Top PDF Bats echolocation-inspired algorithms for global optimisation problems

Bats echolocation-inspired algorithms for global optimisation problems

Bats echolocation-inspired algorithms for global optimisation problems

Solving structural engineering design optimization problems using an artificial bee colony algorithm.. A fuzzified multi objective interactive honey bee mating optimizati[r]

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Bats echolocation-inspired algorithms for global optimisation problems

Bats echolocation-inspired algorithms for global optimisation problems

Looking at the proposed swarm searching strategy, there is a distinct line between the searching strategy of PSO and MABSA. In the PSO, the algorithm utilises the velocity and positioning of particles to evaluate the obtained solution whereas MABSA depends on the transmission and positioning of sound beams. In the real world, birds can fly with a velocity between 20 to 30 mph (Ehrlich et al., 1988). With this fast speed, the searching process of PSO may miss the locations of good solutions on their way towards other possible target solutions. Moreover, the velocity of particles in PSO itself makes the particle or bird to move in a single line thus not covering a broad search area at one time. The sound beams transmitted in MABSA are multi line that are able to disperse and sweep a large search envelope. Thus, the issue of missing good solutions in a smaller area of designated search space does not arise. Hence, the sequence of searching process as applied in any good swarm intelligence method is followed here where coarse searching (diversification) is done first by PSO followed by fine searching (intensification) by MABSA. In this context, labelling PSO as global search agent and MABSA as local search agent in the proposed hybrid algorithm D-PSO-MABSA is a reasonable choice given their characteristics.
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A modified bats echolocation-based algorithm for solving constrained optimisation problems

A modified bats echolocation-based algorithm for solving constrained optimisation problems

Various research works have been reported over the past two decades on dealing with constrained optimisation problems by using swarm intelligence algorithms. The PSO has been the most favourable technique among them. Parsopoulos and Vrahatis (2005) have proposed a variant of PSO scheme, a unified particle swarm optimisation (UPSO) method with a penalty function approach. The proposed algorithm has abilities to explore and exploit the search process without needing extra requirements of function evaluations and also preserves feasibility of the encountered solutions. Cagnina et al. (2008) investigated simple constrained particle swarm optimiser (SiC-PSO) coupled with a constrained-handling technique. The algorithm is faster, more reliable and efficient after combining local best (lbest) and global best (gbest) models to update the velocity as well as adding gbest to the best position of the particles and to its neighbourhood.
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Single-Solution Simulated Kalman Filter Algorithm for Global Optimisation Problems

Single-Solution Simulated Kalman Filter Algorithm for Global Optimisation Problems

Abstract. This paper introduces single-solution Simulated Kalman Filter (ssSKF), a new single-agent optimisa- tion algorithm inspired by Kalman Filter, for solving real-valued numerical optimisation problems. In comparison, the proposed ssSKF algorithm supersedes the original population-based Simulated Kalman Filter (SKF) algorithm by operating with only a single agent, and having less parameters to be tuned. In the proposed ssSKF algorithm, the initialisation parameters are not constants, but, are produced by random numbers taken from a normal dis- tribution in the range of [0, 1], thus excluding them from tuning requirement. In order to balance between the exploration and exploitation in ssSKF, the proposed algorithm uses an adaptive neighbourhood mechanism during its prediction step. The proposed ssSKF algorithm is tested using the 30 benchmark functions of CEC 2014, and its performance is compared to the original SKF algorithm, Black Hole (BH) algorithm, Particle Swarm Optimisation (PSO) algorithm, Grey Wolf Optimiser (GWO) algorithm, and Genetic Algorithm (GA). The results show that the proposed ssSKF algorithm is a promising approach and able to outperform GWO and GA algorithms, significantly. MS received 1 January 2016; revised 1 January 2016; accepted 1 January 2016
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Dual level searching approach for solving multi-objective optimisation problems using hybrid particle swarm optimisation and bats echolocation-inspired algorithms

