Optimal Flock Research Articles

Distributed Fixed-Time Optimal Flocking for Second-Order Multi-Agent Systems

In this paper, we investigate the problem of distributed optimization for second-order multi-agent systems with fixed-time flocking. The objective is to concurrently steer the agents towards a common velocity while optimizing the global objective function. To solve the problem, we first design a fixed-time estimator to predict the global gradient of the objective functions, then based on which, each agent is endowed with fixed-time tracking controller to track the optimal solution. Motivated by the fact that the relative velocity information is difficult to obtain accurately, the proposed algorithm is designed without using neighbors’ velocity. The upper bounds of the settling time are provided without relying on the initial states of the agents, only requiring the adjustment of parameters. The effectiveness of the proposed control protocol is also demonstrated through numerical simulations.

Distributed Adaptive Flocking Control for Large-Scale Multiagent Systems.

This article presents a novel distributed flocking control method for large-scale multiagent systems (LS-MASs) operating in uncertain environments. When dealing with a massive number of flocking agents in uncertain environments, existing flocking methods encounter the problem of communication complexity and "Curse of dimensionality" caused by the exponential growth of agent interactions while solving PDE-based optimal flocking control for large-scale systems. The mean field game (MFG) method addresses this issue by transforming interactions among all agents into the interaction of each individual agent with average effects represented by a probability density function (pdf) of other agents. However, relying solely on a pdf term to consider other agents' states can result in inefficient flocking performance due to the absence of a proficient coordination mechanism encompassing all agents involved in flocking. To overcome these difficulties and achieve the desired flocking performance for LS-MASs, the agents are decomposed into a finite number of subgroups. Each subgroup comprises a leader and followers, and a hybrid game theory is developed to manage both inter-and intragroup interactions. The method incorporates a cooperative game that links leaders from different groups to formulate distributed flocking control, a Stackelberg game that teams up leaders and followers within the same group to extend collective flocking behavior, and an MFG for followers to address the challenges of LS-MASs. Furthermore, to achieve distributed adaptive flocking using the hybrid game structure, we propose a hierarchical actor-critic-mass-based reinforcement learning technique. This approach incorporates a multiactor-critic method for leaders and an actor-critic-mass algorithm for followers, enabling adaptive flocking control in a distributed manner for large-scale agents. Finally, numerical simulation including comparison study and Lyapunov analysis demonstrates the effectiveness of the developed method.

The role of reproductive loss on flock performance: a comparison of nine industry flocks.

The reproductive performance of a sheep flock is dependent on a multitude of complex interacting factors. Attaining optimal flock performance requires information about how the reproductive steps are linked and relate to readily available measurements of the state of the flock. The goal was to use data from nine commercial flocks (greater than 300,000 records) to investigate and model the key reproductive steps affecting flock reproductive performance. We also developed a maximum-likelihood based methodology to predict flock ovulation rate based on measurements of the number of fetuses at mid-pregnancy (detected by ultrasound-scanning). The model was used to determine how changes in premating liveweight, age, predicted ovulation rate, number of fetuses at mid-pregnancy, lamb survival and lamb growth rate affect the total lamb liveweight at weaning per ewe exposed to the ram in each flock. The data from the commercial flocks were also used to investigate the role of ewe age and premating liveweight on each reproductive step. Sensitivity analyses were conducted to identify the key reproductive steps affecting flock reproductive performance, with a focus on understanding how these steps vary between flocks. The elasticity for embryo survival was 60% of that for lamb survival for these flocks and the elasticities for ovulation rate were highly variable between flocks (0.16 to 0.50 for mature ewes). This indicates that ovulation rate was near-optimal for some flocks, whereas there was potential to significantly improve flock performance in suboptimal flocks. The elasticity for ewe premating liveweight was highly variable between flocks (−0.03 to 0.84 for mature ewes and −0.18 to 1.39 for ewe lambs), indicating that premating liveweight ranged from optimal to suboptimal between flocks. For these suboptimal farms, the opportunity exists to increase flock performance through improved management of ewe premating liveweight. Reproductive loss was significantly greater in ewe lambs than mature ewes, although the difference is dependent on the stage of reproduction and flock. Predicted ovulation rate was 25% lower for ewe lambs and there was a 30% relative decrease in the predicted embryo survival probability from ovulation to scanning for ewe lambs. There was a 10% relative decrease in lamb survival probability from birth to weaning for ewe lambs and lamb growth rate was 25% lower for ewe lambs.

