistics sectors.

Jesus L. Lobo, Ibai Laña, Eneko Osaba et al.

AI-based digital twins are at the leading edge of the Industry 4.0 revolution, which are technologically empowered by the Internet of Things and real-time data analysis. Information collected from industrial assets is produced in a continuous fashion, yielding data streams that must be processed under stringent timing constraints. Such data streams are usually subject to non-stationary phenomena, causing that the data distribution of the streams may change, and thus the knowledge captured by models used for data analysis may become obsolete (leading to the so-called concept drift effect). The early detection of the change (drift) is crucial for updating the model's knowledge, which is challenging especially in scenarios where the ground truth associated to the stream data is not readily available. Among many other techniques, the estimation of the model's confidence has been timidly suggested in a few studies as a criterion for detecting drifts in unsupervised settings. The goal of this manuscript is to confirm and expose solidly the connection between the model's confidence in its output and the presence of a concept drift, showcasing it experimentally and advocating for a major consideration of uncertainty estimation in comparative studies to be reported in the future.

Esther Villar-Rodriguez, Eneko Osaba, Izaskun Oregi

Despite being considered as the next frontier in computation, Quantum Computing is still in an early stage of development. Indeed, current commercial quantum computers suffer from some critical restraints, such as noisy processes and a limited amount of qubits, among others, that affect the performance of quantum algorithms. Despite these limitations, researchers have devoted much effort to propose different frameworks for efficiently using these Noisy Intermediate-Scale Quantum (NISQ) devices. One of these procedures is D'WAVE Systems' quantum-annealer, which can be use to solve optimization problems by translating them into an energy minimization problem. In this context, this work is focused on providing useful insights and information into the behaviour of the quantum-annealer when addressing real-world combinatorial optimization problems. Our main motivation with this study is to open some quantum computing frontiers to non-expert stakeholders. To this end, we perform an extensive experimentation, in the form of a parameter sensitive analysis. This experimentation has been conducted using the Traveling Salesman Problem as benchmarking problem, and adopting two QUBOs: state-of-the-art and a heuristically generated. Our analysis has been performed on a single 7-noded instance, and it is based on more than 200 different parameter configurations, comprising more than 3700 unitary runs and 7 million of quantum reads. Thanks to this study, findings related to the energy distribution and most appropriate parameter settings have been obtained. Finally, an additional study has been performed, aiming to determine the efficiency of the heuristically built QUBO in further TSP instances.

Sebastián V. Romero, Eneko Osaba, Esther Villar-Rodriguez et al.

The Bin Packing Problem is a classic problem with wide industrial applicability. In fact, the efficient packing of items into bins is one of the toughest challenges in many logistic corporations and is a critical issue for reducing storage costs or improving vehicle space allocation. In this work, we resort to our previously published quantum-classical framework known as Q4RealBPP, and elaborate on the solving of real-world oriented instances of the Bin Packing Problem. With this purpose, this paper gravitates on the following characteristics: i) the existence of heterogeneous bins, ii) the extension of the framework to solve not only three-dimensional, but also one- and two-dimensional instances of the problem, iii) requirements for item-bin associations, and iv) delivery priorities. All these features have been tested in this paper, as well as the ability of Q4RealBPP to solve real-world oriented instances.

Eneko Osaba, Esther Villar-Rodriguez, Sebastián V. Romero

In this article, a benchmark for real-world bin packing problems is proposed. This dataset consists of 12 instances of varying levels of complexity regarding size (with the number of packages ranging from 38 to 53) and user-defined requirements. In fact, several real-world-oriented restrictions were taken into account to build these instances: i) item and bin dimensions, ii) weight restrictions, iii) affinities among package categories iv) preferences for package ordering and v) load balancing. Besides the data, we also offer an own developed Python script for the dataset generation, coined Q4RealBPP-DataGen. The benchmark was initially proposed to evaluate the performance of quantum solvers. Therefore, the characteristics of this set of instances were designed according to the current limitations of quantum devices. Additionally, the dataset generator is included to allow the construction of general-purpose benchmarks. The data introduced in this article provides a baseline that will encourage quantum computing researchers to work on real-world bin packing problems.