Dual level searching approach for solving multi-objective optimisation problems using hybrid particle swarm optimisation and bats echolocation-inspired algorithms

particle swarm optimisation and modified adaptive bats sonar algorithm is presented. The concept of echolocation of a colony of bats to find prey in the modified adaptive bats sonar algorithm is integrated with the established particle swarm optimisation algorithm. The proposed algorithm incorporates advantages of both particle swarm optimisation and modified adaptive bats sonar algorithm approach to handle the complexity of multi objective optimisation problems. These include swarm flight attitude and swarm searching strategy. The performance of the algorithm is verified through several multi objective optimisation benchmark test functions and problem. The acquired results show that the proposed algorithm perform well to produce a reliable Pareto front. The proposed algorithm can thus be an effective method for solving of multi objective optimisation problems.
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Symbolic approaches and artificial intelligence algorithms for solving multi-objective optimisation problems

Symbolic approaches and artificial intelligence algorithms for solving multi-objective optimisation problems

the generalisations of basic convexity concepts with the hope of extending well known properties, characterizations and applications. Many excellent texts and hundreds of articles have appeared in recent years. The optimisation theory of Dubovitskii and Milyutin (1965) has been used by Censor (1977) to produce optimality conditions for differentiable convex vector optimisation. Benson (1978) has examined the existence of efficient and properly efficient solutions for the vector maximisation problem. Kuhn-Tucker necessary conditions (Miettinen, 1999) for a maximum point of a convex function subject to convex constraints have been stated and proved by Batson (1986). Zalmai (1985a,1985b) has adopted a geometric point of view and developed continuous-time analogues of the Fritz-John (Miettinen, 1999) and Kuhn-Tucker (Miettinen, 1999) optimality conditions in the spirit of finite-dimensional nonlinear programming. Furthermore, the relationship between the first-order stationary-point necessary optimality criteria and saddle-point optimality conditions has been discussed. A generalisation of Kuhn- Tucker sufficiency conditions has been presented by Hanson (1994). The P-norm surrogate constraint method (Li, 1996) has been applied by Li (1999) to make convex non-inferior frontier into non-convex multi-objective optimisation problems under certain conditions. Theoretical results concerning the set of non-inferior solutions and a computational algorithm for obtaining a characteristic set of non-inferior solutions have been discussed by Beeson et al. (1971). Craven (1984) has presented a modified kind of Kuhn-Tucker condition applicable to the minimisation problem but not necessarily assuming convexity.
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Prey capture success revealed by echolocation signals in pipistrelle bats 
(Pipistrellus pygmaeus)

Prey capture success revealed by echolocation signals in pipistrelle bats (Pipistrellus pygmaeus)

The laboratory recordings revealed that three acoustic parameters in post-buzz signals depended on capture success. Their correlation with success was so strong that evaluations of the bats’ success based only on those acoustic parameters gave correct classification of trials in capture/fail in up to 85% of the cases, when all three parameters were combined in a first canonical discriminant factor. However, these are laboratory results and comparative acoustic studies of bats in the laboratory and field do show substantial differences (Britton and Jones, 1999; Surlykke and Moss, 2000). Thus, one should be cautious when applying the laboratory results to field data. Not only are acoustics different and more complicated in the field, but the bats themselves produce different signals in the confined laboratory space compared to the field (Surlykke et al., 1993). Bats can learn to predict the trajectory of catapulted food (Miller and Olesen, 1979). Besides, the prey we offered in the laboratory was of bigger size than most of the natural prey of pipistrelle bats (Swift and Racey, 1985; Barlow, 1997), and none of the laboratory prey items could perform evasive manoeuvres.
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Development and applications of multi layered genetic algorithms to multi dimensional optimisation problems

Development and applications of multi layered genetic algorithms to multi dimensional optimisation problems

Objective value in the Generation Objective value at the end of the beginning of the run run in which first 'good' Best in individual is successful Best in all Average Best Average runs [r]

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Echolocation intensity and directionality of perching and flying fringe-lipped bats, Trachops cirrhosus (Phyllostomidae)

Echolocation intensity and directionality of perching and flying fringe-lipped bats, Trachops cirrhosus (Phyllostomidae)

