Heat sinks are a prevalent and direct solution for addressing the Microelectronic Thermal Management Problem (MTMP), which is critical in today's electronic industry. Specifi-cally, an optimally designed thermodynamic heat sink ensures that microelectronics operate reliably without compromising their lifespan and performance, thereby indirectly safeguarding user safety. Although Metaheuristics (MHs) have proven effective in tackling this complex design challenge due to their robust characteristics, no single MH consistently delivers superior per-formance across all scenarios. The study explores the feasibility of an Automated Metaheuristic Design strategy, employing a hyper-heuristic search to develop a population-based, metaphor-free MH specifically for the MTMP. Various scenarios are assessed by varying the heat sink design specifications and benchmarking the custom MH designs against several state-of-the-art MHs. The findings of this preliminary work provide statistical evidence that the tailored MHs surpass the performance of established MHs in these scenarios. A toolkit of MH components is assembled, which can be customized to construct MHs specifically for MTMPs. This approach enables practitioners to select the most suitable solver for a particular problem without needing extensive expertise in heuristic-based optimization.

Effective optimization of model variables is essential yet demanding in engineering and industrial processes. Metaheuristics (MHs) offer a proficient approach, but their design and tuning incorporate notable challenges. Automated Algorithm Design (AAD) methodologies provide a solution by enabling automated algorithm construction. This study utilizes a Hyper-Heuristic (HH) framework within AAD, which obtains a tailored MH to optimize a Proportional, Integral, and Derivative (PID) controller in an Automatic Voltage Regulation (AVR) system. We identify a preference for search operators from Spiral Dynamic, Swarm Dynamic, and Differential Mutation families, offering valuable insights for MH algorithm design in complex electrical systems. Our contributions include a novel methodology for distilling search operators for specific problem families and presenting effective search operators for MHs in electrical engineering scenarios. The study highlights the importance of precise controller tuning, demonstrated through the effectiveness of the tailored MH compared to others.

Microgrids stand as an alternative for incorporating Renewable Energy Sources into the electrical grid, but they require an adequate control scheme. Although the literature contains plenty of alternatives, it lacks implementations of hybrid controllers based on Hyper-Heuristics (HHs). Hence, we analyze whether they are of benefit. Our goal is simple: to alternate through diverse controllers as the simulation progresses. To this end, we consider some simple sequence-based selection HHs and test them across 13 scenarios. Instead of the customary low-level heuristics, we use predefined controllers that were previously tuned through a Genetic Algorithm. For the most part, at least one of the proposed models outperforms the best available controller. Thus, using HHs as an advanced control scheme seems feasible and should be explored more deeply in future works.

Hyper-heuristics are a broad topic that has drawn increasing attention because of its flexibility. This, however, implies that there are diverse models, including selection hyper-heuristics, where the idea is to derive a model that learns when to use each available solver. Nonetheless, such a learning procedure usually proves difficult and leads to non-ideal selections. Hence, in this work, we propose a recursive hyper-heuristic model allowing more complexity within the selection models. Our idea is straightforward: to have a selection hyper-heuristic to select low-level heuristics and lower-level hyper-heuristics. In doing so, one can merge the combined decisions of existing solvers. We test the feasibility of such a model through experiments on the Job Shop Scheduling Problem that cover small and large datasets of previously tailored instances. We found that increasing the order of the model leads to more stable and better-performing approaches. For example, migrating from a second-order hyper-heuristic to a fourth-order hyper-heuristic reduced the makespan by over 6%. Thus, the proposed model seems feasible and should be further tested under more varied scenarios and conditions.

It is no secret that optimisation is a popular topic in any practical engineering application. Similarly, Metaheuristics (MHs) are a fairly standard approach for solving optimisation problems due to their success, flexibility, and simplicity. However, it is seldom easy to find a solver from the overpopulation of metaheuristics that adequately deals with a given problem. For that reason, the solver selection is even considered an additional problem in many optimisation scenarios. This work investigates the Metaheuristic Composition Optimisation Problem, which involves designing heuristic-based procedures that solve continuous optimisation problems. Therefore, we propose two novel and still simple methodologies based on transfer learning to facilitate the automatic generation of population-based and metaphor-less MHs by using search operators from the literature. To represent these solvers, we adopt our previously proposed unfolded MH model. The first strategy deals with the problem dynamically, building the sequence while solving the low-level problem. In contrast, the second one does it statically by generating the whole candidate sequence before implementing it. Results provide us with information to prove the feasibility of these approaches via experiments using 32 problems with four different characteristic groups and four dimensionalities and varying the number of agents (30, 50, and 100) employed by the search operators. We also remark that one can compare these two methodologies on performance, but we emphasise their potential usage depending on the general application environment.

