The concept of **bacteria** as a model for problem solving is not new. The work in [19] presents a new approach for edge detection using a combination of bacterial foraging (i.e. the **behavior** bacterial organisms develop to obtain enough food to enable them to reproduce) and a technique derived from Ant Colony Systems. The authors claim that the foraging **behavior** of some species of **bacteria** like Escherichia coli can be hypothetically modeled as **an** **optimization** process. This work derives from the previous proposal in [20], where authors explain the social foraging **behavior** of Escherichia coli and Myxococcus xanthus **bacteria** and develop simulation models **based** **on** the principles of foraging theory. Bacterial foraging as **an** **optimization** mechanism is explained in detail in [21]. These last three works focus **on** foraging strategies, as a concept that emphasizes competition in the sense that animals that have successful foraging strategies are more likely to enjoy reproductive success.

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2011 ). Energy of ultrasonic backscattering (Arthur et al., 2003 ) and tissue attenuation (Ueno et al., 1990) are also known to be dependent **on** temperature and have been proposed as methods to monitor temperature using, for example, the gray level information in B-mode images (Alvarenga et al., 2017; Teixeira et al., 2014). Later, in the 2000’s, photoacoustic (PA) imaging was proposed as a technique for temperature estimation **based** **on** PA signal amplitude temperature dependence (Larina et al., 2005; Pramanik and Wang, 2009; Schüle et al., 2004; Shah et al., 2008). Temperature estimative using PA imaging can be **an** interesting approach due to its good spatial resolution and optical contrast besides being capable of imaging at greater depths than purely optical techniques (Wang and Hu, 2012; Xu and Wang, 2006). Generation of PA-**based** thermal images during thermotherapy procedures has been investigated by analyzing the laser-induced pressure profile in PA images (Larina et al., 2005).

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Most of the ideas behind ACO come from the foraging **behavior** observed in real ant colonies (Hölldobler and Wil- son, 1990). When **an** ant moves through the environment and discovers a food source, it deposits a chemical substance **on** the ground, named trail pheromone. The pheromone leads other ants from the nest to the food source. Other ants follow the first ant’s pheromone trail and reinforce it by deposition of additional pheromone. If there are several pheromone trails leading to the same food source, ants will choose probabilistically the path to follow, **based** **on** the pheromone concentrations **on** the existing paths. Ants that traverse the shortest path between a nest and a food source return to the nest sooner than ants that choose longer paths. Thus, after multiple traverses involving nest and food source, the short- est path will have a stronger pheromone concentration than longer paths. Consequently, ants will concentrate **on** this path determining cooperatively the optimal path to the food source. Ants operate under stigmergy (Grassé, 1959), a mechanism of indirect communication that coordinates the work of independent entities which have access only to local information about the environment.

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Abstract—We present **an** adaptive approach for improving the performance in randomly distributed Wireless Sensor Networks (WSNs). The goal is to find the optimal routing not only to maximize the lifetime of the network but also to provide real-time data transmission services. Considering a wireless sensor network where the nodes have limited energy, we propose a novel model Energy ∗ Delay **based** **on** Ant Colony **Optimization** (ACO) **algorithm** (E&D ANTS) to minimize the time delay in transferring a fixed number of data from the source nodes to the destination nodes in **an** energy-constrained manner. In the **algorithm**, **an** amount of artificial ants randomly explored the network and exchanged collected network information to periodically update ant routing-tables which were obtained by having integrated partial pheromones and heuristic values. Our study is focused **on** influence functions of pheromones. Because of the tradeoff of energy and delay in wireless network systems, we propose the Reinforcement Learning (RL) **algorithm** to train our model. The simulation results show that our method boasts undoubtedly a number of attractive features, including adaptation, robustness and stability.

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The population **based** heuristic algorithms have two important groups: evolutionary algorithms (EA) and swarm intelligence (SI) **based** algorithms. Some of the recognized evolutionary algorithms are: Genetic **Algorithm** (GA), Evolution Strategy (ES), Evolution Programming (EP), Differential Evolution (DE), **Bacteria** Foraging **Optimization** (BFO), Artificial Immune **Algorithm** (AIA), etc. Some of the well-known swarm intelligence **based** algorithms are: Particle Swarm **Optimization** (PSO), Shuffled Frog Leaping (SFL), Ant Colony **Optimization** (ACO), Artificial Bee Colony (ABC), Fire Fly (FF) **algorithm**, etc. Besides the evolutionary and swarm intelligence **based** algorithms, there are some other algorithms which work **on** the principles of different natural phenomena. Some of them are: Harmony Search **algorithm** (HSA), Gravitational Search **algorithm** (GSA), Biogeography-**Based** **Optimization** (BBO), Grenade Explosion Method (GEM), etc. (Rao & Patel, 2012).

