Fog computing providers have started providing services in closer proximity to the users by leasing the unused computational resources of users' devices. The leased devices are increasingly used for many time-sensitive and IoT applications. Despite the advantages of Fog, due to the highly mobile and dynamic nature of Fog devices, the resources or devices may fail at any time or may not always be available for the processing of the applications, which leads to degradation of service quality and an increase in application processing time. Hence, effective selection of the resources in the Fog computing environment by considering mobility, heterogeneity, and failure of devices is a complex task. Traditional resource selection techniques may not be applied directly in Fog computing environments due to their dynamic and unique resource characteristics. Therefore, this article proposes a Markov chain-based resource selection model to improve the quality of service by minimizing disruptions and managing device failures. The effectiveness of the proposed algorithm is evaluated using simulations, which take failure traces, current resource usage, and mobility as input from a dataset archive. Our results demonstrate the effectiveness of the proposed algorithm in terms of average disruption rates, average latency, and average overutilization. Our analysis shows significant improvements in average latency reduction of approximately 11.83%, and an average overutilization improvement by 16.17%.

The rate of Successful Exploration is related to the proportion of search solutions from fitter attraction basins that are fitter than the current reference solution. A reference solution that moves closer to its local optimum (i.e. experiences exploitation) will reduce the proportion of these fitter solutions, and this can lead to decreased rates of Successful Exploration/increased rates of Failed Exploration. This effect of Fitness-Based Selection is studied in Particle Swarm Optimization and Differential Evolution with increasing dimensionality of the search space. It is shown that increasing rates of Failed Exploration represent another aspect of the Curse of Dimensionality that needs to be addressed by metaheuristic design.

It is well known that metaheuristics for numerical optimization tend to decrease in performance as dimensionality increases. These effects are commonly referred to as “The Curse of Dimensionality”. An obvious change to search spaces with increasing dimensionality is that their volume grows exponentially, and this has led to large amounts of research on improved exploration. A recent insight is that the shape of attraction basins can also change drastically with increasing dimensionality, and this has led to selection-based approaches to combat the Curse of Dimensionality. Average-Fitness Based Selection is introduced as a means to reduce the selection errors caused by Fitness-Based Selection. Experimental results show that the rate of selection errors grows much more slowly for Average-Fitness Based Selection with Increasing dimensionality.

Random walks are a useful modeling tool for stochastic processes. The addition of model features (e.g. finite travel in one direction) can provide insight into specific practical situations (e.g. gambler's ruin). A series of random walk experiments are designed to study the effects of selection, exploration, and exploitation during the search processes of metaheuristics. We present a set of random walk conditions which leads to greater movement as the dimensionality of the sampling distributions increases. We then implement a version of Simulated Annealing in a similar search space which also achieves improving performance with increasing dimensionality. Conversely, we show that standard Particle Swarm Optimization has decreasing performance with increasing dimensionality which is consistent with the expected effects of the Curse of Dimensionality. These experiments give us insights into future methods that metaheuristics might be able to employ to defeat the Curse of Dimensionality (in globally convex, continuous domain search spaces).

Fog computing is an increasingly popular method with which to process the huge amount of data generated by the Internet of Things (IoT) devices and applications at the edge-level, using the heterogeneous autonomous end-devices of the participating users. To meet the requirements of the IoT and time-sensitive applications, a Fog computing platform needs to select appropriate resources, the availability of which can be guaranteed during the execution of the application. For the proper selection of resources, the platform must be able to predict future availability. Hence, a proper resource availability model which provides knowledge about the future availability of resources in the Fog computing environment is required. However, designing an efficient resource availability model, in a highly distributed and mobile environment like the Fog, is a complex task due to the multidimensional characteristics of Fog devices, such as mobility, lack of centralised control, limited resources, and being battery powered. Existing resource availability models did not consider all the characteristics of a real Fog environment. Therefore, this study aims to provide a generic continuous-time Markov chain (CTMC), based resource availability model for Fog computing environments. The applicability of the model is shown by integrating the model input with the nearest-location best fit (NLBF) and Best-Fit resource selection policies.

