This paper presents a minimal validated framework for designing energy-aware metaheuristics that operate under fixed energy budgets. We introduce a unified operator-level model that quantifies both numerical gain and energy consumption, and define a robust Expected Improvement per Joule (EI/J) score to guide adaptive selection among operator variants during the search. The resulting energy-aware solvers dynamically choose between operators to self-control exploration and exploitation, aiming to maximise fitness gain under limited energy. We instantiate this framework in three representative metaheuristics—steady-state GA, PSO, and ILS—each equipped with two lightweight/heavy update variants in a controlled setting. Experiments on three heterogeneous combinatorial problems (Knapsack, NK-landscapes, and Error-Correcting Codes) show that the energy-aware variants can reach comparable fitness while requiring substantially less energy than their non-energy-aware baselines. EI/J values stabilise early and yield clear operator-selection patterns, with each solver reliably self-identifying the most improvement-per-Joule-efficient operator across problems.

Dock-based bike-sharing systems exhibit spatial imbalances between bicycle supply and user demand, often addressed through overnight truck-based rebalancing. This work studies static overnight rebalancing under demand uncertainty modeled as a tri-objective optimization problem. The objectives minimize total travel distance, expected unmet demand, and a robustness-oriented unmet demand measure over high-demand scenarios. Route plans are evaluated via a recourse simulation that enforces truck loads and station capacity constraints across multiple demand realizations. The robustness objective supports selecting plans that reduce peak-demand service degradation. Trade-off solutions are approximated with Non-dominated Sorting Genetic Algorithm II using a permutation-partition encoding and domain-specific relocation operators, including a biased best-improvement move for station relocation. Experiments on the real Barcelona Bicing system with 460 stations show well-distributed Pareto sets and substantial contributions to the reference non-dominated set. Greedy constructive baselines mainly yield extreme solutions and are often dominated.

Addressing real-world optimization challenges requires not only advanced metaheuristics but also continuous refinement of their internal mechanisms. This paper explores the integration of machine learning in the form of neural surrogate models into metaheuristics through a recent lens: energy consumption. While surrogates are widely used to reduce the computational cost of expensive objective functions, their combined impact on energy efficiency, algorithmic performance, and solution accuracy remains largely unquantified. We provide a critical investigation into this intersection, aiming to advance the design of energy-aware, surrogate-assisted search algorithms. Our experiments reveal substantial benefits: employing a pre-trained surrogate can reduce energy consumption by up to 98%, execution time by approximately 98%, and memory usage by around 99% in our setting. Moreover, increasing the training dataset size may further enhance these gains up to a point by lowering the per-use computational cost, while static pre-training versus continuous (iterative) retraining exhibit different advantages depending on whether we aim at time/energy or accuracy and overall computational cost across instances, respectively. Surrogates may negatively impact cost and accuracy in some cases, and then they cannot be blindly adopted. These findings support a more holistic approach to surrogate-assisted optimization, integrating energy with time and predictive accuracy into performance assessments.

Solving complex real problems often demands advanced algorithms, and then continuous improvements in the internal operations of a search technique are needed. Hybrid algorithms, parallel techniques, theoretical advances, and much more are needed to transform a general search algorithm into an efficient, useful one in practice. In this paper, we study how surrogates are helping metaheuristics from an important and understudied point of view: their energy profile. Even if surrogates are a great idea for substituting a time-demanding complex fitness function, the energy profile, general efficiency, and accuracy of the resulting surrogate-assisted metaheuristic still need considerable research. In this work, we make a first step in analyzing particle swarm optimization in different versions (including pre-trained and retrained neural networks as surrogates) for its energy profile (for both processor and memory), plus a further study on the surrogate accuracy to properly drive the search towards an acceptable solution. Our conclusions shed new light on this topic and could be understood as the first step towards a methodology for assessing surrogate-assisted algorithms not only accounting for time or numerical efficiency but also for energy and surrogate accuracy for a better, more holistic characterization of optimization and learning techniques.

