´
Ecole Polytechnique F´ ed´ erale de Lausanne
{ezequiel.dimario, inaki.navarro, alcherio.martinoli}@epfl.ch
Abstract. In this paper we study the automatic synthesis of **robotic** controllers for the coordinated movement of multiple mobile robots. The algorithm used to learn the controllers is a noise-resistant version of **Particle** **Swarm** **Optimization**, which is applied in two diﬀerent settings: centralized and **distributed** **learning**. In centralized **learning**, every robot runs the same controller and the performance is evaluated with a global metric. In the **distributed** **learning**, robots run diﬀerent controllers and the performance is evaluated independently on each robot with a local metric. Our results from **learning** in simulation show that it is possible to learn a **cooperative** task in a fully **distributed** way employing a local met- ric, and we validate the simulations with real robot experiments where the best solutions from **distributed** and centralized **learning** achieve sim- ilar performances.

Show more
13 Read more

Some researchers have used different **optimization** tech- niques to improve the performance of manually designed flocking controllers, **using** PSO (Lee and Myung, 2013; Etemadi et al., 2012), gradient descent (Chang et al., 2013), Reinforcement **Learning** (Hayes and Dormiani-Tabatabaei, 2002), or Evolutionary Strategies (Celikkanat, 2008). Our approach in this article differs in that our **behaviors** are gen- erated by a highly plastic artificial neural network and not by a specific control design targeted to flocking behavior. In other words, the main goal of this article is to compare cen- tralized and **distributed** **learning** methods for design and op- timization of collaborative **behaviors**, among which flocking has been chosen as a benchmark.

Show more
Intelligence can evolve **using** evolutionary algorithms that try to minimize the sensory surprise of the system. We will show how to apply the free-energy principle, borrowed from statisti- cal physics, to quantitatively describe the **optimization** method (sensory surprise minimization), which can be used to support lifelong **learning**. We provide our ideas about how to combine this **optimization** method with evolutionary algorithms in order to boost the development of specialized Artificial Neural Net- works, which define the proprioceptive configuration of particular **robotic** units that are part of a **swarm**. We consider how **optimization** of the free-energy can promote the homeostasis of the **swarm** system, i.e. ensures that the system remains within its sensory boundaries throughout its active lifetime. We will show how complex **distributed** cognitive systems can be build in the form of hierarchical modular system, which consists of specialized micro-intelligent agents connected through information channels. We will also consider the co-evolution of various **robotic** **swarm** units, which can result in development of proprioception and a comprehensive awareness of the properties of the environment. And finally, we will give a brief outline of how this system can be implemented in practice and of our progress in this area.

Show more
A **Distributed** Noise-Resistant **Particle** **Swarm** **Optimization** Algorithm for High-Dimensional Multi-Robot **Learning**
Ezequiel Di Mario I˜naki Navarro Alcherio Martinoli
Abstract— Population-based **learning** techniques have been proven to be effective in dealing with noise in numerical benchmark functions and are thus promising tools for the high-dimensional **optimization** of controllers for multiple robots with limited sensing capabilities, which have inherently noisy performance evaluations. In this article, we apply a statistical technique called Optimal Computing Budget Allocation to improve the performance of **Particle** **Swarm** **Optimization** in the presence of noise for a multi-robot obstacle avoidance benchmark task. We present a new **distributed** PSO OCBA algorithm suitable for resource-constrained mobile robots due to its low requirements in terms of memory and limited local communication. Our results from simulation show that PSO OCBA outperforms other techniques for dealing with noise, achieving a more consistent progress and a better estimate of the ground-truth performance of candidate solutions. We then validate our simulations with real robot experiments where we compare the controller learned with our proposed algorithm to a potential field controller for obstacle avoidance in a cluttered environment. We show that they both achieve a high performance through different avoidance **behaviors**.

Show more
visited position for the **particle** is p ibest ( p i 1 , p i 2 ,....... p id ) and also the best position explored. The best value so far is global best i.e., p gbest ( p g 1 , p g 2 ,....... p gd ) [ Yong Wang et al. (2009)]. The below Fig.1 shows the searching nature of swarms based on social and cognition factors [Kershner, R. (1939)]. The velocity and positions of each **particle** are updated by the "Eq. (3)" and "Eq. (4)".

Abstract
Without formal structure data are those that have no prearranged form or structure and are full of textual data. Typical unstructured systems include emails, reports, telephone or messaging conversations, etc. The main goal of this work is to extract the keywords from a conversation **using** **particle** **swarm** **optimization**. Keywords are grouped together under their classification and then suggested to the user. In existing work, **using** diverse keyword extraction, to find topic modelling information, representation of the main topics of transcript and diverse keyword selection. It maximizes the coverage of topics that are automatically recognized in transcript of conversation fragment. Once a set of keywords is extracted, it is clustered according to their user queries and recommended to the user. At the end of result, a single implicit query cannot improve user’s satisfaction with the recommended documents. So, **swarm** intelligence technique is to be applied, it will minimize redundancy in a short list of Keywords and provide accurate query result compared to greedy algorithm.

