# Biblio

An Improved Multi-objective Particle Swarm Optimization. 2020 5th International Conference on Computational Intelligence and Applications (ICCIA). :19–23.

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2020. For solving multi-objective optimization problems, this paper firstly combines a multi-objective evolutionary algorithm based on decomposition (MOEA/D) with good convergence and non-dominated sorting genetic algorithm II (NSGA-II) with good distribution to construct. Thus we propose a hybrid multi-objective optimization solving algorithm. Then, we consider that the population diversity needs to be improved while applying multi-objective particle swarm optimization (MOPSO) to solve the multi-objective optimization problems and an improved MOPSO algorithm is proposed. We give the distance function between the individual and the population, and the individual with the largest distance is selected as the global optimal individual to maintain population diversity. Finally, the simulation experiments are performed on the ZDT\textbackslashtextbackslashDTLZ test functions and track planning problems. The results indicate the better performance of the improved algorithms.

Application research and improvement of particle swarm optimization algorithm. 2020 IEEE International Conference on Power, Intelligent Computing and Systems (ICPICS). :238–241.

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2020. Particle swarm optimization (PSO), as a kind of swarm intelligence algorithm, has the advantages of simple algorithm principle, less programmable parameters and easy programming. Many scholars have applied particle swarm optimization (PSO) to various fields through learning it, and successfully solved linear problems, nonlinear problems, multiobjective optimization and other problems. However, the algorithm also has obvious problems in solving problems, such as slow convergence speed, too early maturity, falling into local optimization in advance, etc., which makes the convergence speed slow, search the optimal value accuracy is not high, and the optimization effect is not ideal. Therefore, many scholars have improved the particle swarm optimization algorithm. Taking into account the improvement ideas proposed by scholars in the early stage and the shortcomings still existing in the improvement, this paper puts forward the idea of improving particle swarm optimization algorithm in the future.

An Adaptive Grey Wolf Algorithm Based on Population System and Bacterial Foraging Algorithm. 2020 IEEE International Conference on Artificial Intelligence and Computer Applications (ICAICA). :744–748.

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2020. In this thesis, an modified algorithm for grey wolf optimization in swarm intelligence optimization algorithm is proposed, which is called an adaptive grey wolf algorithm (AdGWO) based on population system and bacterial foraging optimization algorithm (BFO). In view of the disadvantages of premature convergence and local optimization in solving complex optimization problems, the AdGWO algorithm uses a three-stage nonlinear change function to simulate the decreasing change of the convergence factor, and at the same time integrates the half elimination mechanism of the BFO. These improvements are more in line with the actual situation of natural wolves. The algorithm is based on 23 famous test functions and compared with GWO. Experimental results demonstrate that this algorithm is able to avoid sinking into the local optimum, has good accuracy and stability, is a more competitive algorithm.

Design of Self Tuning PID Controller Based on Competitional PSO. 2020 4th Conference on Swarm Intelligence and Evolutionary Computation (CSIEC). :022–026.

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2020. In this work, a new particle swarm optimization (PSO)-based optimization algorithm, and the idea of a running match is introduced and employed in a non-linear system PID controller design. This algorithm aims to modify the formula of velocity calculating of the general PSO method to increase the diversity of the searching process. In this process of designing an optimal PID controller for a non-linear system, the three gains of the PID controller form a particle, which is a parameter vector and will be updated iteratively. Many of those particles then form a population. To reach the PID gains which are optimum, using modified velocity updating formula and position updating formula, the position of all particles of the population will be moved into the optimization direction. In the meanwhile, an objective function may be minimized as the performance of the controller get improved. To corroborate the controller functioning of this method, a non-linear system known as inverted pendulum will be controlled by the designed PID controller. The results confirm that the new method can show excellent performance in the non-linear PID controller design task.

Artificial Intelligence and Internet of Things for Robotic Disaster Response. 2020 International Conference on Advanced Robotics and Intelligent Systems (ARIS). :1–6.

