Dynamic population artificial bee colony algorithm for multi-objective optimal power flow

This paper proposes a novel artificial bee colony algorithm with dynamic population (ABC-DP), which synergizes the idea of extended life-cycle evolving model to balance the exploration and exploitation tradeoff. The proposed ABC-DP is a more bee-colony-realistic model that the bee can reproduce and die dynamically throughout the foraging process and population size varies as the algorithm runs. ABC-DP is then used for solving the optimal power flow (OPF) problem in power systems that considers the cost, loss, and emission impacts as the objective functions. The 30-bus IEEE test system is presented to illustrate the application of the proposed algorithm. The simulation results, which are also compared to nondominated sorting genetic algorithm II (NSGAII) and multi-objective ABC (MOABC), are presented to illustrate the effectiveness and robustness of the proposed method.     

An SOM-based algorithm for optimization with dynamic weight updating

The self-organizing map (SOM), as a kind of unsupervised neural network, has been used for both static data management and dynamic data analysis. To further exploit its search abilities, in this paper we propose an SOM-based algorithm (SOMS) for optimization problems involving both static and dynamic functions. Furthermore, a new SOM weight updating rule is proposed to enhance the learning efficiency; this may dynamically adjust the neighborhood function for the SOM in learning system parameters. As a demonstration, the proposed SOMS is applied to function optimization and also dynamic trajectory prediction, and its performance compared with that of the genetic algorithm (GA) due to the similar ways both methods conduct searches.     

Artificial bee colonies for continuous optimization: Experimental analysis and improvements

The artificial bee colony (ABC) algorithm is a recent class of swarm intelligence algorithms that is loosely inspired by the foraging behavior of honeybee swarms. It was introduced in 2005 using continuous optimization problems as an example application. Similar to what has happened with other swarm intelligence techniques, after the initial proposal, several researchers have studied variants of the original algorithm. Unfortunately, often these variants have been tested under different experimental conditions and different fine-tuning efforts for the algorithm parameters. In this article, we review various variants of the original ABC algorithm and experimentally study nine ABC algorithms under two settings: either using the original parameter settings as proposed by the authors, or using an automatic algorithm configuration tool using a same tuning effort for each algorithm. We also study the effect of adding local search to the ABC algorithms. Our experimental results show that local search can improve considerably the performance of several ABC variants and that it reduces strongly the performance differences between the studied ABC variants. We also show that the best ABC variants are competitive with recent state-of-the-art algorithms on the benchmark set we used, which establishes ABC algorithms as serious competitors in continuous optimization.     

Foraging errors play a role in resource exploration by bumble bees (Bombus terrrestris)

If the cognitive performance of animals reflects their particular ecological requirements, how can we explain appreciable variation in learning ability amongst closely related individuals (e.g. foraging workers within a bumble bee colony)? One possibility is that apparent ‘errors’ in a learning task actually represent an alternative foraging strategy. In this study we investigate the potential relationship between foraging ‘errors’ and foraging success among bumble bee (Bombus terrestris) workers. Individual foragers were trained to choose yellow, rewarded flowers and ignore blue, unrewarded flowers. We recorded the number of errors (visits to unrewarded flowers) each bee made during training, then tested them to determine how quickly they discovered a more profitable food source (either familiar blue flowers, or novel green flowers). We found that error prone bees discovered the novel food source significantly faster than accurate bees. Furthermore, we demonstrate that the time taken to discover the novel, more profitable, food source is positively correlated with foraging success. These results suggest that foraging errors are part of an ‘exploration’ foraging strategy, which could be advantageous in changeable foraging environments. This could explain the observed variation in learning performance amongst foragers within social insect colonies.     