A biologically-inspired reinforcement learning based intelligent distributed flocking control for Multi-Agent Systems in presence of uncertain system and dynamic environment

In this paper, we investigate the real-time flocking control of Multi-Agent Systems (MAS) in the presence of system uncertainties and dynamic environment. To handle the impacts from system uncertainties and dynamic environment, a novel reinforcement learning technique, which is appropriate for real-time implementation, has been integrated with multi-agent flocking control in this paper. The Brain Emotional Learning Based Intelligent Controller (BELBIC) is a biologically-inspired reinforcement learning-based controller relying on a computational model of emotional learning in the mammalian limbic system. The learning capabilities, multi-objective properties, and low computational complexity of BELBIC make it a very promising learning technique for implementation in real-time applications. Firstly, a novel brain emotional learning-based flocking control structure is proposed. Then, the real-time update laws are developed to tune the emotional signals based on real-time operational data. It is important to note that this data-driven reinforcement learning approach relaxes the requirement for system dynamics and effectively handle the uncertain impacts of the environment. Using the tuned emotional signals, the optimal flocking control can be obtained. The Lyapunov analysis has been used to prove the convergence of the proposed design. The effectiveness of the proposed design is also demonstrated through numerical and experimental results based on the coordination of multiple Unmanned Aerial Vehicles (UAVs).

The effect of reproductive loss on the performance of a research flock.

The reproductive performance of a sheep flock is dependent on a multitude of complex interacting factors. Achieving optimal flock performance requires knowledge of the reproductive steps and how these are linked and related to available measurements of the state and performance of the flock. The goal was to use previously collected data from a research flock that had undergone selection for fecundity (11,369 lambing records), to model the key reproductive steps affecting flock reproductive performance. The model was used to investigate how changes in liveweight, age, ovulation rate, number of fetuses at midpregnancy, number of lambs born, and birthweight affect the number of lambs weaned and the weaning weight of each lamb in this flock. The data available from the research flock were used to parameterize models of each reproductive step and assess the role of ewe age and premating liveweight on each reproductive step. These models were then linked together as a simulation tool to assess the role of different parameters on flock reproductive performance, which was defined as the total weight of lambs weaned per ewe exposed to the ram. Flock elasticities were calculated that characterize the relative importance of the effect of average premating ewe liveweight (0.81), average ovulation rate (0.33), variance in ovulation rate (-0.095), embryo survival (0.72), lamb survival (1.03), conception failure (0.35), and average ewe age (0.056) on the total kilograms of lamb liveweight at weaning per ewe exposed to the ram. The largest elasticity for lamb survival indicated that a 1% increase in lamb survival is expected to have a 1.03% increase in the total kilograms of lamb liveweight at weaning per ewe exposed to the ram in this flock. Assuming similar costs, interventions to increase lamb survival for this flock will provide the largest increase in the total kilograms of lamb liveweight at weaning per ewe exposed to the ram, which is a key metric of flock performance.

A Gravitational Search Algorithm-Based Single-Center of Mass Flocking Control for Tracking Single and Multiple Dynamic Targets for Parabolic Trajectories in Mobile Sensor Networks

Developing optimal flocking control procedure is an essential problem in mobile sensor networks (MSNs). Furthermore, finding the parameters such that the sensors can reach to the target in an appropriate time is an important issue. This paper offers an optimization approach based on metaheuristic methods for flocking control in MSNs to follow a target. We develop a non-differentiable optimization technique based on the gravitational search algorithm (GSA). Finding flocking parameters using swarm behaviors is the main contributing of this paper to minimize the cost function. The cost function displays the average of Euclidean distance of the center of mass (COM) away from the moving target. One of the benefits of using GSA is its application in multiple targets tracking with satisfying results. Simulation results indicate that this scheme outperforms existing ones and demonstrate the ability of this approach in comparison with the previous methods.