This paper proposes a multi-criteria approach to optimize urban infrastructure for e-scooters mobility. The problem considers redesigning road infrastructure to integrate e-scooters into a city's multimodal transportation system. This research aims to improve cycle lane coverage and connectivity for e-scooters while minimizing installation costs. Two parallel multi-objective evolutionary algorithms are devised to solve this problem in a real-world instance based on Málaga. The results showed that the algorithms effectively explored the Pareto front, offering diverse trade-off solutions. Key solutions are analyzed to evaluate the trade-offs between travel time improvement, cycle lane connectivity, multimodality, and installation costs. Visualization of proposed infrastructure changes illustrates significant reductions in travel time.

Federated learning is a paradigm that proposes protecting data privacy by sharing local models instead of raw data during each iteration of model training. However, these models can be large, with many parameters, provoking a substantial communication cost and having a notable environmental impact. Reducing communication overhead is paramount but conflictual to maintaining the model’s accuracy. Most research has dealt with the different factors influencing communication reduction separately without addressing their correlations. Moreover, most of them do not consider the heterogeneity of clients’ hardware. Finding the optimal configuration to fulfil all these training aspects can become intractable for classical techniques. This work explores the add-in that multi-objective evolutionary algorithms can provide for solving the communication overhead problem while achieving high accuracy. We do this by 1) realistically modelling and formulating this task as a multi-objective problem by considering the devices’ heterogeneity, 2) including all the communication-triggering aspects, and 3) applying a multi-objective evolutionary algorithm with an intensification operator to solve the problem. A simulated client–server architecture of four devices with four different processing speeds is studied. Both fully connected and convolutional neural network models are investigated with 33,400 and 887,530 weights, respectively. The experiments are performed using the MNIST and Fashion-MNIST datasets. A comparison is made between three approaches using an extensive set of metrics. Results prove that our approach obtains solutions with better accuracy than the full-communication setting and other methods while getting reductions in communications by around 1,000 times in most cases and up to 10,000 times in some cases compared to the maximum communication setting.

Discrete-variable gate-model quantum machines are promising quantum systems considering their wide applicability. Being in their noisy-intermediate-scale era, they allow executing only circuits of limited complexity and fitting the machines' features. Thus, such systems implement a key and unavoidable tailoring process to produce the most possible compact and device-compliant circuit. The qubits' initialisation is a primary and complex step that can ease/jeopardise the tailoring process and restrict/extend the machine's computational capacities. Ultimately, this bottleneck can be responsible of making quantum leaps like quantum supremacy. As a step towards the former, this work investigates how evolutionary algorithms can enhance the qubits' initialisation by tackling it as a single-objective problem using a genetic algorithm. The experiments used instances representing 19 real IBM quantum machines with 7 to 65 qubits and 9 different qubit topologies. Also, 76 GHZ circuits of sizes 7-65 qubits and 25%-100% of entanglement were created and studied. Extensive standard and statistical comparisons have been made against the IBM qubit initialiser that is currently used in real quantum machines. Results showed that the proposal outperforms IBM in 64 instances and is similar to it in 10 ones, with an average circuit-compression gain up to 46%.

Optimization of the production process is important for every factory or organization.The better organization can be done by optimization of the workforce planing.The main goal is decreasing the assignment cost of the workers with the help of which, the work will be done.The problem is NP-hard, therefore it can be solved with algorithms coming from artificial intelligence.The problem is to select employers and to assign them to the jobs to be performed.The constraints of this problem are very strong and for the algorithms is difficult to find feasible solutions.We apply Ant Colony Optimization Algorithm to solve the problem.We investigate the algorithm performance according evaporation parameter.The aim is to find the best parameter setting.

Every organization and factory optimize their production process with a help of workforce planing.The aim is minimization of the assignment costs of the workers, who will do the jobs.The problem is very complex and needs exponential number of calculations, therefore special algorithms are developed to be solved.The problem is to select employers and to assign them to the jobs to be performed.This problem has very strong constraints and it is difficult to find feasible solutions.The objective is to fulfil the requirements and to minimize the assignment cost.We propose a hybrid Ant Colony Optimization (ACO) algorithm to solve the workforce problem, which is a combination between ACO and an appropriate local search procedure.