Artificial root foraging optimizer algorithm with hybrid strategies

In this work, a new plant-inspired optimization algorithm namely the hybrid artificial root foraging optimizion (HARFO) is proposed, which mimics the iterative root foraging behaviors for complex optimization. In HARFO model, two innovative strategies were developed: one is the root-to-root communication strategy, which enables the individual exchange information with each other in different efficient topologies that can essentially improve the exploration ability; the other is co-evolution strategy, which can structure the hierarchical spatial population driven by evolutionary pressure of multiple sub-populations that ensure the diversity of root population to be well maintained. The proposed algorithm is benchmarked against four classical evolutionary algorithms on well-designed test function suites including both classical and composition test functions. Through the rigorous performance analysis that of all these tests highlight the significant performance improvement, and the comparative results show the superiority of the proposed algorithm.     

Learning foraging thresholds for lizards: an analysis of a simple learning algorithm

This paper gives proof of convergence for a learning algorithm that describes how anoles (lizards found in the Caribbean) learn foraging threshold distance. An anole will pursue a prey if and only if it is within this threshold of the anole's perch. The learning algorithm was proposed by Roughgarden and his colleagues. They experimentally determined that this algorithm quickly converges to the foraging threshold that is predicted by optimal foraging theory. We provide analytic confirmation that the optimal foraging behavior as predicted by Roughgarden's model can be attained by a lizard that follows this simple and zoologically plausible rule of thumb. Copyright 1999 Academic Press.     

Inheritance of optimal foraging behaviour in Columbian ground squirrels

Summary I examined the potential inheritance of the ability of Columbian ground squirrels (Spermophilus columbianus) to select an optimal diet. I calculated the diet that would maximize daily energy intake for each of 21 adult females and their litters, using a linear programming optimization model for each individual. The absolute value of the difference between an individual's predicted optimal diet and observed diet (deviation from an optimal diet) was used as a measure of an individual's foraging ability. The foraging ability of individuals was consistent over time and in different foraging environments, so I considered foraging ability to be a potentially heritable trait.Inheritance was determined from correlations of mother and offspring foraging ability. I experimentally removed some mothers just as they weaned their offspring so that offspring could not be influenced by their mother while learning to forage, while leaving the other mothers to raise their litters normally. In both cases, offspring strongly resembled their mother in foraging ability. However, offspring with mothers absent exhibited significantly larger deviations from their optimal diet. Offspring with mothers absent appeared to imitate their mother's diet during lactation, and this tendency partially explained their greater deviation. Consequently, offspring appear to inherit the ability to forage optimally from their mother, perhaps through observational learning or imitation. There may also be a genetic basis to foraging ability, but uncontrolled maternal effects in the experiment prevent a proper test for it.     

Context-dependent behavior and the benefits of communal nesting

We present a model for the behavior of communally nesting insects. Females may forage for food to provision offspring or may remain in the nest, with the option of eating and replacing nest mates' eggs. Orphaned brood are at risk of predation. The optimal behavior of solitary females is determined using stochastic dynamic programming; static and dynamic evolutionarily stable strategies (ESSs) are then calculated for colonies of various sizes. A solitary female should forage if her brood is smaller than a time-dependent threshold. Females in small colonies should forage. In colonies above some threshold size, the static ESS is for one female to forage and the rest to cheat. The dynamic ESS in large colonies is for no females to forage until some time close to the end of the foraging season and for all females to forage thereafter. Mixed dynamic ESSs, with some foragers and some cheats, may arise if individuals differ in their chances of surviving a foraging interval or if females with new offspring vary their guarding behavior, depending on the numbers of cheats and new cells in the nest. We discuss these predictions in the light of published observations and preliminary data on the halictine bee Lasioglossum (Chilalictus) hemichalceum.     

