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# Metaheuristic Algorithms: A Critical Analysis

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A keynote talk at ICHSA2017

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### Metaheuristic Algorithms: A Critical Analysis

1. 1. Metaheuristic Algorithms: A Critical Analysis Xin-She Yang Middlesex University London ICHSA 2017 Xin-She Yang Nature-Inspired Computation ICHSA2017 1 / 54
2. 2. The Essence of an Algorithm The Essence of an Algorithm The Essence of an Algorithm Essence of an Optimization Algorithm To move to a new, better point x(t+1) from an existing location x(t). x1 x2 x(t) x(t+1) ? Population-based algorithms use multiple, interacting paths. Diﬀerent algorithms Diﬀerent strategies/approaches in generating these moves! Xin-She Yang Nature-Inspired Computation ICHSA2017 2 / 54
3. 3. The Essence of an Algorithm The Essence of an Algorithm The Essence of an Algorithm In essence, an algorithm can be written (mathematically) as xt+1 = A(xt , α), For any given xt, the algorithm will generate a new solution xt+1. Functional or a Dynamical System? We can view the above equation as an iterative functional (with ﬁxed points), or a dynamical system (with attractors), or a self-organization system (with organized structures), or a Markov chain (e.g., Markov chain Monte Carlo). The behavoir of the system (algorithm) can be controlled by A and α. For details, please refer to: Xin-She Yang et al., Swarm Intelligence and Bio-Inspired Computation: Theory and Applications, Elsevier, (2013). Xin-She Yang Nature-Inspired Computation ICHSA2017 3 / 54
4. 4. The Essence of an Algorithm What’s Wrong with Traditional Algorithms? What’s Wrong with Traditional Algorithms? Some issues with traditional optimization algorithms such as the Newton-Raphson Method, pattern search, quadratic programming, etc. Traditional algorithms are mostly local search, thus cannot guarantee global optimality (except for linear programming and convex optimization). Results often depend on the initial starting points (except linear and convex problems). Methods tend to be problem-speciﬁc (e.g., k-opt, branch and bound). Cannot deal with highly nonlinear optimization problems eﬃciently. Struggle to cope problems with discontinuity. Xin-She Yang Nature-Inspired Computation ICHSA2017 4 / 54
5. 5. The Essence of an Algorithm Nature-Inspired Optimization Algorithms Nature-Inspired Optimization Algorithms Almost all nature-inspired metaheuristic optimization algorithms (heuristic or metaheuristic algorithms, as a global optimizer) strive to Increase the probability of ﬁnding the global optimality (as a global search tool); Solve a wider class of problems (treating them as a black-box); Try to deal with highly nonlinear problems, problems with discontinuity, and even NP-hard combinatorial problems; Draw design inspiration from Nature. Xin-She Yang Nature-Inspired Computation ICHSA2017 5 / 54
6. 6. Nature-Inspired Algorithms Nature-Inspired Optimization Algorithms Nature-Inspired Optimization Algorithms Genetic algorithms (1960s/1970s), evolutionary strategy (Rechenberg & Swefel 1960s), evolutionary programming (Fogel et al. 1960s). Simulated annealing (Kirkpatrick et al. 1983), Tabu search (Glover 1980s), ant colony optimization (Dorigo 1992), genetic programming (Koza 1992), particle swarm optimization (Kennedy & Eberhart 1995), diﬀerential evolution (Storn & Price 1996/1997) harmony search (Geem et al. 2001), , artiﬁcial bee colony (Karaboga, 2005). Fireﬂy algorithm (Yang 2008), cuckoo search (Yang & Deb 2009), bat algorithm (Yang, 2010), ﬂower pollination algorithm (2012), ... For details, please refer to: Xin-She Yang, Nature-Inspired Optimization Algorithms, Elsevier, (2014). Xin-She Yang Nature-Inspired Computation ICHSA2017 6 / 54