The workforce planning helps organizations to optimize the production process with aim to minimize the assigning costs.A workforce planning problem is very complex and needs special algorithms to be solved.The problem is to select set of employers from a set of available workers and to assign this staff to the jobs to be performed.Each job requires a time to be completed.For efficiency, a worker must performs a minimum number of hours of any assigned job.There is a maximum number of jobs that can be assigned and a maximum number of workers that can be assigned.There is a set of jobs that shows the jobs on which the worker is qualified.The objective is to minimize the costs associated to the human resources needed to fulfill the work requirements.On this work we propose a variant of Ant Colony Optimization (ACO) algorithm to solve workforce optimization problem.The algorithm is tested on a set of 20 test problems.Achieved solutions are compared with other methods, as scatter search and genetic algorithm.Obtained results show that ACO algorithm performs better than other two algorithms.

This paper proposes a novel algorithm combining path relinking with a set of cooperating trajectory based parallel algorithms to yield a new metaheuristic of enhanced search features. Algorithms based on the exploration of the neighborhood of a single solution, like simulated annealing (SA), have offered accurate results for a large number of real-world problems in the past. Because of their trajectory based nature, some advanced models such as the cooperative one are competitive in academic problems, but still show many limitations in addressing large scale instances. In addition, the field of parallel models for trajectory methods has not deeply been studied yet (at least in comparison with parallel population based models). In this work, we propose a new hybrid algorithm which improves cooperative single solution techniques by using path relinking, allowing both to reduce the global execution time and to improve the efficacy of the method. We test here this new model using a large benchmark of instances of two well-known NP-hard problems: MAXSAT and QAP, with competitive results.

In this paper we design a new distributed genetic algorithm, which is able to self-adapt the value of one of the most important parameter in this kind of techniques using the information provided by theoretical models. We study different alternative ways to use the mathematical results in our genetic algorithm. We test our technique on a wide set of instances of the well-known MAX-SAT problem. Experiments show that our self-* proposal is able to obtain similar, or even better, results when it is compared to traditional algorithms whose setting is made by hand. We also show the benefits in terms of saving time and complexity of migration policy settings for distributed genetic algorithms without reducing their efficiency.

High computational requirements of current problems have driven most researches towards efficient processing formulations which require the use of multiple processors interconnected, this is the foundation of the parallel processing mechanism. Among the metrics to measure the performance of parallel algorithms, the most important and used is the speedup, but in the scientific community does not exist a consent on its definition and use. The aim of this work is to study different alternatives evaluating parallel metaheuristics. This report presents the results of several experimental tests to show the use of the speedup evaluating the same parallel distributed Genetic Algorithm in different ways, to solve MAXSAT problem. Our experiments show that depending on how the algorithm speedup is evaluated, different results can be obtained. Taking into account the test results we can conclude that the best scenario for evaluating parallel algorithms is comparing algorithms with the same accuracy, defining the quality of the solutions as stop condition, because all executions reach the optimal value allowing fair comparisons.

In this work we use mathematical models, based on the study of the dynamics of the distributed evolutionary algorithms (dEA), to design self adaptive migration schedule for dEAs. We test our technique on two different problems: MAXSAT (a variant of the satisfiability problem), and a large scale problem, namely the radio network design problem. Its results are compared against the best results produced by distributed configurations with traditional tuning (constant preset migration schedules). Our experiments show that the technique produces results close to the best results obtained with fixed schedules while reducing the heavy cost of the parameter tuning.

The Quadratic Assignment Problem (QAP) is a well-known NP-hard combinatorial optimization problem that is at the core of many real-world optimization problems. We prove that QAP can be written as the sum of three elementary landscapes when the swap neighborhood is used. We present a closed formula for each of the three elementary components and we compute bounds for the autocorrelation coefficient.

This paper presents a theoretical study about the selection pressure and the convergence speed of distributed evolutionary algorithms (dEA). In concrete, we model the best individual's growth curve and the takeover time for usual models of multipopulation EAs found in the literature. The calculation of the takeover time is a common analytical approach to measure the selection pressure of an EA. This work is another step forward to mathematically unify and describe the roles of all the parameters of the migration policy (the migration rate, the migration period, the topology, and the selection/replace schemes of immigrants) in the selection pressure induced by the dynamics of dEAs. In order to achieve these goals we analyze the behaviour of these algorithms and propose a mathematical formula which models that dynamic. The proposed mathematical model is later verified in practice.