Radar Tracking and Motion-Sensitive Cameras on Flowers Reveal the Development of Pollinator Multi-Destination Routes over Large Spatial Scales

Central place foragers, such as pollinating bees, typically develop circuits (traplines) to visit multiple foraging sites in a manner that minimizes overall travel distance. Despite being taxonomically widespread, these routing behaviours remain poorly understood due to the difficulty of tracking the foraging history of animals in the wild. Here we examine how bumblebees (Bombus terrestris) develop and optimise traplines over large spatial scales by setting up an array of five artificial flowers arranged in a regular pentagon (50 m side length) and fitted with motion-sensitive video cameras to determine the sequence of visitation. Stable traplines that linked together all the flowers in an optimal sequence were typically established after a bee made 26 foraging bouts, during which time only about 20 of the 120 possible routes were tried. Radar tracking of selected flights revealed a dramatic decrease by 80% (ca. 1500 m) of the total travel distance between the first and the last foraging bout. When a flower was removed and replaced by a more distant one, bees engaged in localised search flights, a strategy that can facilitate the discovery of a new flower and its integration into a novel optimal trapline. Based on these observations, we developed and tested an iterative improvement heuristic to capture how bees could learn and refine their routes each time a shorter route is found. Our findings suggest that complex dynamic routing problems can be solved by small-brained animals using simple learning heuristics, without the need for a cognitive map.     

Modelling spatial dynamics of fish

Our ability to model spatial distributions of fish populations is reviewed by describing the available modelling tools. Ultimate models of the individual's motivation for behavioural decisions are derived from evolutionary ecology. Mechanistic models for how fish sense and may respond to their surroundings are presented for vision, olfaction, hearing, the lateral line and other sensory organs. Models for learning and memory are presented, based both upon evolutionary optimization premises and upon neurological information processing and decision making. Functional tools for modelling behaviour and life histories can be categorized as belonging to an optimization or an adaptation approach. Among optimization tools, optimal foraging theory, life history theory, ideal free distribution, game theory and stochastic dynamic programming are presented. Among adaptation tools, genetic algorithms and the combination with artificial neural networks are described. The review advocates the combination of evolutionary and neurological approaches to modelling spatial dynamics of fish.     

Balancing organization and flexibility in foraging dynamics

Proper pattern organization and reorganization are central problems facing many biological networks which thrive in fluctuating environments. However, in many cases the mechanisms that organize system activity oppose those that support behavioral flexibility. Thus, a balance between pattern organization and pattern flexibility is critically important for overall biological fitness. We study this balance in the foraging strategies of ant colonies exploiting food in dynamic environments. We present discrete time and space simulations of colony activity that uses a pheromone-based recruitment strategy biasing foraging towards a food source. After food relocation, the pheromone must evaporate sufficiently before foraging can shift colony attention to a new food source. The amount of food consumed within the dynamic environment depends non-monotonically on the pheromone evaporation time constant—with maximal consumption occurring at a time constant which balances trail formation and trail flexibility. A deterministic, ‘mean field’ model of pheromone and foragers on trails mimics our colony simulations. This reduced framework captures the essence of the flexibility-organization balance, and relates optimal pheromone evaporation to the timescale of the dynamic environment. We expect that the principles exposed in our study will generalize and motivate novel analysis across a broad range systems biology.     

An online self-organizing scheme for Parsimonious and Accurate Fuzzy Neural Networks

In this paper, an online self-organizing scheme for Parsimonious and Accurate Fuzzy Neural Networks (PAFNN), and a novel structure learning algorithm incorporating a pruning strategy into novel growth criteria are presented. The proposed growing procedure without pruning not only simplifies the online learning process but also facilitates the formation of a more parsimonious fuzzy neural network. By virtue of optimal parameter identification, high performance and accuracy can be obtained. The learning phase of the PAFNN involves two stages, namely structure learning and parameter learning. In structure learning, the PAFNN starts with no hidden neurons and parsimoniously generates new hidden units according to the proposed growth criteria as learning proceeds. In parameter learning, parameters in premises and consequents of fuzzy rules, regardless of whether they are newly created or already in existence, are updated by the extended Kalman filter (EKF) method and the linear least squares (LLS) algorithm, respectively. This parameter adjustment paradigm enables optimization of parameters in each learning epoch so that high performance can be achieved. The effectiveness and superiority of the PAFNN paradigm are demonstrated by comparing the proposed method with state-of-the-art methods. Simulation results on various benchmark problems in the areas of function approximation, nonlinear dynamic system identification and chaotic time-series prediction demonstrate that the proposed PAFNN algorithm can achieve more parsimonious network structure, higher approximation accuracy and better generalization simultaneously.     