Metaheuristics (MHs) are proven powerful algorithms for solving non-linear optimisation problems over discrete, continuous, or mixed domains. Applications have ranged from basic sciences to applied technologies. Nowadays, the literature contains plenty of MHs based on exceptional ideas, but often, they are just recombining elements from other techniques. An alternative approach is to follow a standard model that customises population-based MHs, utilising simple heuristics extracted from well-known MHs. Different approaches have explored the combination of such simple heuristics, generating excellent results compared to the generic MHs. Nevertheless, they present limitations due to the nature of the metaheuristic used to study the heuristic space. This work investigates a field of action for implementing a model that takes advantage of previously modified MHs by learning how to boost the performance of the tailoring process. Following this reasoning, we propose a hyper-heuristic model based on Artificial Neural Networks (ANNs) trained with processed sequences of heuristics to identify patterns that one can use to generate better MHs. We prove the feasibility of this model by comparing the results against generic MHs and other approaches that tailor unfolded MHs. Our results evidenced that the proposed model outperformed an average of 84 % of all scenarios; in particular, 89 % of basic and 77 % of unfolded approaches. Plus, we highlight the configurable capability of the proposed model, as it shows to be exceptionally versatile in regards to the computational budget, generating good results even with limited resources.

Metaheuristics are a fairly standard approach for solving optimisation problems due to their success, flexibility, and simplicity. However, there is a plethora of metaheuristics available, with different performance levels for various problems. This work proposes a methodology for designing heuristic-based procedures to solve continuous optimisation problems and study how the population size affects its performance. The technique comprises the well-known Simulated Annealing algorithm as a hyper-heuristic, and a heuristic sequence taken from unfolding the conventional scheme of population-based metaheuristics reported in the literature. Our results show that the proposed approach is a reliable alternative for tackling optimisation problems. We find exciting insights, according to our data, about this primary implementation when varying the population size in different challenging problems.

Literature is prolific with metaheuristics for solving continuous optimisation problems. But, in practice, it is difficult to choose one appropriately. Moreover, it is necessary to determine a good enough set of parameters for the selected approach. Hence, this work proposes a strategy based on a hyper-heuristic for tailoring population-based metaheuristics. Besides, our approach considers search operators from well-known techniques as building blocks for new ones. We test this strategy through four benchmark functions and by varying their dimensions. We obtain metaheuristics with diverse configurations. We observe a possible performance boost when two or more search operators are considered. This could be due to previously unexplored interactions between such operators.

This study presents an offline learning Simulated Annealing approach to generate a constructive hyper-heuristic evaluated through training and testing on a set of instances for solving the Job-Shop Scheduling problem. The generated hyperheuristic uses a range of state features to control a set of low-level constructive heuristics. A hyper-heuristic is represented in terms of a set of rules, where each rule contains a fixed set of values for the features in consideration and the low level heuristic to be invoked. At each constructive step, the `closest' rule is selected and then the corresponding constructive low level heuristic is applied. Our distance metric is the Euclidean distance between the values within the rule and the state features characterising the partial schedule along with the remaining jobs to be scheduled for the partial solution. In this paper, we study a set of features computed with various well-known metrics and different feature transformation methods for improving the characterization of the problem instances and solutions to Job-Shop Scheduling as a part of our approach. Eight different scenarios are evaluated on a set of randomly generated problem instances. Each scenario represents a distinct approach combining a different feature transformation applied during the training and testing phases. The empirical results show that transformations can improve the spread of feature values and the choice of the transformation methods is influential on the performance of the overall approach. A particular choice generates a slightly better performance when compared to the standard approach, which uses the original features at all times, indicating the potential of the proposed approach for the future studies.