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or impossible to encounter the optimal stage without diversity across the population. However, in this problem, this does not apply because even without population diversity, it will always be possible to reach the optimal solution. If all the individuals of the population shared the same values for each gene, the crossover process would be redundant, and the **algorithm** is entirely dependent **on** mutations. If this is the case in our problem, it would just be a matter of time until it reaches the desired solution. Thus not having population diversity does not preclude the search for the optimum solution, it only delays it. In this problem, premature convergence may be due to a combination of factors: low population size, aggressive fitness function, and flat mutation rate. If **an** individual had a considerably higher fitness of than its remaining peers, the chances that this individual is replicated more times in the next generation is increased, which contributes to premature convergence. With a low mutation rate, the individuals don’t change much from their previous self, which results in smaller population diversity. Coupling these factors with a moderate population size, increases even more, the chances of **an** early convergence.

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ABSTRACT. This work develops two approaches **based** **on** the fuzzy set theory to solve a class of fuzzy mathematical **optimization** problems with uncertainties in the objective function and in the set of constraints. The first approach is **an** adaptation of **an** iterative method that obtains cut levels and later maximizes the membership function of fuzzy decision making using the bound search method. The second one is a meta- heuristic approach that adapts a standard genetic **algorithm** to use fuzzy numbers. Both approaches use a decision criterion called satisfaction level that reaches the best solution in the uncertain environment. Selected examples from the literature are presented to compare and to validate the efficiency of the methods addressed, emphasizing the fuzzy **optimization** problem in some import-export companies in the south of Spain.

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The demand for different levels of Quality of Service (QoS) in IP networks is growing, mainly to attend multimedia applications. However, not only indicators of quality have conflicting features, but also the problem of determining routes covered by more than two QoS constraints is NP-complete (Nondeterministic Polynomial Time Complete). This work proposes **an** **algorithm** to optimize multiple Quality of Service indices of Multi Protocol Label Switching (MPLS) IP networks. Such **an** approach aims at mini- mizing the network cost and the amount of simultaneous requests rejection, as well as performing load balancing among routes. The proposed **algorithm**, the Variable Neigh- borhood Multiobjective Genetic **Algorithm** (VN-MGA), is a Genetic **Algorithm** **based** **on** the Elitist Non-Dominated Sorted Genetic **Algorithm** (NSGA-II), with a particular fea- ture that different parts of a solution are encoded differently, at Level 1 and Level 2. In order to improve results, both representations are needed. At Level 1, the first part of the solution is encoded by considering as decision variables the arrows that form the routes to be followed by each request (whilst the second part of the solution is kept constant), whereas at Level 2, the second part of the solution is encoded by considering the sequence of requests as decision variables, and first part is kept constant. Pareto- fronts obtained by VN-MGA dominate fronts obtained by fixed-neighborhood encoding schemes. Besides potential benefits of the proposed approach application to packet routing **optimization** in MPLS networks, this work raises the theoretical issue of the sys- tematic application of variable encodings, which allow variable neighborhood searches, as operators inside general evolutionary computation algorithms.

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Abstract. In this paper a filled function method is suggested for solving nonlinear systems of equalities and inequalities. Firstly, the original problem is reformulated into **an** equivalent constrained global **optimization** problem. Subsequently, a new filled function with one parameter is constructed **based** **on** the special characteristics of the reformulated **optimization** problem. Some properties of the filled function are studied and discussed. Finally, **an** **algorithm** **based** **on** the proposed filled function for solving nonlinear systems of equalities and inequalities is presented. The objective function value can be reduced by half in each iteration of our filled function **algorithm**. The implementation of the **algorithm** **on** several test problems is reported with numerical results.

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The problem considered in this paper is motivated by the design of probabilistic controllers [4, 5, 7] for controlled Markov chains, that imply the **optimization** of the Kullback-Leibler divergence. The **optimization** literature (e.g. [6]) refers many minimization algorithms that apply to smooth cost functions. Most methods are **based** **on** a cost function descent towards a local minimum. They provide, at each iteration, a direction computed from the cost functions local properties, usu- ally the gradient and, sometimes, the hessian. Meth- ods **based** **on** the gradient alone are usually slow, while

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Genetic **algorithm** (GA) is **an** adaptive method which is generally employed to solve search and **optimization** problems [6]. It is **based** **on** the genetic processes of biological organisms. We employ it to find the number of clusters and their heads. Particle Swarm **optimization** (PSO), motivated by the social behaviors of animals such as bird flocking and fish schooling, it is widely applied in **optimization** [8]. We employ PSO to overcome the problem of assigning nodes to cluster heads and constructing the clusters.