Esther Villar-Rodriguez, Aitor Gomez-Tejedor, Eneko Osaba

The expectations arising from the latest achievements in the quantum computing field are causing that researchers coming from classical artificial intelligence to be fascinated by this new paradigm. In turn, quantum computing, on the road towards usability, needs classical procedures. Hybridization is, in these circumstances, an indispensable step but can also be seen as a promising new avenue to get the most from both computational worlds. Nonetheless, hybrid approaches have now and will have in the future many challenges to face, which, if ignored, will threaten the viability or attractiveness of quantum computing for real-world applications. To identify them and pose pertinent questions, a proper characterization of the hybrid quantum computing field, and especially hybrid solvers, is compulsory. With this motivation in mind, the main purpose of this work is to propose a preliminary taxonomy for classifying hybrid schemes, and bring to the fore some questions to stir up researchers minds about the real challenges regarding the application of quantum computing.

Alessia Ciacco, Francesca Guerriero, Eneko Osaba

We propose the Steiner Traveling Salesman Problem with Time Windows and Pickup and Delivery, an advanced and practical extension of classical routing models. This variant integrates the characteristics of the Steiner Traveling Salesman Problem with time-window constraints, pickup and delivery operations and vehicle capacity limitations. These features closely mirror the complexities of contemporary logistics challenges, including last-mile distribution, reverse logistics and on-demand service scenarios. To tackle the inherent computational difficulties of this NP-hard problem, we propose two specialized mathematical formulations: an arc-based model and a node-oriented model, each designed to capture distinct structural aspects of the problem. We further introduce a preprocessing reduction method that eliminates redundant arcs, significantly enhancing computational performance and scalability. Both formulations are implemented using classical and quantum optimization approaches. In particular, the classical models are solved with Gurobi, whereas the quantum implementation is carried out on D-Wave's LeapCQMHybrid platform, a hybrid quantum-classical environment that integrates quantum annealing with classical optimization techniques for constrained problem solving. Numerical experiments are conducted to validate the proposed formulations and the preprocessing reduction method. The analyses performed assess the structural properties of the two models, their computational behavior, and the impact of preprocessing on problem size and solution efficiency.

Andoni Aranguren, Eneko Osaba, Silvia Urra-Uriarte et al.

The application of routing algorithms to real-world situations is a widely studied research topic. Despite this, routing algorithms and applications are usually developed for a general purpose, meaning that certain groups, such as ageing people, are often marginalized due to the broad approach of the designed algorithms. This situation may pose a problem in cities which are suffering a slow but progressive ageing of their populations. With this motivation in mind, this paper focuses on describing our implemented Age-Friendly Route Planner, whose goal is to improve the experience in the city for senior citizens. In order to measure the age-friendliness of a route, several variables have been deemed, such as the number of amenities along the route, the amount of comfortable elements found, or the avoidance of sloppy sections. In this paper, we describe one of the main features of the Age-Friendly Route Planner: the preference-based routes, and we also demonstrate how it can contribute to the creation of adapted friendly routes.

Eneko Osaba, Esther Villar-Rodriguez, Antón Asla

In the current NISQ-era, one of the major challenges faced by researchers and practitioners lies in figuring out how to combine quantum and classical computing in the most efficient and innovative way. In this paper, we present a mechanism coined as Quantum Initialization for Warehouse Optimization Problem that resorts to D-Wave's Quantum Annealer. The module has been specifically designed to be embedded into already existing classical software dedicated to the optimization of a real-world industrial problem. We preliminary tested the implemented mechanism through a two-phase experiment against the classical version of the software.

Eneko Osaba, Gorka Benguria, Jesus L. Lobo et al.