nostrils. Nose leaves of phyllostomids are fairly similar in over- all shape but differ greatly in size ( Vanderelst et al., 2010 ). It is generally accepted that phyllostomids emit echolocation calls through the nostrils. In all probability, the nose leaf, which is not found in mouth-emitting bat families like e.g., Vespertilionidae or Emballonuridae, has a role in shaping and steering the sonar sound beam ( Hartley and Suthers, 1987; Vanderelst et al., 2010 ). However, directionality has rarely been measured directly, and new data from flying Carollia perspicilliata ( Brinkløv et al., 2011 ) demonstrated a narrower sonar beam when flying than ear- lier data from sitting bats had indicated ( Hartley and Suthers, 1987 ). Thus, phyllostomid bats, like vespertilionids, may have the ability to flexibly modify their beam shapes to adapt to a given situation ( Surlykke et al., 2009b; Jakobsen and Surlykke, 2010; Jakobsen et al., 2013 ). Since Trachops hunts while hang- ing from a perch as well as on the wing, it offers an excellent opportunity to study whether sonar search volume (intensity and directionality) is adapted to hunting strategy. In addition to lis- tening for the sounds of its prey, we also frequently observed that T. cirrhosus opened its mouth while echolocating from a perch. Several other phyllostomid species have also been observed to open the mouth while echolocating (Tschapka, page 11 in LaVal and Rodriìguez-H, 2002 ), which might influence the sound emission by changing the emission site or altering the head- related transfer function. Thus, a second purpose of this study was to determine if T. cirrhosus adds an extra level to its sonar flexibility by being able to echolocate both through the nostrils and through the open mouth.
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Echolocation behavior in big brown bats is not impaired after intense broadband noise exposures

Echolocation behavior in big brown bats is not impaired after intense broadband noise exposures

All four bats had substantial prior experience flying through straight corridors (widths 40 to 100 cm) in this chain array (Wheeler et al., 2016), so no progressive familiarization with the flight task itself over test days interfered with any effects of the noise exposure. Bats were flown through the array on four consecutive test days ( pre-exposure, and 20 min, 24 h and 48 h post-exposure). The shape of the corridor alternated between left and right curvatures from one test day to the next (Fig. 1), preventing the formation of a stereotyped spatial map of the array (Barchi et al., 2013). The flight room was kept dark except for a small dim (90 lx) light near the corridor entrance. On each test day, the bat was released by experimenter 1 by hand from a fixed point at the entrance. The first test day was a pre-exposure (baseline) day, during which each bat was randomly assigned to fly through either a left or a right curved corridor. On the second test day, the bat was exposed to noise, as described below, and then 20 min later was flown through the array with the opposite corridor curvature. Each bat was flown again through the array on two subsequent days, 24 h and 48 h after noise exposure, with the corridor curvature alternating on each day. The post-exposure time points of 20 min, 24 h and 48 h are the same as those used in our previous psychophysical experiments (Simmons et al., 2016). On each test day, the bat was flown through the array for a total of 15 – 22 flights (Table 1). If the bat navigated the corridor without striking or colliding with any of the chains and then landed on the back wall of the flight room, it was rewarded by experimenter 2 with a piece of mealworm. These flights are called successful flights. Unsuccessful flights, in which the bat collided with a chain or fell to the floor before reaching the end of the corridor, were not rewarded. Any flights, successful or unsuccessful, marred by experimenter error or equipment malfunction were eliminated.
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Time variant spectral peak and notch detection in echolocation call sequences in bats

Time variant spectral peak and notch detection in echolocation call sequences in bats

order 62. The detection threshold for variations of spectral peaks was measured by varying the modulation depth (in % of the CF) of the time-variant filtered echolocation-call sequence. To measure the bats’ sensitivity to the CF modulation, we presented modulation depths of 100, 52, 40, 30, 24, 18, 14, 11 and 9% of the CF. A modulation depth of 100% defined a frequency range of ± one octave around the CF and produced filter CFs between 30 and 120·kHz. The modulation rate of the CF modulation was 2, 4, 8 or 16·Hz. One echolocation-call sequence always contained two modulation periods. In consequence, the overall duration of the echolocation-call sequence and the temporal separation between the echolocation calls in the sequence decreased with increasing modulation rate. For a modulation rate of 2·Hz, the echolocation- call sequence was 1·s long and the temporal separation between the echolocation calls was about 61·ms; for a modulation rate of 16·Hz, the echolocation-call sequence was 125·ms long and the temporal separation between the echolocation calls was about 6·ms. Spectrograms of an unfiltered call and time-variant and time- invariant echolocation-call sequences are shown in Fig.·1A,B. These echolocation-call sequences simulate a bat moving twice around an abstract virtual acoustic object and ensonifying it from eight different angles. Different flight speeds are represented by modulation rates between 2 and 16·Hz. While this range of modulation rates is low compared with many auditory studies on the perception and encoding of time-variant signals, the rates are certainly high enough to include the speed of spectro-temporal modulations encountered by a bat when it moves around an object ensonifying it from different angles.
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Solving dynamic optimisation problems by combining evolutionary algorithms with KD-tree