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Most of the improvements achieved **on** BA were not inspired by natural bee behaviors. However, the imitation of the best characteristics in nature can lead to efficient metaheuristic algorithms [22]. Therefore, it is good to search for additional natural bee aspects that can be modeled in BA and improve its performance. There are numerous biological features in nature associated with honeybee foragers and food sources that can be beneficial if they are properly modeled and incorporated into Basic BA. Among these features that we can model are the distribution of food sources and the distribution of honeybees when they fly away from the hive foraging for food. In nature, flowers are usually distributed in patches that regenerate and are rarely completely depleted [23]. In addition, a scout honeybee flies away from the hive and moves randomly throughout the space according to Levy flight motion [24-26], which has been found to constitute the optimal search strategy [23, 24, 27]. During the harvesting season, a portion of the colony population is kept as scout bees foraging for new food sources **on** the global scale [10, 28]. Furthermore, in nature, it has been found that Levy looping search triggers the flight paths that is performed by honeybee foragers conducting a local search around a known food source [25]. Consequently, in this paper, we enhance PLIA-BA, and propose **an** improved version of BA called Patch-Levy-**based** Bees **Algorithm** (PLBA). PLBA utilizes the PLIA for initialization stage [21], a new local search **algorithm** that models Levy looping flights, and **an** enhanced global search that is improved **based** **on** the

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The 'narrow band’ assumption is made when analysing the performance of **an** adaptive array signal processing or estimation scheme. A vague definition of narrow band given in the literature[9] is that there essentially no decorrelation between signals received **on** opposite ends of the array.

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Membrane computing is **an** emergent branch of natural computing, which has been extensively used to solve various NP-complete and intractable problems. In this paper, a bio- inspired **algorithm** **based** **on** membrane computing (BIAMC) is proposed to solve the engineering design problem. BIAMC is designed with the framework and rules of a cell-like P systems, and particle swarm **optimization** with the neighborhood search. Simulation and experimental results demonstrate that the improved **algorithm** is valid and outperforms other evolutionary algorithms for engineering design problems.

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The topological derivative measures the sensitivity of a shape functional with respect to **an** infinitesimal singular domain perturbation, such as the insertion of holes, inclusions or source-terms. The topological derivative has been successfully applied in obtaining the optimal topology for a large class of physics and engineering problems. In this paper the topological derivative is applied in the context of topology **optimization** of structures subject to multiple load-cases. In particular, the structural compliance under plane stress or plane strain assumptions is minimized under volume constraint. For the sake of completeness, the topological asymptotic analy- sis of the total potential energy with respect to the nucleation of a small circular inclusion is developed in all details. Since we are dealing with multiple load-cases, a multi-objective **optimization** problem is proposed and the topological sensitivity is obtained as a sum of the topological derivatives associated with each load-case. The volume constraint is im- posed through the Augmented Lagrangian Method. The obtained result is used to devise a topology **optimization** **algorithm** **based** **on** the topological derivative together with a level-set domain representation method. Finally, several finite element-**based** examples of structural **optimization** are pre- sented.

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A new noise-assisted data analysis (NADA) method, Ensemble EMD (EEMD) [11] proposed, to alleviate the mode mixing problem in EMD. Recently EEMD **based** ECG denoising methods were proposed in the literature [12]. Even though EEMD method can be used to fix the mode mixing issue, computational complexity in EEMD because of the multiple iterations is a primary concern for real-time applications. Most of the real-time ECG monitoring devices are used computationally less powerful DSP or ARM processors because of its cost effectiveness. **An** ECG denoising **algorithm** is a pre-processing **algorithm** which is followed by other algorithms that are used to identify different arrhythmias and heart diseases automatically. So the complexity of noise removal **algorithm**, in terms of computational time is **an** important criterion for real-time ECG monitoring applications. The optimized implementation of EMD introduced in [13], in which the author tried to optimize the EMD implementation and characterized the performance of **optimization** **based** **on** various lengths of ECG data sets.