In the last years, one of the fields of artificial intelligence that has been investigated the most is nature-inspired computing. The research done on this specific topic showcases the interest that sparks in researchers and practitioners, who put their focus on this paradigm because of the adaptability and ability of nature-inspired algorithms to reach high-quality outcomes on a wide range of problems. In fact, this kind of methods has been successfully applied to solve real-world problems in heterogeneous fields such as medicine, transportation, industry, or software engineering. Our main objective with this paper is to describe a tool based on nature-inspired computing for solving a specific software engineering problem. The problem faced consists of optimizing Infrastructure as Code deployment configurations. For this reason, the name of the system is IaC Optimizer Platform. A prototypical version of the IOP was described in previous works, in which the functionality of this platform was introduced. With this paper, we take a step forward by describing the final release of the IOP, highlighting its main contribution regarding the current state-of-the-art, and justifying the decisions made on its implementation. Also, we contextualize the IOP within the complete platform in which it is embedded, describing how a user can benefit from its use. To do that, we also present and solve a real-world use case.

Eneko Osaba, Guillaume Gelabert, Esther Villar-Rodriguez et al.

One of the problems in quantitative finance that has received the most attention is the portfolio optimization problem. Regarding its solving, this problem has been approached using different techniques, with those related to quantum computing being especially prolific in recent years. In this study, we present a system called Quantum Computing-based System for Portfolio Optimization with Future Asset Values and Automatic Universe Reduction (Q4FuturePOP), which deals with the Portfolio Optimization Problem considering the following innovations: i) the developed tool is modeled for working with future prediction of assets, instead of historical values; and ii) Q4FuturePOP includes an automatic universe reduction module, which is conceived to intelligently reduce the complexity of the problem. We also introduce a brief discussion about the preliminary performance of the different modules that compose the prototypical version of Q4FuturePOP.

Eneko Osaba, Esther Villar-Rodriguez, Izaskun Oregi et al.

Quantum Computing is an emerging paradigm which is gathering a lot of popularity in the current scientific and technological community. Widely conceived as the next frontier of computation, Quantum Computing is still at the dawn of its development. Thus, current solving systems suffer from significant limitations in terms of performance and capabilities. Some interesting approaches have been devised by researchers and practitioners in order to overcome these barriers, being quantum-classical hybrid algorithms one of the most often used solving schemes. The main goal of this paper is to extend the results and findings of the recently proposed hybrid Quantum Computing - Tabu Search Algorithm for partitioning problems. To do that, we focus our research on the adaptation of this method to the Asymmetric Traveling Salesman Problem. In overall, we have employed six well-known instances belonging to TSPLIB to assess the performance of Quantum Computing - Tabu Search Algorithm in comparison to QBSolv, a state-of-the-art decomposing solver. Furthermore, as an additional contribution, this work also supposes the first solving of the Asymmetric Traveling Salesman Problem using a Quantum Computing based method. Aiming to boost whole community's research in QC, we have released the project's repository as open source code for further application and improvements.

Eneko Osaba, Esther Villar-Rodriguez, Antón Asla

Research focused on the conjunction between quantum computing and routing problems has been very prolific in recent years. Most of the works revolve around classical problems such as the Traveling Salesman Problem or the Vehicle Routing Problem. The real-world applicability of these problems is dependent on the objectives and constraints considered. Anyway, it is undeniable that it is often difficult to translate complex requirements into these classical formulations.The main objective of this research is to present a solving scheme for dealing with realistic instances while maintaining all the characteristics and restrictions of the original real-world problem. Thus, a quantum-classical strategy has been developed, coined Q4RPD, that considers a set of real constraints such as a heterogeneous fleet of vehicles, priority deliveries, and capacities characterized by two values: weight and dimensions of the packages. Q4RPD resorts to the Leap Constrained Quadratic Model Hybrid Solver of D-Wave. To demonstrate the application of Q4RPD, an experimentation composed of six different instances has been conducted, aiming to serve as illustrative examples.

Eneko Osaba, Esther Villar-Rodriguez

In this paper, we propose a quantum computing oriented benchmark for combinatorial optimization. This benchmark, coined as QOPTLib, is composed of 40 instances equally distributed over four well-known problems: Traveling Salesman Problem, Vehicle Routing Problem, one-dimensional Bin Packing Problem and the Maximum Cut Problem. The sizes of the instances in QOPTLib not only correspond to computationally addressable sizes, but also to the maximum length approachable with non-zero likelihood of getting a good result. In this regard, it is important to highlight that hybrid approaches are also taken into consideration. Thus, this benchmark constitutes the first effort to provide users a general-purpose dataset. Also in this paper, we introduce a first full solving of QOPTLib using two solvers based on quantum annealing. Our main intention with this is to establish a preliminary baseline, hoping to inspire other researchers to beat these outcomes with newly proposed quantum-based algorithms.