Solving dynamic optimisation problems by combining evolutionary algorithms with KD-tree

Abstract—In this paper we propose a novel evolutionary algorithm that is able to adaptively separate the explored and unexplored areas to facilitate detecting changes and tracking the moving optima. The algorithm divides the search space into multiple regions, each covers one basin of attraction in the search space and tracks the corresponding moving optimum. A simple mechanism was used to estimate the basin of attraction for each found optimum, and a special data structure named KD- Tree was used to memorise the searched areas to speed up the search process. Experimental results show that the algorithm is competitive, especially against those that consider change detection an important task in dynamic optimisation. Compared to existing multi-population algorithms, the new algorithm also offers less computational complexity in term of identifying the appropriate sub-population/region for each individual.
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Biologically Inspired Optimisation Algorithms for Transparent Knowledge Extraction 

Allied to Engineering Materials Processing

Biologically Inspired Optimisation Algorithms for Transparent Knowledge Extraction Allied to Engineering Materials Processing

premise part of FRBSs. The parameters of the linear consequents are computed via a ‘recursive least-squares’ method. Chiu (1997) further extended the above fuzzy modelling methodology to a fuzzy classification scenario. A gradient decent algorithm was developed to tune the parameters pertaining to the membership functions in a bid to improve the classification accuracy. Genther et al. (1994) argued that fuzzy (soft) clustering is more suitable for the elicitation of FRBSs than hard clustering methods (e.g. Subtractive Clustering). Their argument is based on the fact that nature objects tend to belong with certain degrees of membership to all classes, which seems to have more intuitive connection with the concept behind the fuzzy sets. In order to associate the information provided by FCM with fuzzy membership functions, the authors approximated the projections of the cluster on each dimension via triangular membership functions. Such a ‘projection’ idea has also been adopted by Delgado et al. (1996), in which a set of fuzzy measures work in conjunction with a hierarchical clustering algorithm to automatically detect the suitable number of clusters. Such pre-processed clustering are then used to initialise the algorithms of the FCM type. Delgado et al. (1997) further proposed and compared various clustering based fuzzy modelling implementations, ranging from the direct use of the clusters’ membership function (refer to Eq. 4.8) to the projections of the clusters, and from clustering on the product space of inputs and outputs to clustering on separate spaces. The conclusions drawn from their work are that the direct use of the clusters’ membership function normally leads to an accurate initial fuzzy model; while on the other hand, projection based method tend to produce descriptive FRBSs at the cost of their accuracy.
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Parallel and interacting stochastic approximation annealing algorithms for global optimisation.

Parallel and interacting stochastic approximation annealing algorithms for global optimisation.

In this article, we develop the parallel and interacting stochastic approximation annealing (PISAA), a general purpose stochastic optimisation algorithm, that extends SAA (Liang et al., 2014) by using population Monte Carlo ideas (Song et al., 2014; Bornn et al., 2013; Liang and Wong, 2000, 2001; Wu and Liang, 2011). Essentially, PISAA works on a population of SAA chains that interact each other in a manner that eliminates the aforementioned problematic behaviour of SAA, and accelerates the overall convergence. This allows the proposed algorithm to demonstrate great performance, and address challenging optimisation problems with high-dimensional and very rugged cost functions. PISAA is enabled to use advanced MCMC transitions that incorporate crossover operations. These operations allow the distributed information across chains of the population to be used in guiding further simulations, and therefore lead to a more efficient exploration of the sampling space. Furthermore, PISAA is equipped with a more accurate and stable self-adjusting mechanism for the target density, that uses information gained from the whole population, and therefore accelerates the overall convergence of the algorithm to the global minimum. The use of multiple chains allows PISAA to initialise from various locations and search for the global minimum at different regions of the sampling space simultaneously. PISAA can be implemented in parallel, if parallel computing environment is available, and hence the computational overhead due to the generation of multiple chains can be reduced dramatically. It is worth emphasising that PISAA is not just an implementation of the SAA running in parallel; its key feature is the way the parallel chains interact in order to overcome the aforesaid problematic behaviour and improve performance. Our numerical examples suggest that the performance of PISAA improves with the size of the population. Also, in problems where the cost function is rugged or high-dimensional, PISAA significantly outperforms other competitors, SA, ASAMC, and SAA, and their population analogues, VFSA, AESAMC, as it was able to discover the global minimum much quicker.
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The peripheral auditory characteristics of noctuid moths: responses to the search phase echolocation calls of bats