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Genetic **Algorithm** is **an** **optimization** and search technique **based** **on** selection mechanism and natural evolution, following Darwin’s theory of species’ evolution, which explains the history of life through the action of physical processes and genetic operators in populations or species. GA allows a population composed of many individuals to evolve under specified selection rules to a state that maximizes the “fitness” (maximizes or minimizes a cost function). Such **an** **algorithm** became popular through the work of John Holland in the early 1970s, and particularly his book Adaptation in Natural and Artificial Systems (1975). The **algorithm** can be implemented in a binary form or in a continuous (real-valued) form. This paper considers the latter case.

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Evolutionary algorithms (EAs) are population-**based** global search methods. They have been successfully applied to many complex **optimization** problems. However, EAs are frequently incapable of finding a convergence solution in default of local search mechanisms. Memetic Algorithms (MAs) are hybrid EAs that combine genetic operators with local search methods. With global exploration and local exploitation in search space, MAs are capable of obtaining more high-quality solutions. **On** the other hand, mixed-integer hybrid differential evolution (MIHDE), as **an** EA-**based** search **algorithm**, has been successfully applied to many mixed-integer **optimization** problems. In this paper, a memetic **algorithm** **based** **on** MIHDE is developed for solving mixed-integer **optimization** problems. However, most of real-world mixed-integer **optimization** problems frequently consist of equality and/or inequality constraints. In order to effectively handle constraints, **an** evolutionary Lagrange method **based** **on** memetic **algorithm** is developed to solve the mixed-integer constrained **optimization** problems. The proposed **algorithm** is implemented and tested **on** two benchmark mixed-integer constrained **optimization** problems. Experimental results show that the proposed **algorithm** can find better optimal solutions compared with some other search algorithms. Therefore, it implies that the proposed memetic **algorithm** is a good approach to mixed-integer **optimization** problems.

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A relatively new meta-heuristic approach, where its application in portfolio **optimization** is still limited, is particle swarm **optimization** (PSO). Mous et al. (2006) compared PSO and GA which was applied to portfolio selection, Xu et al. (2007) and Gao and Chu (2010) proposed improved PSO algorithms for portfolio problem with transaction costs and quality constraints. Mishra et al. (2009) studied portfolio **optimization** problem from multi-objective perspective and considered four well- known multi-objective evolutionary algorithms including multi-objective PSO (MOPSO) which outperformed its counterparts for some numerical experiments. Cura (2009) presented a PSO **algorithm** to solve cardinality constrained portfolio. Compared with other meta-heuristics, PSO is simple, high speed, large scope and easy to be implemented by programs. However, there are still many issues in particle swarm, such as slow convergence during the latter search, poor precision and converging to local optimum. To overcome the above problems, a lot of revised PSO have emerged. Investors generally incline to restrict the number of assets in the portfolio and purchase just a subset of them. Therefore, cardinality is a practical constraint that has to be considered in decisions. In this paper, we address a portfolio **optimization** problem with floor, ceiling, and cardinality constraints. This problem is a mixed integer programming with quadratic objective function where traditional **optimization** methods fail to find the optimal solution, efficiently. We propose a new hybrid solution approach **based** **on** **an** improved PSO (IPSO) and a simulated annealing (SA) procedure to optimize the cardinality constrained portfolio problem. Our proposed **algorithm** takes advantage of inertia weights mechanism and constriction factor approach in updating the particle’s velocity to improve the PSO searching capabilities. In addition, **an** SA procedure is embedded into IPSO to improve the capacity of fine-tuning solution in the latter period of the search. Incorporating SA procedure can enhance the ability of IPSO for jumping out of the local optimum. Computational experiments **on** standard benchmark problems are carried out to assess the effectiveness of the IPSO-SA **algorithm** to solve cardinality constrained portfolio problem.

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Nowadays, digital image compression has become a crucial factor of modern telecommunication systems. Image compression is the process of reducing total bits required to represent **an** image by reducing redundancies while preserving the image quality as much as possible. Various applications including internet, multimedia, satellite imaging, medical imaging uses image compression in order to store and transmit images in **an** efficient manner. Selection of compression technique is **an** application-specific process. In this paper, **an** improved compression technique **based** **on** Butterfly-Particle Swarm **Optimization** (BPSO) is proposed. BPSO is **an** intelligence-**based** iterative **algorithm** utilized for finding optimal solution from a set of possible values. The dominant factors of BPSO over other **optimization** techniques are higher convergence rate, searching ability and overall performance. The proposed technique divides the input image into 8 blocks. Discrete Cosine Transform 8 (DCT) is applied to each block to obtain the coefficients. Then, the threshold values are obtained from BPSO. **Based** **on** this threshold, values of the coefficients are modified. Finally, quantization followed by the Huffman encoding is used to encode the image. Experimental results show the effectiveness of the proposed method over the existing method.

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