Eneko Osaba, Pablo Miranda-Rodriguez, Andreas Oikonomakis et al.

This paper presents a novel hybrid approach to solving real-world drone routing problems by leveraging the capabilities of quantum computing. The proposed method, coined Quantum for Drone Routing (Q4DR), integrates the two most prominent paradigms in the field: quantum gate-based computing, through the Eclipse Qrisp programming language; and quantum annealers, by means of D-Wave System's devices. The algorithm is divided into two different phases: an initial clustering phase executed using a Quantum Approximate Optimization Algorithm (QAOA), and a routing phase employing quantum annealers. The efficacy of Q4DR is demonstrated through three use cases of increasing complexity, each incorporating real-world constraints such as asymmetric costs, forbidden paths, and itinerant charging points. This research contributes to the growing body of work in quantum optimization, showcasing the practical applications of quantum computing in logistics and route planning.

Esther Villar-Rodriguez, Eneko Osaba, Izaskun Oregi et al.

Quantum computing is poised to transform computational paradigms across science and industry. As the field evolves, it can benefit from established classical methodologies, including promising paradigms such as Transfer of Knowledge (ToK). This work serves as a brief, self-contained reference for ToK, unifying its core principles under a single formal framework. We introduce a joint notation that consolidates and extends prior work in Transfer Learning and Transfer Optimization, bridging traditionally separate research lines and enabling a common language for knowledge reuse. Building on this foundation, we classify existing ToK strategies and principles into a structured taxonomy that helps researchers position their methods within a broader conceptual map. We then extend key transfer protocols to quantum computing, introducing two novel use cases (reverse annealing and multitasking QAOA) alongside a sequential VQE approach that supports and validates prior findings. These examples highlight ToK's potential to improve performance and generalization in quantum algorithms. Finally, we outline challenges and opportunities for integrating ToK into quantum computing, emphasizing its role in reducing resource demands and accelerating problem-solving. This work lays the groundwork for future synergies between classical and quantum computing through a shared, transferable knowledge framework.

Alessia Ciacco, Francesca Guerriero, Eneko Osaba

The Steiner Traveling Salesman Problem (STSP) is a variant of the classical Traveling Salesman Problem. The STSP involves incorporating steiner nodes, which are extra nodes not originally part of the required visit set but that can be added to the route to enhance the overall solution and minimize the total travel cost. Given the NP-hard nature of the STSP, we propose a quantum approach to address it. Specifically, we employ quantum annealing using D-Wave's hardware to explore its potential for solving this problem. To enhance computational feasibility, we develop a preprocessing method that effectively reduces the network size. Our experimental results demonstrate that this reduction technique significantly decreases the problem complexity, making the Quadratic Unconstrained Binary Optimization formulation, the standard input for quantum annealers, better suited for existing quantum hardware. Furthermore, the results highlight the potential of quantum annealing as a promising and innovative approach for solving the STSP.

Aitor Gomez-Tejedor, Eneko Osaba, Esther Villar-Rodriguez

This study addresses the minor-embedding problem, which involves mapping the variables of an Ising model onto a quantum annealing processor. The primary motivation stems from the observed performance disparity of quantum annealers when solving problems suited to the processor's architecture versus those with non-hardware-native topologies. Our research has two main objectives: i) to analyze the impact of embedding quality on the performance of D-Wave Systems quantum annealers, and ii) to evaluate the quality of the embeddings generated by Minorminer, the standard minor-embedding technique in the quantum annealing literature, provided by D-Wave. Regarding the first objective, our experiments reveal a clear correlation between the average chain length of embeddings and the relative errors of the solutions sampled. This underscores the critical influence of embedding quality on quantum annealing performance. For the second objective, we evaluate Minorminer's embedding capabilities, the quality and robustness of its embeddings, and its execution-time performance. We also compare its performance with Clique Embedding, another algorithm developed by D-Wave, which is deterministic and designed to embed fully connected Ising models into quantum annealing processors, serving as a worst-case scenario. The results demonstrate that there is significant room for improvement for Minorminer, suggesting that more effective embedding strategies could lead to meaningful gains in quantum annealing performance.