A pre- and postpartum study of selected biochemical parameters in ewes for the early detection of pregnancy toxemia

A field investigation on the incidence of subclinical ovine ketosis was performed in two large sheep flocks in an agricultural region of central Greece. Sixty - four animals were allocated in 2 study groups: group C, consisted of 29 non-pregnant females and group S of 35 end-term pregnant ewes. The trial lasted 6 weeks, including the immediate pre- and postpartal period. Blood samples were collected on weekly intervals and used for determining the concentrations of ß-hydroxybutyrate (BHB), acetoacetate (AcAc), glucose, total (TB) and conjugated (CB) bilirubin, calcium (Ca), inorganic phosphorus (P), sodium (Na), potassium (K), magnesium (Mg) and the activity of sorbitol dehydrogenase (SDH) and γ-glutamyl transferase (yGT). All the animals remained clinically healthy throughout the trial and parturition was uneventful. Eighteen group S ewes (51.4%) delivered 1 lamb, 12 (34,3%) twins, 4 (11.4%) triplets and 1 (2.9%) 4 lambs. Although the overall evaluation of the biochemical analysis did not support the existence of subclinical ketosis, blood glucose remained significantly lower (P<0.05) in group S sheep, with its lowest value (2.3±0.34 mmol/1) recorded 1 week prior to parturition. Sporadic cases of subclinical hyperketonemia may occur, despite optimal flock management.

Optimal flock structure of pig farm providing minimum costs

The study deals with the analysis of production costs, as well as the net area in the production of the herd of organizational structures at the pig farm. The question arises of the optimum production structure in the cooperative household, which is mainly oriented to the production of Pigmeat. In this paper, a concrete model of linear programming for the optimal organizational structure of the herd of pig farms of the net effective area was defned. The research covered the cooperative farm “1.Decembr” in Žitorađa in Toplicki district. For 2013, the production technology of agricultural animals was followed, and economic results were analyzed. In the observed period of one year. It was found that there were 28,252 throats on the farm. Total agricultural growth in 2013 amounted to 664,920 kg, in the amount of 781,569.7 €. Total death: piglets on wolves 6,315 throats, stuffed pigs 3,425 throats, 17,150 kg, tooth 928 throats, 40,980 kg, pigs 67 throats 13,930 kg, immature 3 throat 890 kg

Flocking of Multi-Agent Systems Using a Unified Optimal Control Approach

In this paper, the multi-agent flocking problem is investigated in a unified optimal control framework. The flocking characteristics, such as velocity alignment, navigation, cohesion, and collision/obstacle avoidance, are accomplished by formulating them into respective cost function terms. The resultant nonquadratic cost function poses a challenging optimal control problem. A novel inverse optimal control strategy is adopted to derive an analytical optimal control law. The optimality and asymptotic stability are proved and the distributed feedback control law only requires local information to achieve the flocking behaviors. Various simulation scenarios are used to demonstrate the effectiveness of the optimal flocking algorithm.

Emergence of Anisotropy in Flock Simulations and Its Computational Analysis

In real flocks, it was revealed that the angular density of nearest neighbors shows a strong anisotropic structure of individuals by very recent extensive field studies [Ballerini et al, Proceedings of the National Academy of Sciences USA, 105, pp. 1232-1237 (2008)]. In this paper, we show this structure of anisotropy also emerges in an artificial flock simulation, namely, Boid simulation. To quantify the anisotropy, we evaluate a useful statistics, that is to say, the so-called γ-value which is defined as an inner product between the vector in the direction of the lowest angular density of flocks and the vector in the direction of moving of the flock. Our results concerning the emergence of the anisotropy through the γ-value might enable us to judge whether an optimal flock simulation seems to be realistic or not.

Structure and Dynamics of Mixed-Species Flocks in a Hawaiian Rain Forest

Abstract Mixed-species flocks of native and introduced birds were studied for four years in an upper elevation Hawaiian rain forest. Those flocks were characterized by strong seasonality, large size, low species richness, high intraspecific abundance, a lack of migrants, and a general lack of territoriality or any sort of dominance hierarchy. There was high variability among years in patterns of occurrence at the species level, and high variability within years at the individual level. These flocks are loosely structured social groupings with apparently open membership. The fluid, unstable movement patterns, high degree of variability in size and composition, and lack of positive interspecific associations are not consistent with the “foraging enhancement” hypothesis for flocking. Two resident, endangered insectivores, the Akepa (Loxops coccineus) and Hawaii Creeper (Oreomystis mana) served as “nuclear” species. Flock composition was compared between two study sites that differed significantly in density of these two nuclear species. Flock size was similar at the two sites, primarily because the nuclear species were over-represented relative to their density. This observation suggests that birds are attempting to achieve a more optimal flock size at the lower density site.