Nonlinear system modelling via optimal design of neural trees

This paper introduces a flexible neural tree model. The model is computed as a flexible multi-layer feed-forward neural network. A hybrid learning/evolutionary approach to automatically optimize the neural tree model is also proposed. The approach includes a modified probabilistic incremental program evolution algorithm (MPIPE) to evolve and determine a optimal structure of the neural tree and a parameter learning algorithm to optimize the free parameters embedded in the neural tree. The performance and effectiveness of the proposed method are evaluated using function approximation, time series prediction and system identification problems and compared with the related methods.     

A Mixture of Delta-Rules Approximation to Bayesian Inference in Change-Point Problems

Error-driven learning rules have received considerable attention because of their close relationships to both optimal theory and neurobiological mechanisms. However, basic forms of these rules are effective under only a restricted set of conditions in which the environment is stable. Recent studies have defined optimal solutions to learning problems in more general, potentially unstable, environments, but the relevance of these complex mathematical solutions to how the brain solves these problems remains unclear. Here, we show that one such Bayesian solution can be approximated by a computationally straightforward mixture of simple error-driven ‘Delta’ rules. This simpler model can make effective inferences in a dynamic environment and matches human performance on a predictive-inference task using a mixture of a small number of Delta rules. This model represents an important conceptual advance in our understanding of how the brain can use relatively simple computations to make nearly optimal inferences in a dynamic world.     

Artificial neural network based soft estimator for estimation of transducer static nonlinearity

In this work, the development of an Artificial Neural Network (ANN) based soft estimator is reported for the estimation of static-nonlinearity associated with the transducers. Under the realm of ANN based transducer modeling, only two neural models have been suggested to estimate the static-nonlinearity associated with the transducers with quite successful results. The first existing model is based on the concept of a functional link artificial neural network (FLANN) trained with mu-LMS (Least Mean Squares) learning algorithm. The second one is based on the architecture of a single layer linear ANN trained with alpha-LMS learning algorithm. However, both these models suffer from the problem of slow convergence (learning). In order to circumvent this problem, it is proposed to synthesize the direct model of transducers using the concept of a Polynomial-ANN (polynomial artificial neural network) trained with Levenberg-Marquardt (LM) learning algorithm. The proposed Polynomial-ANN oriented transducer model is implemented based on the topology of a single-layer feed-forward back-propagation-ANN. The proposed neural modeling technique provided an extremely fast convergence speed with increased accuracy for the estimation of transducer static nonlinearity. The results of convergence are very stimulating with the LM learning algorithm.     

Cooperative optimal control: broadening the reach of bio-inspiration

Inspired by the process by which ants gradually optimize their foraging trails, this paper investigates the cooperative solution of a class of free final time, partially constrained final state optimal control problems by a group of dynamical systems. We propose an iterative, pursuit-based algorithm which generalizes previously proposed models and converges to an optimal solution by iteratively optimizing an initial feasible trajectory/control pair. The proposed algorithm requires only short-range, limited interactions between group members, avoids the need for a 'global map' of the environment in which the group evolves, and solves an optimal control problem in 'small' pieces, in a manner which will be made precise. The performance of the algorithm is illustrated in a series of simulations and laboratory experiments.     