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2020. After the Fukushima nuclear disaster and the Wenchuan earthquake, the relevant government agencies recognized the urgency of disaster-straining robots. There are many natural or man-made disasters in Taiwan, and it is usually impossible to dispatch relevant personnel to search or explore immediately. The project proposes to use the architecture of Intelligent Internet of Things (AIoT) (Artificial Intelligence + Internet of Things) to coordinate with ground, surface and aerial and underwater robots, and apply them to disaster response, ground, surface and aerial and underwater swarm robots to collect environmental big data from the disaster site, and then through the Internet of Things. From the field workstation to the cloud for “training” deep learning model and “model verification”, the trained deep learning model is transmitted to the field workstation via the Internet of Things, and then transmitted to the ground, surface and aerial and underwater swarm robots for on-site continuing objects classification. Continuously verify the “identification” with the environment and make the best decisions for the response. The related tasks include monitoring, search and rescue of the target.

Joint User Association and Power Allocation Using Swarm Intelligence Algorithms in Non-Orthogonal Multiple Access Networks. 2020 9th International Conference on Modern Circuits and Systems Technologies (MOCAST). :1–4.

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2020. In this paper, we address the problem of joint user association and power allocation for non-orthogonal multiple access (NOMA) networks with multiple base stations (BSs). A user grouping procedure into orthogonal clusters, as well as an allocation of different physical resource blocks (PRBs) is considered. The problem of interest is mathematically described using the maximization of the weighted sum rate. We apply two different swarm intelligence algorithms, namely, the recently introduced Grey Wolf Optimizer (GWO), and the popular Particle Swarm Optimization (PSO), in order to solve this problem. Numerical results demonstrate that the above-described problem can be satisfactorily addressed by both algorithms.

Particle Swarm Optimization Algorithm with Variety Inertia Weights to Solve Unequal Area Facility Layout Problem. 2020 Chinese Control And Decision Conference (CCDC). :4240–4245.

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2020. The unequal area facility layout problem (UA-FLP) is to place some objects in a specified space according to certain requirements, which is a NP-hard problem in mathematics because of the complexity of its solution, the combination explosion and the complexity of engineering system. Particle swarm optimization (PSO) algorithm is a kind of swarm intelligence algorithm by simulating the predatory behavior of birds. Aiming at the minimization of material handling cost and the maximization of workshop area utilization, the optimization mathematical model of UA-FLPP is established, and it is solved by the particle swarm optimization (PSO) algorithm which simulates the design of birds' predation behavior. The improved PSO algorithm is constructed by using nonlinear inertia weight, dynamic inertia weight and other methods to solve static unequal area facility layout problem. The effectiveness of the proposed method is verified by simulation experiments.

Analysis of Human Behaviors in Real-Time Swarms. 2020 10th Annual Computing and Communication Workshop and Conference (CCWC). :0104–0109.

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2020. Many species reach group decisions by deliberating in real-time systems. This natural process, known as Swarm Intelligence (SI), has been studied extensively in a range of social organisms, from schools of fish to swarms of bees. A new technique called Artificial Swarm Intelligence (ASI) has enabled networked human groups to reach decisions in systems modeled after natural swarms. The present research seeks to understand the behavioral dynamics of such “human swarms.” Data was collected from ten human groups, each having between 21 and 25 members. The groups were tasked with answering a set of 25 ordered ranking questions on a 1-5 scale, first independently by survey and then collaboratively as a real-time swarm. We found that groups reached significantly different answers, on average, by swarm versus survey ( p=0.02). Initially, the distribution of individual responses in each swarm was little different than the distribution of survey responses, but through the process of real-time deliberation, the swarm's average answer changed significantly ( ). We discuss possible interpretations of this dynamic behavior. Importantly, the we find that swarm's answer is not simply the arithmetic mean of initial individual “votes” ( ) as in a survey, suggesting a more complex mechanism is at play-one that relies on the time-varying behaviors of the participants in swarms. Finally, we publish a set of data that enables other researchers to analyze human behaviors in real-time swarms.

Multi-Robot System Based on Swarm Intelligence for Optimal Solution Search. 2020 International Congress on Human-Computer Interaction, Optimization and Robotic Applications (HORA). :1–5.

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2020. This work presents the results of the Multi-Robot System designing that works on the basis of Swarm Intelligence models and is used to search for optimal solutions. The process of searching for optimal solutions is performed based on a field of gradient vectors that can be generated by ionizing radiation sources, radio-electro-magnetic devices, temperature generating sources, etc. The concept of the operation System is based on the distribution in the search space of a multitude of Mobile Robots that form a Mesh network between them. Each Mobile Robot has a set of ultrasonic sensors for excluding the collisions with obstacles, two sensors for identifying the gradient vector of the analyzed field, resources for wireless storage, processing and communication. The direction of the Mobile Robot movement is determined by the rotational speed of two DC motors which is calculated based on the models of Artificial Neural Networks. Gradient vectors generated by all Mobile Robots in the system structure are used to calculate the movement direction.