Factors causing variation in flock size: Decision making to join a foraging flock

In order to clarify the temporal variation of flock size, we examined factors that cause the temporal variation of foraging flock size in a wintering population of the Yellow‐throated bunting (Emberiza elegans). We conducted field observations to examine whether the flock size varies greatly and whether non‐random associations between individuals exist. We confirmed that flock size varied greatly and some individuals showed non‐random associations with other flock members. Then, we carried out computer simulations that assume stochastic risky situation, the condition of hunger level and non‐random associations between individuals. In the simulation, the condition of hunger level caused the variation of flock size. However, the distribution of flock size differed from observed ones. When the condition of non‐random association was added to the simulation, the variation of flock size became large and the distribution of flock size was similar to that of the observed one. In wintering flocks of Yellow‐throated bunting, each individual attempts to forage in an optimal flock size. However, if they are extremely starved, it is suggested that they adopt a conditional strategy to join a flock independently of the flock size to acquire the energy necessary for survival. Simultaneously, they may decide to forage under the effect of non‐random association between individuals.

A current view of veterinary flock health management: Developing “growing pains”

At the present time, avicultural medicine as the term is generally applied in clinical settings lacks a systematic means with which to evaluate and examine the nondomestic bird flock. These systematic evaluations are a key to developing a true flock health program. Without a proper physical examination of the flock, it is virtually impossible to make complete and balanced managerial recommendations for the individual patient as well as in the overall flock. The breeding collection of nondomestic birds in the private avicultural sector is in many ways the most important and most neglected patient in avian medicine today. Properly executed complete flock evaluation techniques will lead to sound flock management with proven value, resulting in documentation of optimal flock health management programs and techniques for future reference. Incompletely performed, flock medical intervention can become harmful if not devastating. This report will review the basics of proper flock evaluation techniques and itemize some of the more common specific errors encountered in flock diagnoses and veterinary intervention.

The effects of habitat density and the spatial distribution of food on the social behaviour of captive wintering American Tree Sparrows

Two artificial habitats containing 15% (low density) and 40% (high density) coniferous ground cover, and three feeding patterns representing different levels of spatial food distribution were used to investigate the effects of factors influencing individual spacing on the behaviour of captive, wintering American Tree Sparrows (Spizella arborea). Specifically, three aspects of social behaviour were examined: the frequency of agonistic encounters, the percentage of interactions initiated by dominants, and nearest-neighbour distances. Temperature effects were also considered. Interaction rates were lowest when food was most dispersed, and at higher temperatures. More interactions were recorded in the higher density habitat, as compared with the low density habitat, but the trend was reversed when food was highly dispersed. Nearest-neighbour distances decreased with increasing habitat density and food dispersion and were shortest in the high density habitat. Dominant birds initiated most encounters (70.7%), but less frequently when food was abundant or temperatures high, contradicting an assumption of previous models of optimal flock behaviour. It is suggested that these models, which rely on predicted changes in the allocation of available time by dominant birds to predict flock size, could be improved by considering the effects of habitat density and food dispersion, as well as differences in the social optimization strategies of different flocking species.

Benefits and Costs of Social Foraging and Optimal Flock Size in Goldfinches (Carduelis carduelis)

AbstractDuring the breeding season, the costs and benefits of social foraging of goldfinches (Carduelis carduelis L.) feeding in groups of different sizes was evaluated. With increasing flock size (up to six individuals) individuals became less alert: the individual head‐jerk rate decreased but the whole group vigilance level increased. The handling time for the consumption of a Rumex seed was simultaneously reduced. Compared with individuals feeding alone, in a group of six birds the consumption of corns amounts to 20 % more within the same period of time. However, with increasing group size, the individuals have to fly greater distances to reach another profitable plant, which consumes more time. Another cost of flocking may be that larger flocks are more easily spotted by predators. Thus, flocking involves benefits in shortening handling time of the consumed seeds but also causes costs in having a larger travelling time to the next plant stem. Besides plant density calculated optimal foraging group size depends on the number of seeds provided by one seed head.

A NOTE ON LIVESTOCK BREEDING POLICIES IN STABLE AND DEVELOPMENT SITUATIONS

Multi‐stage linear programming is used to develop sheep replacement policies in a number of different situations. Policies are developed for eight and sixteen year periods assuming, firstly a constant feed supply, and secondly, an increasing feed supply over the period. The results show the optimal flock composition together with the sheep sale activities for each year of the plan. The marginal value products indicate which constraints are the most important and whether any should be relaxed in order to make the model more realistic. It is concluded that it is not necessary to use a very long planning period in order to determine the activities for the early years. The results from the shorter planning period appear to be consistent with long‐term goals.