Cellular genetic algoritms (cGAs) are characterized by its grid structure population, in which individuals can only interact with their neighbors. This kind of algorithms has demonstrated to have a high numerical performance thanks to the good exploration/exploitation balance they perform in the search space. Although cGAs seem very appropriate for parallelism, there is a low number of works proposing or studing parallel models for clusters of computers. This is probably because the model requires a high communication level between sub-populations due to the tight interactions among individuals. These parallel versions are however needed to cope with the high computational requirements of the current real-world problems. This article proposes a new parallel cellular genetic algorithm which maintains (or even improves because its asynchronicity) the numerical behaviour of a serial cGA, while at the same time it provokes an important reduction on the execution time for finding the optimal solution.

The DNA fragment assembly problem is to re construct a DNA chain from multiple fragments that have previously been sequenced in a laboratory. This is a critical step in any genomic project, since the resulting chains are the basis of all the work. Therefore, the quality of these chains is a prime importance to the correct development of the project. The methods typically applied to this problem usually encounter difficulties on large instances, so more efficient techniques are necessary. In this context, this work proposes a new method combining a general purpose metaheuristic (an advanced cellular genetic algorithm which automatically regulates the intensity of the search) with a local search method specifically designed for this problem (PALS). This local search method (recently published) finds very accurate solutions in very short times. As a result, our proposal is a very accurate and efficient hybrid technique clearly outperforming the other existing ones.

Many specific algorithms and metaheuristics have been proposed for solving the DNA fragment assembly problem, but new algorithms with more capacity for solving this problem are necessary. The fragment assembly problem consists in building the DNA sequence from several hundreds (or even, thousands) of fragments obtained by biologists in the laboratory. This is an important task in any genome project since the rest of the phases depend on the accuracy of the results of this stage. In order to achieve this objective we propose a hybrid algorithm that achieves very accurate results in comparison with other metaheuristics.

Workforce planning is an important activity that enables organizations to determine the workforce needed for a given task. Solving a workforce planning problem is a hard combinatorial process requiring modern techniques such advanced metaheuristics. In this work, we analyze several options to design a parallel genetic algorithm, which can find high-quality solutions to realistic size problem instances.

Workforce planning is an important activity that enables organizations to determine the workforce needed for continued success. A workforce planning problem is a very complex task that requires modern techniques to be solved adequately. In this work, we describe the development of two parallel metaheuristic methods, a parallel genetic algorithm and a parallel scatter search, which can find high-quality solutions to 20 different problem instances. Our experiments show that parallel versions do not only allow to reduce the execution time but they also improve the solution quality

This paper presents a study of different models for the best individual's growth curve and the takeover time in a distributed evolutionary algorithm (dEA). The calculation of the takeover time is a common analytical approach to measure the selection pressure of an EA. This work is another step forward to mathematically unify and describe the roles of several parameters of the migration policy: the migration rate, the migration frequency, and the topology in the selection pressure induced by the dynamics of dEAs. In order to achieve these goals we comparatively evaluate the appropriateness of the well-known panmictic logistic model, hypergraph model and two new models for dEAs. We introduce new accurate models for growth curves and takeover times in dEAs, and analytically explain the effects of the migration rate, migration frequency, and topology

As more research centers embark on sequencing new genomes, the problem of DNA fragment assembly for shotgun sequencing is growing in importance and complexity. Accurate and fast assembly is a crucial part of any sequencing project and since the DNA fragment assembly problem is NP-hard, exact solutions are very difficult to obtain. Various heuristics, including genetic algorithms, were designed for solving the fragment assembly problem. While the sequential genetic algorithm has given good results, it is unable to sequence very large DNA molecules. In this work, we present two parallel methods, a distributed genetic algorithm and a parallel simulated annealing, to solve problem instances that are 77K base pairs long accurately