Prioritizing Policy Objectives in Polarized Groups using Artificial Swarm Intelligence. 2020 IEEE Conference on Cognitive and Computational Aspects of Situation Management (CogSIMA). :1–9.

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2020. Groups often struggle to reach decisions, especially when populations are strongly divided by conflicting views. Traditional methods for collective decision-making involve polling individuals and aggregating results. In recent years, a new method called Artificial Swarm Intelligence (ASI) has been developed that enables networked human groups to deliberate in real-time systems, moderated by artificial intelligence algorithms. While traditional voting methods aggregate input provided by isolated participants, Swarm-based methods enable participants to influence each other and converge on solutions together. In this study we compare the output of traditional methods such as Majority vote and Borda count to the Swarm method on a set of divisive policy issues. We find that the rankings generated using ASI and the Borda Count methods are often rated as significantly more satisfactory than those generated by the Majority vote system (p\textbackslashtextless; 0.05). This result held for both the population that generated the rankings (the “in-group”) and the population that did not (the “out-group”): the in-group ranked the Swarm prioritizations as 9.6% more satisfactory than the Majority prioritizations, while the out-group ranked the Swarm prioritizations as 6.5% more satisfactory than the Majority prioritizations. This effect also held even when the out-group was subject to a demographic sampling bias of 10% (i.e. the out-group was composed of 10% more Labour voters than the in-group). The Swarm method was the only method to be perceived as more satisfactory to the “out-group” than the voting group.

SQMAA: Security, QoS and Mobility Aware ACO Based Opportunistic Routing Protocol for MANET. 2018 4th International Conference for Convergence in Technology (I2CT). :1–6.

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2018. The QoS performance of MANET routing protocols is significantly affected by the mobility conditions in network. Secondly, as MANET open nature network, there is strong possibility of different types of vulnerabilities such as blackhole attack, malicious attack, DoS attacks etc. In this research work, we are designing the novel opportunistic routing protocol in order to address the challenges of network security as well as QoS improvement. There two algorithms designed in this paper. First we proposed and designed novel QoS improvement algorithm based on optimization scheme called Ant Colony Optimization (ACO) with swarm intelligence approach. This proposed method used the RSSI measurements to determine the distance between two mobile nodes in order to select efficient path for communication. This new routing protocol is named as QoS Mobility Aware ACO (QMAA) Routing Protocol. Second, we designed security algorithm for secure communication and user's authentication in MANET under the presence attackers in network. With security algorithm the QoS aware protocol is proposed named as Secure-QMAA (SQMAA). The SQMAA achieved secure communications while guaranteed QoS performance against existing routing protocols. The simulation results shows that under the presence of malicious attackers, the performance of SQMAA are efficient as compared to QMAA and state-of-art routing protocol.

Clustering Algorithm Optimized by Brain Storm Optimization for Digital Image Segmentation. 2019 7th International Symposium on Digital Forensics and Security (ISDFS). :1–6.

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2019. In the last several decades digital images were extend their usage in numerous areas. Due to various digital image processing methods they became part areas such as astronomy, agriculture and more. One of the main task in image processing application is segmentation. Since segmentation represents rather important problem, various methods were proposed in the past. One of the methods is to use clustering algorithms which is explored in this paper. We propose k-means algorithm for digital image segmentation. K-means algorithm's well known drawback is the high possibility of getting trapped into local optima. In this paper we proposed brain storm optimization algorithm for optimizing k-means algorithm used for digital image segmentation. Our proposed algorithm is tested on several benchmark images and the results are compared with other stat-of-the-art algorithms. The proposed method outperformed the existing methods.

Intrusion Detection Using Swarm Intelligence. 2019 UK/ China Emerging Technologies (UCET). :1–5.