With the increasing number of Internet of Things (IoT) devices, the volume and variety of data being generated by these devices are increasing rapidly. Cloud computing cannot process this data due to its high latency and scalability. In order to process this data in less time, fog computing has evolved as an extension to Cloud computing. In a fog computing environment, a resource monitoring service plays a vital role in providing advanced services, such as scheduling, scaling and migration. Most of the research in fog computing has assumed that a resource monitoring service is already available. Conventional methods proposed for other distributed systems may not be suitable due to the unique features of a fog environment. To improve the overall performance of fog computing and to optimise resource usage, effective resource monitoring techniques are required. Hence, we propose a support and confidence based (SCB) technique which optimises the resource usage in the resource monitoring service. The performance of our proposed system is evaluated by examining a real-time traffic use case in a fog emulator with synthetic data. The experimental results obtained from the fog emulator show that the proposed technique consumes 19 percent lesser resources compared with the existing technique.

The goal of exploration to produce diverse search points throughout the search space can be countered by the goal of selection to focus search around the fittest current solution(s). In the limit, if all exploratory search points are rejected by selection, then the behaviour of the metaheuristic will be equivalent to one which performs no exploration at all (e.g. hill climbing). The effects of selection on exploration are clearly important, but our review of the literature indicates limited coverage. To address this deficit, we introduce new experiments which can specifically highlight the occurrence of “failed exploration” and its effects through selection that can trap a metaheuristic in a less promising part of the search space. We subsequently propose new lines of research to reduce the effects of selection and failed exploration which we believe are distinctly different from traditional lines of research to increase (pre-selection) exploration.

This study uses a real-coded representation to encode discrete strategies for playing a simple grid based game. This representation is able to adapt itself on the fly to the local situation in the game. This adaptability makes the representation particularly suitable for finding good play strategies which, in turn, permit us to explore biases in the play strategies and even to compare instances of the game for difficulty. Variability in the best results achieved by the solver can be used to gauge difficulty, while the shape of the distribution of best results can indicate how interesting an instance is. Results indicate that the variety and combination of affordances produce instances of the game with varying degrees of anticipated difficulty and interestingness, and confirm that the solver can be used to evaluate the quality of different affordance combinations for producing good game instances. Design principles may also be discovered through post hoc analysis of instances with high or low average best score.

This study compares an adaptive and a nonadaptive representation for finding long walks on obstructed grids. This process models adaption of a simple plant to an environment where the plant's ability to grow is impeded by obstructions such as resource poor areas like bare rock. The intent of the adaptive representation is to model the biological phenomenon of phenotypic plasticity in which gene regulation is at least partially in response to environmental cues, in this case the obstructions. The adaptive representation is found to have a substantial advantage, with the greatest level of advantage at intermediate levels of obstruction. Agents are asked to solve multiple problem instances simultaneously (i.e. using the same chromosome). The advantage of the adaptive representation is also found to be higher when more boards are used in fitness evaluation.

The use of water resources for agricultural purposes, particularly in arid and semi-arid regions, is a matter of increasing concern across the world. Optimisation techniques can play an important role in improving the allocation of land to different crops, based on a utility function (such as net revenue) and the water resources needed to support these. Recent work proposed a model formulation for an agricultural region in the Murrumbidgee Irrigation Area of the Murray-Darling River basin in Australia, and found that the well-known NSGA-II technique could produce sensible crop mixes while preserving ground and surface water for environmental purposes. In the present study we apply Differential Evolution using two different solution representations, one of which explores the restricted space in which no land is left fallow. The results improve on those of the prior NSGA-II and demonstrate that a combination of solution representations allows Differential Evolution to more thoroughly explore the multiobjective space of profit versus environment.

This study is the second using real-coded representation for problems usually solved with a discrete coding. The adaptive generative representation is able to adapt itself on the fly to prior parts of the construction of an object as it assembles it. In the initial study the ability of the representation to take user supplied or problem supplied biases that change its behavior was demonstrated but not explored. In this study the bias is used to change the way evolution explores a fitness landscape for both an RFID antenna design problem and small instances of the traveling salesman problem. Addition of a bias to two different generative representations promotes the evolution of longer antenna designs (a heuristic objective associated with good antennas) while leading the algorithm to generate designs with distinctive shape characteristics. For the traveling salesman, a simple inverse-distance bias for the adaptive generative representation causes a large improvement in performance over a random key representation in 99 of 100 instances studied.

This study introduces a novel generative representation that is able to modify its expression in response to admissibility constraints that unfold as solutions are generated. The effect is that this self-adaptation in expression makes many inadmissible structures impossible to encode. The resulting reduction in the effective size of the search space yields performance increases amounting to several orders of magnitude for some problems. In addition to defining and exploring the capabilities of the self-adaptive representation, a technique for biasing its expression with numerical weights that strongly influences which optima are located is introduced. This both permits enhancement of optima with desirable properties and permits the inclusion of domain knowledge to improve performance. The test problems used are the self-avoiding walk problem, a surrogate for RFID tag antenna design, and the Towers of Hanoi problem.