Eneko Osaba, Esther Villar-Rodriguez, Pablo Miranda-Rodriguez et al.

Recent research at the intersection of quantum computing and routing problems has been highly prolific. Much of this work focuses on classical problems such as the Traveling Salesman Problem and the Vehicle Routing Problem. The practical applicability of these problems depends on the specific objectives and constraints considered. However, it is undeniable that translating complex real-world requirements into these classical formulations often proves challenging. In this paper, we resort to our previously published quantum-classical technique for addressing real-world-oriented routing problems, known as Quantum for Real Package Delivery (Q4RPD), and elaborate on solving additional realistic problem instances. Accordingly, this paper emphasizes the following characteristics: i) simultaneous pickup and deliveries, ii) time-windows, and iii) mobility restrictions by vehicle type. To illustrate the application of Q4RPD, we have conducted an experimentation comprising seven instances, serving as a demonstration of the newly developed features.

Alessia Ciacco, Francesca Guerriero, Eneko Osaba

We address a novel staff allocation problem that arises in the organization of collaborators among multiple school sites and educational levels. The problem emerges from a real case study in a public school in Calabria, Italy, where staff members must be distributed across kindergartens, primary, and secondary schools under constraints of availability, competencies, and fairness. To tackle this problem, we develop an optimization model and investigate a solution approach based on quantum annealing. Our computational experiments on real-world data show that quantum annealing is capable of producing balanced assignments in short runtimes. These results provide evidence of the practical applicability of quantum optimization methods in educational scheduling and, more broadly, in complex resource allocation tasks.

Eneko Osaba, Estibaliz Garrote, Pablo Miranda-Rodriguez et al.

This work explores the application of hybrid quantum-classical algorithms to optimize robotic inspection trajectories derived from Computer-Aided Design (CAD) models in industrial settings. By modeling the task as a 3D variant of the Traveling Salesman Problem, incorporating incomplete graphs and open-route constraints, this study evaluates the performance of two D-Wave-based solvers against classical methods such as GUROBI and Google OR-Tools. Results across five real-world cases demonstrate competitive solution quality with significantly reduced computation times, highlighting the potential of quantum approaches in automation under Industry 4.0.

Eneko Osaba, Esther Villar-Rodriguez

Being immersed in the NISQ-era, current quantum annealers present limitations for solving optimization problems efficiently. To mitigate these limitations, D-Wave Systems developed a mechanism called Reverse Annealing, a specific type of quantum annealing designed to perform local refinement of good states found elsewhere. Despite the research activity around Reverse Annealing, none has theorized about the possible benefits related to the transfer of knowledge under this paradigm. This work moves in that direction and is driven by experimentation focused on answering two key research questions: i) is reverse annealing a paradigm that can benefit from knowledge transfer between similar problems? and ii) can we infer the characteristics that an input solution should meet to help increase the probability of success? To properly guide the tests in this paper, the well-known Knapsack Problem has been chosen for benchmarking purposes, using a total of 34 instances composed of 14 and 16 items.

Eneko Osaba, Josu Diaz-de-Arcaya, Juncal Alonso et al.

Multiobjective optimization is a hot topic in the artificial intelligence and operations research communities. The design and development of multiobjective methods is a frequent task for researchers and practitioners. As a result of this vibrant activity, a myriad of techniques have been proposed in the literature to date, demonstrating a significant effectiveness for dealing with situations coming from a wide range of real-world areas. This paper is focused on a multiobjective problem related to optimizing Infrastructure-as-Code deployment configurations. The system implemented for solving this problem has been coined as IaC Optimizer Platform (IOP). Despite the fact that a prototypical version of the IOP has been introduced in the literature before, a deeper analysis focused on the resolution of the problem is needed, in order to determine which is the most appropriate multiobjective method for embedding in the IOP. The main motivation behind the analysis conducted in this work is to enhance the IOP performance as much as possible. This is a crucial aspect of this system, deeming that it will be deployed in a real environment, as it is being developed as part of a H2020 European project. Going deeper, we resort in this paper to nine different evolutionary computation-based multiobjective algorithms. For assessing the quality of the considered solvers, 12 different problem instances have been generated based on real-world settings. Results obtained by each method after 10 independent runs have been compared using Friedman's non-parametric tests. Findings reached from the tests carried out lad to the creation of a multi-algorithm system, capable of applying different techniques according to the user's needs.