Hyper-heuristics are potent techniques that represent the synergy of low-level heuristics when solving optimization problems. This synergy usually leads to better solutions. Similarly, fuzzy logic has been successfully applied to several domains, thanks to the expert knowledge it encompasses. Thus, combining the benefits of both approaches should lead to a more reliable and effective method. Hence, in this work, we propose a fuzzy-based selection hyper-heuristic model. We considered seven features and four low-level heuristics, which represent the inputs and output of the fuzzy inference system, respectively. Each input was defined with two membership functions. Since there is no expert knowledge available, we lay out all the rules (128) and use a genetic algorithm to find optimum values for the consequents of these rules. In other words, the genetic algorithm will evolve the rules of the fuzzy inference system until it become an expert, and will then save such knowledge as the set of fuzzy rules. The main concern of this paper is to find out if a fuzzy inference system can help to get better results in the inner working of a hyperheuristic. To prove this, we make a comparison between a fuzzy hyper-heuristic model optimized by a genetic algorithm against three traditional selection hyper-heuristic models (with a different number of rules) optimized by a particle swarm optimization method. We applied all these methods using the same set of low-level heuristics to solve an 800 instance set of the 0-1 Knapsack problem as a testbed.

Recent years have witnessed an escalating interest for methods that automatically adapt to different types of problems. In this regard, the term hyper-heuristics-heuristics that either select or generate new heuristics-is a relevant concept. Experimental evidence supports the idea that hyperheuristics can outperform single, isolated heuristics. However, commonly used hyper-heuristic models require several inputs. One of them is a set of features that accurately characterize the instances, which limits their applicability. Thus, in this work, we analyze how to implement a simple evolutionary algorithm to produce feature-independent hyper-heuristics. We compare its performance against that of simple heuristics, for the domain of the knapsack problem. Our research focuses on two elements: performance and frequency. In the former, we analyze how the performance of the learning stage varies across different scenarios. In the latter, we examine how frequently heuristics interact within the hyper-heuristic. We show that the proposed hyper-heuristic model solves most of the instances considered in this work. Moreover, it does so more efficiently than isolated heuristics. At the same time, the model offers a straightforward parameter setting and requires little or no problem characterization, which simplifies its use on new problem domains.

It is common to find that training of selection hyper-heuristics is done perturbatively. The process usually starts with a random selection module and iterates over a set of instances until finding appropriate values for such module. In this work, however, we present a model for creating selection hyper-heuristics constructively. To achieve so, we use a set of instances evolved for such a task. For each low-level heuristic, we evolved a set of problem instances that are more easily solvable by that particular heuristic (compared to the other ones). Each group contains instances easily solvable with the corresponding heuristic but not with the remaining ones. Thus, our model creates its selector by calculating the centroid of each group. For doing so, the model defines a rule that maps said centroid to one corresponding action (in this case, a low-level heuristic). To test our approach, we select the one-dimensional Bin Packing Problem and set four target performance levels (which we refer to as deltas) for instance generation. Then, we analyze all the possible combinations of deltas. We study how performance of the generated hyper-heuristics shift when they are created using a different number of instances. Our data shows the feasibility of creating a hyper-heuristic under the stated conditions. Effectiveness of the model depends on the deltas used though we observed that higher deltas are useful while lower deltas are not. For example, when considering a delta level of 2.0, our method produced hyper-heuristics with an accumulated average waste 12% lower than that of the best heuristic. But, for a delta level of 0.5, it became impossible to outperform the heuristics.

Job Shop Scheduling problems (JSSPs) have become increasingly popular due to their application in supply chain systems. Several solution approaches have appeared in the literature. One of them is the use of low-level heuristics. These methods approximate a solution but only work well on some kind of problems. Hence, combining them may improve performance. In this paper, we use the classical stochastic local optimization algorithm Simulated Annealing to train a selection hyper-heuristic for solving JSSPs. To do so, we use an instance generator provided in literature to create training sets with a different number of instances: 20, 40, and 60. In addition, we select instances from the literature to create two test scenarios, one similar to the training instances, and another with bigger problems. Our results suggest that training with the highest number of instances lead to better and more stable hyper-heuristics. For example, in the first test scenario, we achieved a reduction in the data range of over 60% and an improvement in the median performance of almost 30%. Moreover, under these conditions about 75% of the generated hyper-heuristics were able to perform equal to or better than the best heuristic. Even so, less than 25% were able to outperform the synthetic Oracle. Because of the aforementioned, we strongly support the idea of using a selection hyper-heuristic model powered by Simulated Annealing for creating a high-level solver for Job Shop Scheduling problems.