7. 7. Nature-Inspired Algorithms Three diﬀerent ways of thinking ... Three diﬀerent ways of thinking ... Particle swarm optimization: swarm intelligence Harmony search: music-inspired Cuckoo search: swarm intelligence and also scale-free search Xin-She Yang Nature-Inspired Computation ICHSA2017 7 / 54
8. 8. Swarm Intelligence Seeking Inspiration in Nature: Swarm Intelligence Seeking Inspiration in Nature: Swarm Intelligence Swarm Intelligence Ants, bees, birds, ﬁsh ... Simple rules lead to complex behaviour. Swarming Starlings (YouTube Video) Xin-She Yang Nature-Inspired Computation ICHSA2017 8 / 54
9. 9. Swarm Intelligence PSO PSO Particle Swarm Optimization (Kennedy and Eberhart, 1995) xi g∗ xj vt+1 i = vt i + αǫ1(g∗ − xt i ) + βǫ2(x∗ i − xt i ), xt+1 i = xt i + vt+1 i . α, β = learning parameters, ǫ1, ǫ2=random numbers. Xin-She Yang Nature-Inspired Computation ICHSA2017 9 / 54
10. 10. Swarm Intelligence PSO Demo and Disadvantages PSO Demo and Disadvantages The updating equations in PSO form a linear system:   xi vi   t+1 =   1 1 −(αǫ1 + βǫ2) 1     xi vi   t +   0 αǫ1g∗ + βǫ2x∗ i  . PSO Demo Premature convergence Xin-She Yang Nature-Inspired Computation ICHSA2017 10 / 54
11. 11. Swarm Intelligence Fireﬂy Algorithm Fireﬂy Algorithm Fireﬂy Video (YouTube) Fireﬂy Behaviour and Idealization (Yang, 2008) Fireﬂies are unisex and brightness varies with distance. Less bright ones will be attracted to bright ones. If no brighter ﬁreﬂy can be seen, a ﬁreﬂy will move randomly. xt+1 i = xt i + β0e−γr2 ij (xj − xi ) + α ǫt i . ⋄ The objective landscape maps to a light-based landscape, and ﬁreﬂies swarm into the brightest points/regions. ⋄ There is no g∗, therefore, there is no leader. Also, a highly nonlinear iterative system, so subdivision into multiswarms is possible. Xin-She Yang Nature-Inspired Computation ICHSA2017 11 / 54
12. 12. Swarm Intelligence FA Demo and Advantages FA Demo and Advantages Paths of ﬁreﬂies for 3D Rosenbrock function (Husselmann, 2014). Xin-She Yang Nature-Inspired Computation ICHSA2017 12 / 54
13. 13. Swarm Intelligence Why is FA so eﬃcient? Why is FA so eﬃcient? FA Demo Multimodal optimality Advantages of Fireﬂy Algorithm over PSO Automatically subdivide the whole population into subgroups, and each subgroup swarms around a local mode/optimum. Control modes/ranges by varying γ. Control randomization by tuning parameters such as α. Suitable for multimodal, nonlinear, global optimization problems. Xin-She Yang Nature-Inspired Computation ICHSA2017 13 / 54
14. 14. Swarm Intelligence Fireﬂy algorithm is Not PSO Fireﬂy algorithm is Not PSO Though both algorithms (in fact, almost all algorithms) use a population and some update equations, FA is not PSO (not even similar to PSO). Main diﬀerences FA uses a nonlinear attraction mechanism (inverse-quare law plus exponential decay). PSO mechanism is simply linear (xt i − g∗). The population in the FA can subdivide into subgroups and thus can form multi-swarm automatically (PSO cannot). The standard FA does not use g∗ (though PSO uses g∗). xt+1 i = xt i + β0e−γr2 ij (xj − xi ) + α ǫt i . FA can ﬁnd multiple optimal solutions simultaneously (PSO cannot). FA has a fractal-like search structure (PSO cannot). Xin-She Yang Nature-Inspired Computation ICHSA2017 14 / 54