Show more
The most familiar technique in NN **learning** is called Backpropogation (BP) algorithm. BP is widely used to solve many real world problems by **using** the concept of Multilayer Perceptron (MLP) training and testing. However, the major disadvantages of BP are its convergence rate relatively slow (Zweiri et al., 2003) and being trapped at the local minima. Since BP **learning** is basically a hill climbing technique, it runs the risk of being trapped in local minima where every small change in synaptic weight increases the cost function. But somewhere else in the weight space there exist another set of synaptic weight for which the cost function is smaller than the local minimum in which the network is stuck. It is clearly undesirable to have the **learning** process terminate at a local minimum. There are many solutions proposed by many NN researcher to overcome the slow converge rate problem. Many powerful **optimization** algorithms have been devised, most of which have been based on simple gradient descent algorithm as explain by C.M. Bishop (1995) such as conjugate gradient decent, scaled conjugate gradient descent, quasi-Newton BFGS and Levenberg-Marquardt methods. The classical solutions are by improving the program codes and upgrading the machine’s hardware. Lately, latest solutions proposed by NN researcher try to guide the **learning** so that the converge speed become faster. The guidelines to select better functions, **learning** rate, momentum rate and activation functions. Genetic Algorithm (GA) is one of the algorithms proposed to determine the **learning** rate and momentum rate and will produce a set of weight that can be used for testing related data. Table 1 briefly described the finding from several researchers in order to increase **learning** speed (Fnaiech et al., 2002), avoid from trapped into local minima (Wyeth et al., 2000) and better classification result.

Show more
83 Read more

An Artificial Neural Network (ANN) or commonly referred as Neural Network (NN) is an information processing paradigm that is inspired by the way biological nervous systems process the information. The computation is highly complex, nonlinear and parallel. Many applications have been deve loped **using** NN algorithm and most of the applications are on predicting future events based on historical data. Processing power in ANN allows the network to learn and adapt, in addition to making it particularly well suited to tasks such as classification, pattern recognition, memory recall, prediction, **optimization**, and noise filtering (Luger, 2002).

Show more
26 Read more

Each **particle** position of the **swarm** is represented by a set of the weights for the current iteration. The dimension of the practical **swarm** determines the weight number of the network. In order to minimize the **learning** error, the **particle** should move within the weight space. Updating the weight of the network means changing the position in order to reduce the number of iterations. For each iteration, a new velocity calculation takes place to determine the new **particle** position movement. A set of new weights is used to obtain the new error, thus a new position. For PSO, the new weights are registered even if there is no noticeable improvement. This process applies for all particles. The global best **particle** position is the one with the least number of errors. The training process stops when the target minimum error is reached or the numbers of computational processes exceed the number of iterations allowable. When the training is complete, the weights are used to compute the classification error for the training patterns. The same patterns are used to test the network by **using** the same set of weights.

Show more
15 Read more

As BPSO and BQPSO described, each **particle** represents a complete solution vector for the objective function f ( X ) f X 1 , X 2 , , X N . Each update step is also performed on a full D-dimensional vector. Then it may be appear the possibility that some dimension in the solution vector have moved closer to the global optimum, while others moved away from the global optimum. Whereas the objective function value of the solution vector is worse than the former value. BPSO and BQPSO take the new solution vector for a complete vector and neglect the deteriorated components during the iterations. As long as the current objective function value is better than the former value, then update pbest and gbest . Therefore, the current solution vector can be give up in next iteration and the valuable information of the solution vector is lost unknowingly. In order to make full use of the beneficial information, the **cooperative** method [10,11] is introduced to BQPSO. In the proposed method, we expect that the operation can avoid the undesirable behavior, which is a case of taking two steps forward (some dimension improved), and one step back (some dimension deteriorated).

Show more
Within the last two decades, **optimization** algorithms with mathematical programing have proved to be effective in solving large complex **optimization** problems. Recently, **swarm** intelligence techniques have gained popularity because of their capacity to locate partially optimal solutions for combinatorial **optimization** problems [1, 2]. These techniques have been applied in various areas, such as economics, engineering, bioinformatics, and industry. These problems are better solved **using** **swarm** intelligence techniques because they are usually very hard to solve accurately due to the lack of any precise algorithm to solve them [1, 2]. The **swarm** intelligence algorithms mainly depend on updating the population of individuals by applying some operators according to the fitness information obtained from the environment. With these updates, the individuals in a population are expected to move towards an optimum solution.