The assessment of strengths and weaknesses of a solver is often limited by the diversity of the cases where it is tested upon. As such, it is paramount to have a versatile tool which finds the problem instances where such a solver excels/fails. In this manuscript, we propose to use an evolutionary algorithm for creating this tool. To validate our approach, we conducted several tests on four heuristics for the knapsack problem. Although, the process can be extended to other domains with relatively few changes. The tests cover different sets of instances, both favoring the performance of one heuristic while hindering that of the remaining ones, and vice versa. To further test our evolutionary-based model, we also apply it on a recent approach that combines the strengths of different heuristics to improve its performance (usually referred to as a hyper-heuristic). We show that it is possible to tailor instances in which even this more complex model excels/fails. Throughout our approach, a researcher can test a solver under different kinds of scenarios, delving deeper into the conditions that make it perform well/poorly. Therefore, we recommend using the proposed approach as a means to grasp better insights about strengths and weaknesses of different solvers.

Hyper-heuristics are powerful search methodologies that can adapt to different kinds of problems. One element of paramount importance, however, is the selection module that they incorporate. Traditional approaches define a set of features for characterizing a problem and, thus, define how to best solve it. However, some features may vary nonlinearly as the solver progresses, requiring higher resolution in specific areas of the feature domain. This work focuses on assessing the advantage of using feature transformations to improve the given resolution and, as a consequence, to improve the overall performance of a hyper-heuristic. We provide evidence that using feature transformations may result in a better discrimination of the problem instance and, as consequence, a better performance of the hyper-heuristics. The feature transformation strategy was applied to an evolutionary-based hyper-heuristic model taken from the literature and tested on constraint satisfaction problems The proposed strategy increased the median success rate of hyper-heuristics by more than 13% and reduced its standard deviation in about 7%, while reducing the median number of adjusted consistency checks by almost 30%.

Hyper-heuristics have emerged as an important strategy for combining the strengths of different heuristics into a single method. Although hyper-heuristics have been found to be successful in many scenarios, little attention has been paid to the subsets of heuristics that these methods manage and apply. In several cases, heuristics can interfere with each other and can be harmful for the search. Thus, obtaining information about the differences among heuristics, and how they contribute to the search process is very important. The main contribution of this paper is an automatic heuristic-filtering process that allows hyper-heuristics to exclude heuristics that do not contribute to improving the solution. Based on some previous works in feature selection, two methods are proposed that rank heuristics and sequentially select only suitable heuristics in a hyper-heuristic framework. Our experiments over a set of Constraint Satisfaction Problem instances show that a hyper-heuristic with only selected heuristics obtains significantly better results than a hyper-heuristic containing all heuristics, in terms of running times. In addition, the success rate of solving such instances is better for the hyper-heuristic with the suitable heuristics than for the hyper-heuristic without our proposed filtering process.

Nowadays, heuristics represent a commonly used alternative to solve complex optimization problems. This, however, has given rise to the problem of choosing the most effective heuristic for a given problem. In recent years, one of the most used strategies for this task has been the hyper-heuristics, which aim at selecting/generating heuristics to solve a wide range of optimization problems. Most of the existing selection hyper-heuristics attempt to recommend only one heuristic for a given instance. However, for some classes of problems, more than one heuristic can be suitable. With this premise, in this paper, we address this issue through an evolutionary multilabel learning approach for building hyper-heuristics. Unlike traditional approaches, in the multilabel formulation, the result could not be a single recommendation, but a set of potential heuristics. Due to the fact that cooperative coevolutionary algorithms allow us to divide the problem into several subproblems, it results in a natural approach for dealing with multilabel classification. The proposed cooperative coevolutionarymultilabel approach aims at choosing the most relevant patterns for each heuristic. For the experimental study included in this paper, we have used a set of constraint satisfaction problems as our study case. Our experimental results suggest that the proposed method is able to generate accurate hyper-heuristics that outperform reference methods.

Constraint satisfaction problems (CSP) are defined by a set of variables, where each variable contains a series of values it can be instantiated with. There is a set of constraints among the variables that restrict the different values they can take simultaneously. The task is to find one assignment to all the variables without breaking any constraint. To solve a CSP instance, a search tree is created where each node represents a variable of the instance. The order in which the variables are selected for instantiation changes the form of the search tree and affects the cost of finding a solution. Many heuristics have been proposed to help to decide the next variable to instantiate during the search and they have proved to be helpful for some instances. In this paper we explore the use of learning classifier systems to construct selective hyper-heuristics that dynamically select, from a set of variable ordering heuristics for CSPs, the one that best matches the current problem state in order to perform well on a wide range of instances. During a training phase, the system constructs state-heuristic rules as it explores the search space. Heuristics with good performance at certain points are rewarded and become more likely to be applied in similar situations. The approach is tested on random instances, providing promising results with respect to the median performance of the variable ordering heuristics used in isolation.