The application of statistical decision theory to animal behaviour

Statistical decision theory is discussed as a general framework for analysing how animals should learn. Attention is focused on optimal foraging behaviour in stochastic environments. We emphasise the distinction between the mathematical procedure that can be used to find optimal solutions and the mechanism an animal might use to implement such solutions. The mechanisms might be specific to a restricted class of problems and produce suboptimal behaviour when faced with problems outside this class. We illustrate this point by an example based on what is known in the literature on animal learning as the partial reinforcement effect.     

Risk-Sensitive Foraging in a Patch Departure Context: A Test with Worker Bumble Bees

Typically, tests of risk-sensitive foraging involve observinga subject's choices of alternative prey types differing in somecombination of mean and variance of expected foraging gain.Here, we consider the problem of risk-sensitive foraging whenthere is a single prey type. We observed worker bumble bees(Bombus occidentalis) foraging in an array of artificial 2-flowerinflorescences. After visiting the bottom flower in an inflorescenceand obtaining a reward of some size, the bee decides whetherto visit the top flower or to move to a new inflorescence (apatch departure). Here, risk-sensitive behavior is expressedas the forager's choice of patch departure threshold (PDT) ofreward obtained in the bottom flower. We measured the PDTs ofbees whose colony energy stores (and therefore energy requirements)had been manipulated (Enhanced or Depleted). Simulations ledus to predict that shortfall-minimizing bees should decreasetheir PDTs when their colony energy reserves were depleted,relative to when the reserves were enhanced. Bees did not usea strict patch departure threshold, but instead the probabilityof departure varied with nectar volume in the bottom flower.Colony energy stores did affect patch departure behavior, butthis effect was confounded by the order in which manipulationof colony reserves was applied. Further, simulations of observedbee patch departure decisions did not produce behavior expectedif the decisions were based on shortfall-minimization. We concludethat a bee's decision of when to leave an inflorescence is notpredicted by a static shortfall-minimizing model. Our resultsalso implicate an important interaction between learning andforaging requirements. We review risk-sensitivity in bees, anddiscuss why risk-sensitive foraging may be adaptive for bumblebees.     

The simultaneous recurrent neural network for addressing the scaling problem in static optimization.

A trainable recurrent neural network, Simultaneous Recurrent Neural network, is proposed to address the scaling problem faced by neural network algorithms in static optimization. The proposed algorithm derives its computational power to address the scaling problem through its ability to "learn" compared to existing recurrent neural algorithms, which are not trainable. Recurrent backpropagation algorithm is employed to train the recurrent, relaxation-based neural network in order to associate fixed points of the network dynamics with locally optimal solutions of the static optimization problems. Performance of the algorithm is tested on the NP-hard Traveling Salesman Problem in the range of 100 to 600 cities. Simulation results indicate that the proposed algorithm is able to consistently locate high-quality solutions for all problem sizes tested. In other words, the proposed algorithm scales demonstrably well with the problem size with respect to quality of solutions and at the expense of increased computational cost for large problem sizes.     

Colour biases in learned foraging preferences in Trinidadian guppies

Learning allows animals to adaptively adjust their behaviour in response to variable but predictable environments. Stable aspects of the environment may result in evolved or developmental biases in the systems impacting learning, allowing for improved learning performance according to local ecological conditions. Guppies (Poecilia reticulata), like many animals, show striking colour preferences in foraging and mating contexts and guppy artificial selection experiments have found that the form and progress of evolved responses to coloured stimuli differ depending on stimulus colour. Blue colouration is thought to typically be a relatively unimportant food cue in guppies. This raises the possibility that learned foraging associations with blue objects are formed less readily than with other colours. Here, guppies were rewarded for foraging at green or blue objects in two experiments. Guppies readily foraged from these objects, but learning performance differed with rewarded object colour. With equal amounts of training, the preference for green objects became stronger than the preference for blue objects. These differences in performance were not attributable to differences in initial preferences or to foraging more on one colour during training. These findings suggest that associative pairings within a single sensory modality that do not have a historic relevancy can be more difficult for animals to learn even when there is no clear initial bias present.