Show more
Pokud vezmeme konfiguraci, která nám dává nejv ě tší zrychlení, tak z nam ěř ených hodnot dostáváme hodnotu 4 TIPS 10 (tato hodnota však není ani teoreticky možná, proto[r]

57 Read more

A number of variations of both PSO and DE have been developed in the past decade to improve the performance of these algorithms (Engelbrecht, 2005; Price et al. 2005). One class of variations includes hybrids between PSO and DE, where the advantages of the two approaches are combined. The barebones DE (BBDE) is a PSO-DE hybrid algorithm proposed by Omran et al. (2007) which combines concepts from the barebones PSO (Kennedy 2003) and the recombination operator of DE. The resulting algorithm eliminates the control parameters of PSO and replaces the static DE control parameters with dynamically changing parameters to produce an almost parameter-free, self-adaptive, **optimization** algorithm.

Show more
15 Read more

The proposed T-PSO is tested **using** CEC2014’s benchmark functions. Its performance is then benchmarked with S-PSO and A-PSO. The findings show that T-PSO is able to achieve better rank than S- PSO and A-PSO. In the following section, both S-PSO and A-PSO algorithms are reviewed. The T-PSO algorithm is discussed in section 3. Next, the results of the experiment conducted are presented in section 4. Lastly this work is concluded in section 5.

According to (2)-(3) or Fig. 1, the PSO must use ran- dom weighting to simulate birds flocking or fish searching for food. An intelligent **particle** by implication exhibits chaos- like behavior. Ref. [13] proposed a kind of chaotic neuron, which includes relative refractoriness in the model to sim- ulate chaos in a biology brain. The convergence theorems of (7)have been given in [16] and [18], but the theorems were proposed based on many limitations associated with energy functions. Ref. [17] presented a convergence theorem for the HNN with arbitrary energy functions and discrete- time dynamics for discrete neuronal input-output functions. The theorem is that for a network of neurons with discrete input–output neuronal response functions, for any change of state in any neuron i, the energy is guaranteed to decrease 4J j

Show more
The remaining structure of this dissertation is as following. In Chapter II, a comprehensive literature survey is performed on related computational intelligence paradigms to prepare for the following chapters. Chapter III firstly elaborates on a paradigm based upon the intrasociety and intersociety interaction in order to simulate an algorithm to solve single objective **optimization** problems. Next the proposed modifications to this social-based heuristics will be introduced. This proposal has two aspects: one is based upon the idea of adopting information from all individuals in the society (i.e., not only the best performing individuals). The second proposal is based on the fact that different societies have different collective behavior. Politically speaking, the collective behavior of the societies have been quantified into a measure called the liberty rate. In the real sociological context, individuals in a democratic society will have more flexibility and freedom to choose a better environment to live. In contrast, individuals in a dictatorship society will suppress the politically environmental change. While individuals in a liberal society can freely move to be closer to the leaders, individual in a less liberal society will have restriction to move near the leaders. Hence the higher liberty rate a society has, the more flexibility an individual in such society can move. At the end of this chapter, simulation result for a real world mechanical problem is used to test the performance of two proposed modifications.

Show more
308 Read more

The BPSO process suffers from getting trapped in a local optimum which results in premature convergence. In order to prevent this from happening, we used chaotic binary **particle** **swarm** **optimization** to overcome the disadvantage. Chaos is a deterministic dynamic system and is very sensitive to initial values. A chaotic map is used to determine the inertia weight value in each iteration. Logistic map is the most frequently used chaotic behavior and is a bounded unstable dynamic behavior. In this paper, we used logistic map to determine the inertia weight value [11]. The inertia weight value is modified according to

Show more
that features better search efficiency than classical **particle** **swarm** **optimization** (PSO) is presented. More importantly, it can per- form a global search over the entire search space with faster convergence speed. The APSO consists of two main steps. First, by evaluating the population distribution and **particle** fitness, a real-time evolutionary state estimation procedure is performed to identify one of the following four defined evolutionary states, in- cluding exploration, exploitation, convergence, and jumping out in each generation. It enables the automatic control of inertia weight, acceleration coefficients, and other algorithmic parameters at run time to improve the search efficiency and convergence speed. Then, an elitist **learning** strategy is performed when the evolutionary state is classified as convergence state. The strategy will act on the globally best **particle** to jump out of the likely local optima. The APSO has comprehensively been evaluated on 12 unimodal and multimodal benchmark functions. The effects of parameter adaptation and elitist **learning** will be studied. Results show that APSO substantially enhances the performance of the PSO par- adigm in terms of convergence speed, global optimality, solution accuracy, and algorithm reliability. As APSO introduces two new parameters to the PSO paradigm only, it does not introduce an additional design or implementation complexity.

Show more
21 Read more