Eneko Osaba, Javier Del Ser, Ponnuthurai N. Suganthan

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.

Eneko Osaba, Aritz D. Martinez, Javier Del Ser

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.

Eneko Osaba, Esther Villar-Rodriguez, Izaskun Oregi et al.

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.

Eneko Osaba, Javier Del Ser, Aritz D. Martinez et al.

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.

Eneko Osaba, Esther Villar-Rodriguez, Javier Del Ser

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.

Jesus L. Lobo, Javier Del Ser, Eneko Osaba et al.

Data stream mining extracts information from large quantities of data flowing fast and continuously (data streams). They are usually affected by changes in the data distribution, giving rise to a phenomenon referred to as concept drift. Thus, learning models must detect and adapt to such changes, so as to exhibit a good predictive performance after a drift has occurred. In this regard, the development of effective drift detection algorithms becomes a key factor in data stream mining. In this work we propose CU RIE, a drift detector relying on cellular automata. Specifically, in CU RIE the distribution of the data stream is represented in the grid of a cellular automata, whose neighborhood rule can then be utilized to detect possible distribution changes over the stream. Computer simulations are presented and discussed to show that CU RIE, when hybridized with other base learners, renders a competitive behavior in terms of detection metrics and classification accuracy. CU RIE is compared with well-established drift detectors over synthetic datasets with varying drift characteristics.

Aritz D. Martinez, Javier Del Ser, Esther Villar-Rodriguez et al.

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.

Eneko Osaba, Aritz D. Martinez, Jesus L. Lobo et al.

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.

Antonio LaTorre, Daniel Molina, Eneko Osaba et al.

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.

Javier Del Ser, Ibai Lana, Eric L. Manibardo et al.

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.

Eneko Osaba, Aritz D. Martinez, Akemi Galvez et al.

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.

Eneko Osaba

Transportation is an essential area in the nowadays society, both for business sector and citizenry. There are different kinds of transportation systems, each one with its own characteristics. In the same way, various areas of knowledge can deal efficiently with the transport planning. The majority of the problems related with the transport and logistics have common characteristics, so they can be modeled as optimization problems, being able to see them as special cases of other generic problems. These problems fit into the combinatorial optimization field. Much of the problems of this type have an exceptional complexity. A great amount of meta-heuristics can be found the literature, each one with its advantages and disadvantages. Due to the high complexity of combinatorial optimization problems, there is no technique able to solve all these problems optimally. This fact makes the fields of combinatorial optimization and vehicle routing problems be a hot topic of research. This doctoral thesis will focus its efforts on developing a new meta-heuristic to solve different kind of vehicle routing problems. The presented technique offers an added value compared to existing methods, either in relation to the performance, and the contribution of conceptual originality. With the aim of validating the proposed model, the results obtained by the developed meta-heuristic have been compared with the ones obtained by other four algorithms of similar philosophy. Four well-known routing problems have been used in this experimentation, as well as two classical combinatorial optimization problems. In addition to the comparisons based on parameters such as the mean, or the standard deviation, two different statistical tests have been carried out. Thanks to these tests it can be affirmed that the proposed meta-heuristic is competitive in terms of performance and conceptual originality.

Eneko Osaba, Javier Del Ser, Xin-She Yang et al.

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.

Eneko Osaba, Aritz D. Martinez, Jesus L. Lobo et al.

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.

Aritz D. Martinez, Eneko Osaba, Javier Del Ser et al.

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.

Eneko Osaba, Xin-She Yang, Fernando Diaz et al.

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.