Variable ordering has been a recurrent topic of study in the field of constraint satisfaction because of its impact in the cost of the search. Various variable ordering heuristics have been proposed to help guiding the search under different situations. One important direction of the study about variable ordering is the use of distinct heuristics as the search progresses to reduce the cost of the search. Even though the idea of combining heuristics goes back to the 60's, only a few works that study which heuristics to use and how they interact with each other have been described. In this investigation, we analyse the interactions of four important variable ordering heuristics by combining them through hyper-heuristics that decide the heuristic to apply based on the depth of the nodes in the search tree. The paper does not include any specific model for generating such hyperheuristics; instead, it presents an analysis of the changes in the cost when different heuristics are applied during the search by using one simple hyper-heuristic representation. The results show that selectively applying distinct heuristics as the search progresses may lead to important reductions in the cost of the search with respect to the performance of the same heuristics used in isolation.

In computer science it is a common practice to evaluate the performance of algorithms using a set of benchmark or randomly generated instances. However, following that approach, the weaknesses of the algorithms may not be exposed. This work is the first phase of research project on coevolution of solutions methods versus problem instances. The goal of study is to generate a method to find difficult to solve problem instances capable of challenging the solution methods or algorithms under analysis, helping to discover opportunities for improvement. An evolutionary model is proposed to find hard binary constraint satisfaction problem instances for different variable ordering heuristics. We characterize the search space by generating random instances with different values for the constraint density and tightness. For all the heuristics, the most difficult problems are located in the same region of the space near to the phase transition. However, there are certain regions of the search space where a heuristic dominates the others, especially where the problems are solvable. Finally, we compare the hardest instances found during the search space exploration with the outcome instances of the evolutionary model. The results show that evolved instances are harder to solve than the ones randomly generated.

Hyper-heuristics enable us to selectively apply the most suitable low-level heuristic depending on the properties of the problem at hand. They can be used for solving Constraint Satisfaction Problems (CSP) in different ways considering the variety of hyper-heuristics and low-level heuristics. A particular approach which has been receiving attention in the recent years is based on variable ordering using hyper-heuristics. A hyper-heuristic decides the next variable to process using a set of predefined heuristics considering the features that describe the instance at a given point during the search in this framework. This study explores an approach in which each hyper-heuristic is represented as a set of vectors mapping instance features to heuristics for variable ordering. The results suggest that the proposed approach is able to combine the strengths of different heuristics and compensate for their weaknesses performing better than each heuristic in isolation across a range of instances.

Hyper-heuristics are high level search methodologies that operate over a set of heuristics which operate directly on the problem domain. In one of the hyper-heuristic frameworks, the goal is automating the process of selecting a human-designed low level heuristic at each step to construct a solution for a given problem. Constraint Satisfaction Problems (CSP) are well know NP complete problems. In this study, behaviours of two variable ordering heuristics Max-Conflicts (MXC) and Saturation Degree (SD) with respect to various combinations of constraint density and tightness values are investigated in depth over a set of random CSP instances. The empirical results show that the performance of these two heuristics are somewhat complementary and they vary for changing constraint density and tightness value pairs. The outcome is used to design three hyper-heuristics using MXC and SD as low level heuristics to construct a solution for unseen CSP instances. It has been observed that these hyper-heuristics improve the performance of individual low level heuristics even further in terms of mean consistency checks for some CSP instances.

This paper introduces a neuro-evolutionary approach to produce hyper-heuristics for the dynamic variable ordering for hard binary constraint satisfaction problems. The model uses a GA to evolve a population of neural networks architectures and parameters. For every cycle in the GA process, the new networks are trained using backpropagation. When the process is over, the best trained individual in the last population of neural networks represents the general hyper-heuristic.

The idea behind hyper-heuristics is to discover some combination of straightforward heuristics to solve a wide range of problems. To be worthwhile, such combination should outperform the single heuristics. This paper presents a GA-based method that produces general hyper-heuristics for the dynamic variable ordering within Constraint Satisfaction Problems. The GA uses a variable-length representation, which evolves combinations of condition-action rules producing hyper-heuristics after going through a learning process which includes training and testing phases. Such hyper-heuristics, when tested with a large set of benchmark problems, produce encouraging results for most of the cases. The testebed is composed of problems randomly generated using an algorithm proposed by Prosser.