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2019. Recent advances in networking and communication technologies have enabled Internet-of-Things (IoT) devices to communicate more frequently and faster. An IoT device typically transmits data over the Internet which is an insecure channel. Cyber attacks such as denial-of-service (DoS), man-in-middle, and SQL injection are considered as big threats to IoT devices. In this paper, an anomaly-based intrusion detection scheme is proposed that can protect sensitive information and detect novel cyber-attacks. The Artificial Bee Colony (ABC) algorithm is used to train the Random Neural Network (RNN) based system (RNN-ABC). The proposed scheme is trained on NSL-KDD Train+ and tested for unseen data. The experimental results suggest that swarm intelligence and RNN successfully classify novel attacks with an accuracy of 91.65%. Additionally, the performance of the proposed scheme is also compared with a hybrid multilayer perceptron (MLP) based intrusion detection system using sensitivity, mean of mean squared error (MMSE), the standard deviation of MSE (SDMSE), best mean squared error (BMSE) and worst mean squared error (WMSE) parameters. All experimental tests confirm the robustness and high accuracy of the proposed scheme.

An Intrusion Detection System using Opposition based Particle Swarm Optimization Algorithm and PNN. 2019 International Conference on Machine Learning, Big Data, Cloud and Parallel Computing (COMITCon). :184–188.

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2019. Network security became a viral topic nowadays, Anomaly-based Intrusion Detection Systems [1] (IDSs) plays an indispensable role in identifying the attacks from networks and the detection rate and accuracy are said to be high. The proposed work explore this topic and solve this issue by the IDS model developed using Artificial Neural Network (ANN). This model uses Feed - Forward Neural Net algorithms and Probabilistic Neural Network and oppositional based on Particle Swarm optimization Algorithm for lessen the computational overhead and boost the performance level. The whole computing overhead produced in its execution and training are get minimized by the various optimization techniques used in these developed ANN-based IDS system. The experimental study on the developed system tested using the standard NSL-KDD dataset performs well, while compare with other intrusion detection models, built using NN, RB and OPSO algorithms.

A Swarm Intelligence Approach to Avoid Local Optima in Fuzzy C-Means Clustering. 2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). :1–6.

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2019. Clustering analysis is an important computational task that has applications in many domains. One of the most popular algorithms to solve the clustering problem is fuzzy c-means, which exploits notions from fuzzy logic to provide a smooth partitioning of the data into classes, allowing the possibility of multiple membership for each data sample. The fuzzy c-means algorithm is based on the optimization of a partitioning function, which minimizes inter-cluster similarity. This optimization problem is known to be NP-hard and it is generally tackled using a hill climbing method, a local optimizer that provides acceptable but sub-optimal solutions, since it is sensitive to initialization and tends to get stuck in local optima. In this work we propose an alternative approach based on the swarm intelligence global optimization method Fuzzy Self-Tuning Particle Swarm Optimization (FST-PSO). We solve the fuzzy clustering task by optimizing fuzzy c-means' partitioning function using FST-PSO. We show that this population-based metaheuristics is more effective than hill climbing, providing high quality solutions with the cost of an additional computational complexity. It is noteworthy that, since this particle swarm optimization algorithm is self-tuning, the user does not have to specify additional hyperparameters for the optimization process.

An Effective Swarm Optimization Based Intrusion Detection Classifier System for Cloud Computing. 2019 5th International Conference on Advanced Computing Communication Systems (ICACCS). :185–188.

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2019. Most of the swarm optimization techniques are inspired by the characteristics as well as behaviour of flock of birds whereas Artificial Bee Colony is based on the foraging characteristics of the bees. However, certain problems which are solved by ABC do not yield desired results in-terms of performance. ABC is a new devised swarm intelligence algorithm and predominately employed for optimization of numerical problems. The main reason for the success of ABC algorithm is that it consists of feature such as fathomable and flexibility when compared to other swarm optimization algorithms and there are many possible applications of ABC. Cloud computing has their limitation in their application and functionality. The cloud computing environment experiences several security issues such as Dos attack, replay attack, flooding attack. In this paper, an effective classifier is proposed based on Artificial Bee Colony for cloud computing. It is evident in the evaluation results that the proposed classifier achieved a higher accuracy rate.

Feature-Weighted Fuzzy K-Modes Clustering. Proceedings of the 2019 3rd International Conference on Intelligent Systems, Metaheuristics & Swarm Intelligence. :63–68.