Solution representation can have a large impact on the performance of heuristic solvers. When tackling bounded self-avoiding walk problems, such as the meander line RFID antenna design problem, solutions may be represented in terms of the absolute or relative direction of travel at each step. Encoding these instructions in a continuous space is required in order to apply continuous solvers, but also allows for an adaptive interpretation of each instruction that promotes longer paths. Using path length as a proxy for antenna quality, this work demonstrates that the adaptive solution representations outperform their non-adaptive counterparts, and that starting from a corner node in the square design space positively influences algorithm performance. The superior performance of a relative encoding over an absolute one is confirmed, in both the single objective of maximising path length and in a substantial investigation of the multi-objective antenna design problem. In the multi-objective case, simplifying the problem by fixing the antenna start node can assist the algorithm to perform well, but allowing the algorithm to evolve antennas starting from any point leads to more consistent results.

When optimizing multi-modal spaces, effective search techniques must carefully balance two conflicting tasks: exploration and exploitation. The first refers to the process of identifying promising areas in the search space. The second refers to the process of actually finding the local optima in these areas. This balance becomes increasingly important in stochastic search, where the only knowledge about a function's landscape relies on the relative comparison of random samples. Thresheld convergence is a technique designed to effectively separate the processes of exploration and exploitation. This paper addresses the design of thresheld convergence in the context of evolution strategies. We analyze the behavior of the standard (μ, λ)-ES on multi-modal landscapes and argue that part of it's shortcomings are due to an ineffective balance between exploration and exploitation. Afterwards we present a design for thresheld convergence tailored to ES, as a simple yet effective mechanism to increase the performance of (μ, λ)-ES on multimodal functions.

Optimisation in multimodal landscapes involves two distinct tasks: identifying promising regions and location of the (local) optimum within each region. Progress towards the second task can interfere with the first by providing a misleading estimate of a region's value. Thresheld convergence is a generally applicable “meta”-heuristic designed to control an algorithm's rate of convergence and hence which mode of search it is using at a given time. Previous applications of thresheld convergence in differential evolution (DE) have shown considerable promise, but the question of which threshold values to use for a given (unknown) function landscape remains open. This work explores the use of clustering-based method to infer the distances between local optima in order to set a series of decreasing thresholds in a multi-start DE algorithm. Results indicate that on those problems where normal DE converges, the proposed strategy can lead to sizable improvements.

Many heuristic search techniques have concurrent processes of exploration and exploitation. In particle swarm optimization, an improved pbest position can represent a new more promising region of the search space (exploration) or a better solution within the current region (exploitation). The latter can interfere with the former since the identification of a new more promising region depends on finding a (random) solution in that region which is better than the current pbest. Ideally, every sampled solution will have the same relative fitness with respect to its nearby local optimum - finding the best region to exploit then becomes the problem of finding the best random solution. However, a locally optimized solution from a poor region of the search space can be better than a random solution from a good region of the search space. Since exploitation can interfere with subsequent/concurrent exploration, it should be prevented during the early stages of the search process. In thresheld convergence, early exploitation is “held” back by a threshold function. Experiments show that the addition of thresheld convergence to particle swarm optimization can lead to large performance improvements in multi-modal search spaces.

During the search process of differential evolution (DE), each new solution may represent a new more promising region of the search space (exploration) or a better solution within the current region (exploitation). This concurrent exploitation can interfere with exploration since the identification of a new more promising region depends on finding a (random) solution in that region which is better than its target solution. Ideally, every sampled solution will have the same relative fitness with respect to its nearby local optimum - finding the best region to exploit then becomes the problem of finding the best random solution. However, differential evolution is characterized by an initial period of exploration followed by rapid convergence. Once the population starts converging, the difference vectors become shorter, more exploitation is performed, and an accelerating convergence occurs. This rapid convergence can occur well before the algorithm's budget of function evaluations is exhausted; that is, the algorithm can converge prematurely. In thresheld convergence, early exploitation is “held” back by a threshold function, allowing a longer exploration phase. This paper presents a new adaptive thresheld convergence mechanism which helps DE achieve large performance improvements in multi-modal search spaces.