The peripheral auditory characteristics of noctuid moths: responses to the search phase echolocation calls of bats

(total system linear ±3 dB 200 Hz to 120 kHz). The trajectory of the bats flying towards the microphone was recorded using multiflash stereophotogrammetry, and sequences of calls were selected only if the bat was flying directly towards the microphone (Waters and Jones, 1995). These calls were characterised by high bandwidth and good signal-to-noise ratio (>40 dB). These calls were sampled from the tape by an Ultra Sound Advice S-350 memory bat recorder at a sampling rate of 400 kHz and played into a Kay DSP 5500 Sonagraph at 10 3 time expansion. Calls from R. ferrumequinum were recorded from the wild in a stone mine using an Ultra Sound Advice S- 25 bat detector, sampled by the S-350 memory bat recorder and downloaded at 10 3 time expansion onto metal tape using a Sony WM-DC6 Professional Walkman. Single calls were edited and compiled with 11 s of silence on either side to create a 22 s sequence. This was downloaded onto a Sony TCD-D3 digital audio tape (DAT) recorder. Three calls from one individual of each of the six species were selected and spaced evenly throughout the tape. An identical sequence was created using a different individual bat from each species to control for intraspecific differences in call structure between bats. To broadcast call sequences, they were replayed into the S-350 at a sampling rate of 40 kHz and recompressed back to real time. The signals were high-pass-filtered at 18 kHz prior to the input to the Ultra Sound Advice amplifier. This process did not significantly affect the structure of any of the calls (Waters and Jones, 1995). While call structures obtained in the laboratory
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Echolocation and passive listening by foraging mouse eared bats
Myotis myotis and M  blythii

Echolocation and passive listening by foraging mouse eared bats Myotis myotis and M blythii

being released back at the roost: in no case did we observe loss of body mass. All bats maintained their health during captivity. Bat activity was watched remotely using an IR video-camera placed at 1·m from the feeding arena and recorded with a videotape recorder. The video system consisted of a time-lapse video recorder (Sanyo, bSRT-7168P, Osaka, Japan) and an infrared camera (Videotronic, CCD-7012P, Neumünster, Germany) with an automatic iris. The focus and sharpness of the image were controlled with a small portable monitor (Sony, GV-D800, Tokyo, Japan), which was also used for surveying the experiments. The operator stayed outside the flight room and was visually sheltered by a panel covering the cage wall. We confirmed that equipment in the flight room did not produce ultrasound by listening with a bat detector. Bat echolocation calls were monitored using the frequency division mode of a Pettersson D980 bat detector (Pettersson Elektronik AB, Uppsala, Sweden). The microphone, placed inside the room (at ca. 15·cm from ground and 1.5·m from the leaf litter tray), was connected to the detector with a 5-m cable. The detector was operated outside the room. Directional effects of the echolocation calls were not considered in power measurements. However, such factors are unlikely to have affected our analysis significantly because (1) the microphone was set close to the feeding tray, i.e. to prey; (2) the directionality of the recording microphone at the relevant frequencies (~50·kHz) is very broad and thus results in a maximum potential underestimation of –2 to –9dB for an angle of ±20° at frequencies of 30 and 50·kHz, respectively (L. Pettersson, personal communication); and (3) during the final approach to prey, bats followed a direct trajectory. Moreover, any influence from directional effects probably affected each sequence randomly so we expected no significant effect on the comparison between species that we carried out.
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Intense echolocation calls from two `whispering' bats, Artibeus
jamaicensis and Macrophyllum macrophyllum (Phyllostomidae)

Intense echolocation calls from two `whispering' bats, Artibeus jamaicensis and Macrophyllum macrophyllum (Phyllostomidae)