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2019. Fuzzy k-modes (FKM) are variants of fuzzy c-means used for categorical data. The FKM algorithms generally treat feature components with equal importance. However, in clustering process, different feature weights need to be assigned for feature components because some irrelevant features may degrade the performance of the FKM algorithms. In this paper, we propose a novel algorithm, called feature-weighted fuzzy k-modes (FW-FKM), to improve FKM with a feature-weight entropy term such that it can automatically compute different feature weights for categorical data. Some numerical and real data sets are used to compare FW-FKM with some existing methods in the literature. Experimental results and comparisons actually demonstrate these good aspects of the proposed FW-FKM with its effectiveness and usefulness in practice.

A Bi-objective Routing Model for Underwater Wireless Sensor Network. Proceedings of the 2019 3rd International Conference on Intelligent Systems, Metaheuristics & Swarm Intelligence. :78–82.

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2019. Underwater wireless communication is a critical and challenging research area wherein acoustic signals are used to transfer data. The Underwater Wireless Sensor Network (UWSN) is used to transmit data sensed by the sensors in the sea bed to the surface sinks through intermediate nodes for seismic surveillance, border security and underwater environment monitoring applications. The nodes comprising of UWSN are battery operated and are subjected to failures leading to connectivity loss. And the propagation delay in sending the data in the form of acoustic signals is found to be high and as the depth increases the transmission delay also increases. Hence, routing in UWSN is a complex problem. The simulation experiments of the delay sensitive protocols are found to minimize the delay at the expense of network throughput which is not acceptable. The energy aware routing protocols on the other hand reduces energy consumption and routing overhead but has high delay involved in transmission. In this study, transmission delay and reliability estimation models are developed using which bi-objective routing model is proposed considering both delay and reliability in route selection. In the simulation studies, the bi-objective model reduced delay on an average by 9% and the reliability of the network is improved by 34% when compared to the delay sensitive and reliable routing strategies.

An Online Password Guessing Method Based on Big Data. Proceedings of the 2019 3rd International Conference on Intelligent Systems, Metaheuristics & Swarm Intelligence. :59–62.

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2019. Password authentication is the most widely used authentication method in information systems. The traditional proactive password detection method is generally implemented by counting password length, character class number and computing password information entropy to improve password security. However, passwords that pass proactive password detection do not represent that they are secure. In this paper, based on the research of the characteristics of password distribution under big data, we propose an online password guessing method, which collects a dataset of guessing passwords composed of weak passwords, high frequency passwords and personal information related passwords. It is used to guess the 13k password dataset leaked in China's largest ticketing website, China Railways 12306 website. The experimental results show that even if our guess object has passed the strict proactive password detection, we can construct a guessing password dataset contain only 100 passwords, and effectively guess 4.84% of the passwords.

Towards Swarm Intelligence Architectural Patterns: an IoT-Big Data-AI-Blockchain convergence perspective. Proceedings of the 4th International Conference on Big Data and Internet of Things. :1–8.

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2019. The Internet of Things (IoT) is exploding. It is made up of billions of smart devices -from minuscule chips to mammoth machines - that use wireless technology to talk to each other (and to us). IoT infrastructures can vary from instrumented connected devices providing data externally to smart, and autonomous systems. To accompany data explosion resulting, among others, from IoT, Big data analytics processes examine large data sets to uncover hidden patterns, unknown correlations between collected events, either at a very technical level (incident/anomaly detection, predictive maintenance) or at business level (customer preferences, market trends, revenue opportunities) to provide improved operational efficiency, better customer service, competitive advantages over rival organizations, etc. In order to capitalize business value of the data generated by IoT sensors, IoT, Big Data Analytics/IA need to meet in the middle. One critical use case for IoT is to warn organizations when a product or service is at risk. The aim of this paper is to present a first proposal of IoT-Big Data-IA architectural patterns catalogues with a Blockchain implementation perspective in seek of design methodologies artifacts.

Evolutionary and swarm-intelligence algorithms through monadic composition. Proceedings of the Genetic and Evolutionary Computation Conference Companion. :1382–1390.