Particle Swarm Optimization (PSO) is a popular algorithm used extensively in continuous optimization. One of its well-known drawbacks is its propensity for premature convergence. Many techniques have been proposed for alleviating this problem. One of the alternative approaches is hybridization. Genetic Algorithms (GA) are one of the possible techniques used for hybridization. Most often, a mutation scheme is added to the PSO, but some applications of crossover have been added more recently. Some of these schemes use adaptive parameterization when applying the GA operators. In this work, adaptively parameterized mutation and crossover operators are combined with a PSO implementation individually and in combination to test the effectiveness of these additions. The results indicate that an adaptive approach with position factor is more effective for the proposed PSO hybrids. Compared to single PSO with adaptive inertia weight, all the PSO hybrids with adaptive probability have shown satisfactory performance in generating near-optimal solutions for all tested functions.

Ant Colony Optimisation (ACO) algorithms use two heuristics to solve computational problems: one long-term (pheromone) and the other short-term (local heuristic). This paper details the development of antennation, a mid-term heuristic based on an analogous process in real ants. This is incorporated into ACO for the Travelling Salesman Problem (TSP). Antennation involves sharing information of the previous paths taken by ants, including information gained from previous meetings. Antennation was added to the Ant System (AS), Ant Colony System (ACS) and Ant Multi-Tour System (AMTS) algorithms. Tests were conducted on symmetric TSPs of varying size. Antennation provides an advantage when incorporated into algorithms without an inbuilt exploration mechanism and a disadvantage to those that do. AS and AMTS with antennation have superior performance when compared to their canonical form, with the effect increasing as problem size increases.

Stochastic search techniques for multi-modal search spaces require the ability to balance exploration with exploitation. Exploration is required to find the best region, and exploitation is required to find the best solution (i.e. the local optimum) within this region. Compared to hill climbing which is purely exploitative, simulated annealing probabilistically allows “backward” steps which facilitate exploration. However, the balance between exploration and exploitation in simulated annealing is biased towards exploitation - improving moves are always accepted, so local (greedy) search steps can occur at even the earliest stages of the search process. The purpose of “thresheld convergence” is to have these early-stage local search steps “held” back by a threshold function. It is hypothesized that early local search steps can interfere with the effectiveness of a search technique's (concurrent) mechanisms for global search. Experiments show that the addition of thresheld convergence to simulated annealing can lead to significant performance improvements in multi-modal search spaces.

Differential evolution (DE) is a widely-effective population-based continuous optimiser that requires convergence to automatically scale its moves. However, once its population has begun to converge its ability to conduct global search is diminished, as the difference vectors used to generate new solutions are derived from the current population members' positions. In multi-modal search spaces DE may converge too rapidly, i.e., before adequately exploring the search space to identify the best region(s) in which to conduct its finer-grained search. Traditional crowding or niching techniques can be computationally costly or fail to compare new solutions with the most appropriate existing population member. This paper proposes a simple intervention strategy that compares each new solution with the population member it is most likely to be near, and prevents those moves that are below a threshold that decreases over the algorithm's run, allowing the algorithm to ultimately converge. Comparisons with a standard DE algorithm on a number of multi-modal problems indicate that the proposed technique can achieve real and sizable improvements.

Standard particle swarm optimization cannot guarantee convergence to the global optimum in multi-modal search spaces, so multiple swarms can be useful. The multiple swarms all need initial positions and initial velocities for their particles. Several simple strategies to select initial positions and initial velocities are presented. A series of experiments isolates the effects of these selected initial positions and velocities compared to random initial positions and velocities. A first set of experiments shows how locust swarms benefit from "scouting" for initial positions and the use of initial velocities that "launch away" from the previous optimum. A second set of experiments show that the performance of WoSP (Waves of Swarm Particles) can be improved by using new search strategies to select the initial positions and initial velocities for the particles in its sub-swarms.

Differential evolution (DE) has been traditionally applied to solving benchmark continuous optimisation functions. To enable it to solve a combinatorially oriented design problem, such as the construction of effective radio frequency identification antennas, requires the development of a suitable encoding of the discrete decision variables in a continuous space. This study introduces an encoding that allows the algorithm to construct antennas of varying complexity and length. The DE algorithm developed is a multiobjective approach that maximises antenna efficiency and minimises resonant frequency. Its results are compared with those generated by a family of ant colony optimisation (ACO) metaheuristics that have formed the standard in this area. Results indicate that DE can work well on this problem and that the proposed solution encoding is suitable. On small antenna grid sizes (hence, smaller solution spaces) DE performs well in comparison to ACO, while as the solution space increases its relative performance decreases. However, as the ACO employs a local search operator that the DE currently does not, there is scope for further improvement to the DE approach.