A. jamaicensis : source levels and foraging ecology Like most other phyllostomid bats, the frugivorous A. jamaicensis is mainly a narrow space gleaning forager. A. jamaicensis is often difficult to detect on a bat detector, supposedly because it is very quiet. Consequently, our results, which show that this bat can emit intense calls with mean source levels of 96 dB SPL and maximum levels of 110 dB SPL, are surprising. The maximum levels exceeded even those recorded for the insectivorous M. macrophyllum. It is perhaps not so surprising that A. jamaicensis can produce higher intensities that M. macrophyllum considering the large difference in size between the two species. A. jamaicensis (40–55 g) is approximately six times larger than M. macrophyllum (6–9 g). Yet high source levels disagree with common difficulties in detecting and recording phyllostomids. However, our experimental design focused on determining the highest source levels. Hence, the mean source levels that we report here for A. jamaicensis may represent the upper range of its normal output intensity: a conclusion that is supported by our data screening. We restricted our analyses to recordings with a S/N ratio of +10 dB or better to permit accurate acoustic positioning. Only 45 out of 250 files recorded from A. jamaicensis fulfilled this criterion, in contrast to more than 50% of the files recorded from M. macrophyllum. The majority of discarded files from A. jamaicensis were not empty but contained echolocation calls below criterion, indicating that most of the time they emitted quiet calls. Predominantly quiet echolocation calls agree well with the gleaning behaviour of a frugivore at close range, when the bat has already detected fruit at longer range by smell and then approaches the fruit in dense vegetation. In addition, the large difference in recorded amplitude on the four microphones in the array suggested that A. jamaicensis may emit a narrow echolocation beam, adding to the difficulties in detecting this species acoustically. Beam width might relate to the difference in capture technique between the two species. M. macrophyllum uses the feet and tail membrane to capture moving insects and a broader beam reduces the risk of losing the insect whereas A. jamaicensis picks stationary fruit with its mouth and may therefore benefit from the more precise localisation of a narrow beam.
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A New Approach in Deterministic Global Optimisation of Problems with Ordinary Differential Equations

A New Approach in Deterministic Global Optimisation of Problems with Ordinary Differential Equations

In order to overcome the convergence to local minima, stochastic search [7] as well as deterministic [17] methods can be applied. The former class of methods [19, 4] consists in sampling the feasible domain to locate the global optimum. But although they improve the likelihood of finding the global optimum, no theoretical guarantee can be given in a finite number of iterations. From this point of view, deterministic methods are more interesting since they guarantee ε-convergence to the global solution in finite time. Global optimisation of dynamic problem based on the simultaneous discretisation approach has been addressed by Smith and Pantelides [31] and, more recently, by Esposito and Floudas [12] who applied the αBB approach [21, 3, 1] with applications to parameter estimation. However, such algorithms are inherently limited to moderately sized optimisation problems, and were shown to perform poorly for nonlinear systems.
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A honeybees-inspired heuristic algorithm for numerical optimisation

A honeybees-inspired heuristic algorithm for numerical optimisation

A number of other metaheuristic and/or swarm intelli- gence algorithms have also attempted to solve the bench- marks we considered, recently. Based on the relevance that the same functions have been attempted, it is decided to include these studies in the review to help grasp the diffi- culty of the problems attended. Gong et al. [7], Liu et al. [23], Zhao and Tang [35] and Xin et al. [32] have published their results for the benchmark problems up to 30 dimen- sions using different variants of particle swarm optimisa- tion, differential evolution and a particular algorithm so- called monkey algorithm. Their results are apparently either not better than, or remain competitive with ours. Likewise, Han et al. [10], Rahmani and Yusof [28] and Alam et al. [1, 3] have introduced their approaches for 30 and 50 dimensions, where our approach usually outper- forms them or remain competitive. None of the following references have attempted dimensions larger than 50, but, the majority of them have only considered up to 30, while our approach outperform them in major [2, 5, 8, 17, 26]. These studies have mostly compared their result with those produced by Suganthan et al. [31] in which a comprehen- sive study is extensively reported on solving a number of numerical optimisation benchmarks.
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Solving of Optimisation Tasks Inspired by Living Organisms

Solving of Optimisation Tasks Inspired by Living Organisms

U SCP je ze seznamu nenavˇ st´ıven´ ych mˇ est odebr´ ano dalˇ s´ı navˇ st´ıven´ e mˇ esto a kromˇ e toho jsou odebr´ ana i mˇ esta reprezentuj´ıc´ı mnoˇ ziny, kter´ e obsahuj´ı pouze bo[r]

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