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2019. Reproducible experimental work is a vital part of the scientific method. It is a concern that is often, however, overlooked in modern computational intelligence research. Scientific research within the areas of programming language theory and mathematics have made advances that are directly applicable to the research areas of evolutionary and swarm intelligence. Through the use of functional programming and the established abstractions that functional programming provides, it is possible to define the elements of evolutionary and swarm intelligence algorithms as compositional computations. These compositional blocks then compose together to allow the declarations of an algorithm, whilst considering the declaration as a "sub-program". These sub-programs may then be executed at a later time and provide the blueprints of the computation. Storing experimental results within a robust data-set file format, which is widely supported by analysis tools, provides additional flexibility and allows different analysis tools to access datasets in the same efficient manner. This paper presents an open-source software library for evolutionary and swarm-intelligence algorithms which allows the type-safe, compositional, monadic and functional declaration of algorithms while tracking and managing effects (e.g. usage of a random number generator) that directly influences the execution of an algorithm.

Learning How to Flock: Deriving Individual Behaviour from Collective Behaviour with Multi-agent Reinforcement Learning and Natural Evolution Strategies. Proceedings of the Genetic and Evolutionary Computation Conference Companion. :169–170.

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2018. This work proposes a method for predicting the internal mechanisms of individual agents using observed collective behaviours by multi-agent reinforcement learning (MARL). Since the emergence of group behaviour among many agents can undergo phase transitions, and the action space will not in general be smooth, natural evolution strategies were adopted for updating a policy function. We tested the approach using a well-known flocking algorithm as a target model for our system to learn. With the data obtained from this rule-based model, the MARL model was trained, and its acquired behaviour was compared to the original. In the process, we discovered that agents trained by MARL can self-organize flow patterns using only local information. The expressed pattern is robust to changes in the initial positions of agents, whilst being sensitive to the training conditions used.

How Swarm Size During Evolution Impacts the Behavior, Generalizability, and Brain Complexity of Animats Performing a Spatial Navigation Task. Proceedings of the Genetic and Evolutionary Computation Conference. :77–84.

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2018. While it is relatively easy to imitate and evolve natural swarm behavior in simulations, less is known about the social characteristics of simulated, evolved swarms, such as the optimal (evolutionary) group size, why individuals in a swarm perform certain actions, and how behavior would change in swarms of different sizes. To address these questions, we used a genetic algorithm to evolve animats equipped with Markov Brains in a spatial navigation task that facilitates swarm behavior. The animats' goal was to frequently cross between two rooms without colliding with other animats. Animats were evolved in swarms of various sizes. We then evaluated the task performance and social behavior of the final generation from each evolution when placed with swarms of different sizes in order to evaluate their generalizability across conditions. According to our experiments, we find that swarm size during evolution matters: animats evolved in a balanced swarm developed more flexible behavior, higher fitness across conditions, and, in addition, higher brain complexity.

Evolving Hardware Instinctive Behaviors in Resource-scarce Agent Swarms Exploring Hard-to-reach Environments. Proceedings of the Genetic and Evolutionary Computation Conference Companion. :1497–1504.

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2018. This work introduces a novel adaptation framework to energy-efficiently adapt small-sized circuits operating under scarce resources in dynamic environments, as autonomous swarm of sensory agents. This framework makes it possible to optimally configure the circuit based on three key mechanisms: (a) an off-line optimization phase relying on R2 indicator based Evolutionary Multi-objective Optimization Algorithm (EMOA), (b) an on-line phase based on hardware instincts and (c) the possibility to include the environment in the optimization loop. Specifically, the evolutionary algorithm is able to simultaneously determine an optimal combination of static settings and dynamic instinct for the hardware, considering highly dynamic environments. The instinct is then run on-line with minimal on-chip resources so that the circuit efficiently react to environmental changes. This framework is demonstrated on an ultrasonic communication system between energy-scarce wireless nodes. The proposed approach is environment-adaptive and enables power savings up to 45% for the same performance on the considered case studies.

Comparative study on discrete SI approaches to the graph coloring problem. :81–82.

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2018. The Graph Coloring Problem is an important benchmark problem for decision and discrete optimization problems. In this work, we perform a comparative experimental study of four algorithms based on Swarm Intelligence for the 3-Graph Coloring Problem: Particle Swarm Optimization (PSO), Artificial Bee Colonies (ABC), Cuckoo Search (CS) and FireFly Algorithm (FFA). For each algorithm, we test parameter settings published in the literature, as well as parameters found by an automated tuning methodology (irace). This comparison may shed some light at the strengths and weaknesses of each algorithm, as well as their dependence on parameter values.