The automotive deployment problem is a real-world constrained multiobjective assignment problem in which software components must be allocated to processing units distributed around a car's chassis. Prior work has shown that evolutionary algorithms such as NSGA-II can produce good quality solutions to this problem. This paper presents a population-based ant colony optimisation (PACO) approach that uses a single pheromone memory structure and a range of local search operators. The PACO and prior NSGA-II are compared on two realistic problem instances. Results indicate that the PACO is generally competitive with NSGA-II and performs more effectively as problem complexity---size and number of objectives---is increased.

Common explanations of DE's search behaviour as its crossover rate Cr is varied focus on the directionality of the search, as low values make moves aligned with a small number of axes while high values search at angles to the axes. While the direction of search is important, an analysis of moves generated by mutating differing numbers of dimensions suggests that the probability of making a successful move is more strongly related to the move's magnitude than to the number of dimensions in which it occurs. Low Cr moves are generally much smaller than those generated with high values, and more likely to succeed, but moves in many dimensions can produce greater improvements in solution quality. Although DE behaves differently at low and high Cr, both extremes can produce effective searches. Results suggest this is because low Cr searches make frequent, small improvements to all population members while high Cr searches produce less frequent, large improvements, followed by contraction of the population and a resultant reduction in move size. The interaction of F and population size with these different modes of search is investigated and recommendations made to achieve good results with both.

A key parameter affecting the operation of differential evolution (DE) is the crossover rate Cr ϵ [0, 1]. While very low values are recommended for and used with separable problems, on non-separable problems, which include most real-world problems, Cr = 0.9 has become the de facto standard, working well across a large range of problem domains. Recent work on separable and non-separable problems has shown that lower-dimensional searches can play an important role in the performance of search techniques in higher-dimensional search spaces. However, the standard value of Cr = 0.9 implies a very high-dimensional search, which is not effective for other search techniques. An analysis of Cr across its range [0, 1] provides insight into how its value affects the performance of DE and suggests how low values may be used to improve the performance of DE. This new understanding of the operation of DE at high and low crossover rates is useful for analysing how adaptive parameters affect DE performance and leads to new suggestions for how adaptive DE techniques might be developed.

In the commonly used DE/rand/1 variant of differential evolution the primary mechanism of generating new solutions is the perturbation of a randomly selected point by a difference vector. The newly selected point may, if good enough, then replace a solution from the current generation. As the magnitude of difference vectors diminishes as the population converges, the size of moves made also diminishes, an oft-touted and obvious benefit of the approach. Additionally, when the population splits into separate clusters difference vectors exist for both small and large moves. Given that a replaced solution is not the one perturbed to create the new, candidate solution, are the large difference vectors responsible for movement of population members between clusters? This paper examines the mechanisms of small and large moves, finding that small moves within one cluster result in solutions from another being replaced and so appearing to move a large distance. As clusters tighten this is the only mechanism for movement between them.

Ant colony optimization (ACO) is a constructive metaheuristic that uses an analogue of ant trail pheromones to learn about good features of solutions. Critically, the pheromone representation for a particular problem is usually chosen intuitively rather than by following any systematic process. In some representations, distinct solutions appear multiple times, increasing the effective size of the search space and potentially misleading ants as to the true learned value of those solutions. In this article, we present a novel system for automatically generating appropriate pheromone representations, based on the characteristics of the problem model that ensures unique pheromone representation of solutions. This is the first stage in the development of a generalized ACO system that could be applied to a wide range of problems with little or no modification. However, the system we propose may be used in the development of any problem-specific ACO algorithm.

Ant colony optimization techniques are usually guided by pheromone and heuristic cost information when choosing the next element to add to a solution. However, while an individual element may be attractive, usually its long term consequences are neither known nor considered. For instance, a short link in a traveling salesman problem may be incorporated into an ant's solution, yet, as a consequence of this link, the rest of the path may be longer than if another link was chosen. The Accumulated Experience Ant Colony uses the previous experiences of the colony to guide in the choice of elements. This is in addition to the normal pheromone and heuristic costs. Two versions of the algorithm are presented, the original and an improved AEAC that makes greater use of accumulated experience. The results indicate that the original algorithm finds improved solutions on problems with less than 100 cities, while the improved algorithm finds better solutions on larger problems.