15. 15. Swarm Intelligence Harmony Search Harmony Search Zong Woo Geem et al. (2001). Music-inspired metaheuristic. Now almost 14,000 papers [Google scholar] with diverse applications: Variants for speciﬁc applications: Continuous optimization ... Discrete variants for scheduling, travelling-salesman problem, combinatorial optimization ... Water distribution, network optimization ... Clustering, classiﬁcations and feature selection ... Multiobjective harmony search ... Hybridization with other algorithms. A diverse range of applications, for example, see ICHSA2017. Xin-She Yang Nature-Inspired Computation ICHSA2017 15 / 54
16. 16. Swarm Intelligence Cuckoo Breeding Behaviour Cuckoo Breeding Behaviour Cuckoo Behavior (YouTube Video) Evolutionary Advantages Parallism: Dumps eggs in the nests of (multiple) host birds and let these host birds raise their chicks, so minimum eﬀorts and maximum success. Timing: Cuckoo’s eggs hatch slightly earlier. Fitness: Similarity of eggs in terms of texture, colour, etc. Xin-She Yang Nature-Inspired Computation ICHSA2017 16 / 54
17. 17. Swarm Intelligence Cuckoo Search (Yang and Deb, 2009) Cuckoo Search (Yang and Deb, 2009) Cuckoo Behaviour and Idealization Each cuckoo lays one egg (solution) at a time, and dumps its egg in a randomly chosen nest. The best nests with high-quality eggs (solutions) will carry out to the next generation. The egg laid by a cuckoo can be discovered by the host bird with a probability pa and a nest will then be built. Xin-She Yang Nature-Inspired Computation ICHSA2017 17 / 54
18. 18. Swarm Intelligence Cuckoo Search Cuckoo Search Local random walk: xt+1 i = xt i + s ⊗ H(pa − ǫ) ⊗ (xt j − xt k). [xi , xj , xk are 3 diﬀerent solutions, H(u) is a Heaviside function, ǫ is a random number drawn from a uniform distribution, and s is the step size. Global random walk via L´evy ﬂights: xt+1 i = xt i + αL(s, λ), L(s, λ) = λΓ(λ) sin(πλ/2) π 1 s1+λ , (s ≫ s0). Generation of new moves by L´evy ﬂights, random walk and elitism. Xin-She Yang Nature-Inspired Computation ICHSA2017 18 / 54
19. 19. Swarm Intelligence The normal distribution p(x; µ, σ2 ) = 1 σ √ 2π exp[− (x − µ)2 2σ2 ], −∞ < x < ∞. Isotropic Random Walks SN = N i=1 Xi = X1 + ... + XN = SN−1 + XN, s Xin-She Yang Nature-Inspired Computation ICHSA2017 19 / 54
20. 20. Swarm Intelligence L´evy Distribution and L´evy Flights L´evy Distribution and L´evy Flights L(s) = 1 π ∞ 0 cos(τs)e−α τγ dτ, (0 < γ ≤ 2), = γ 2π exp − γ 2(s − µ) 1 (s − µ)3/2 , 0 < µ < s < ∞ (for steps µ > 0). s Self-similar, multi-scale, global random walks. Xin-She Yang Nature-Inspired Computation ICHSA2017 20 / 54
21. 21. Swarm Intelligence Bat Algorithm (Yang, 2010) Bat Algorithm (Yang, 2010) BBC Video Microbats use echolocation for hunting Ultrasonic short pulses as loud as 110dB with a short period of 5 to 20 ms. Frequencies of 25 kHz to 100 kHz. Speed up pulse-emission rate and increase loudness when homing at a prey. Xin-She Yang Nature-Inspired Computation ICHSA2017 21 / 54
22. 22. Swarm Intelligence Bat Algorithm Bat Algorithm Acoustics of bat echolocation λ = v f ∼ 2 mm to 14 mm. Rules used in the bat algorithm: fi = fmin + (fmax − fmin)β, β ∈ [0, 1], vt+1 i = vt i + (xt i − x∗)fi , xt+1 i = xt i + vt i . Variations of Loudness and Pulse Rate At+1 i ← αAt i , α ∈ (0, 1], rt+1 i = r0 i [1 − exp(−γt)]. Xin-She Yang Nature-Inspired Computation ICHSA2017 22 / 54
23. 23. Swarm Intelligence Other Algorithms Other Algorithms Genetic algorithms Diﬀerential evolution Artiﬁcial immune system Flower pollination algorithm Memetic algorithm ... Reviews Yang, X. S., Nature-Inspired Optimization Algorithms, Elsevier, (2014). Xin-She Yang Nature-Inspired Computation ICHSA2017 23 / 54
24. 24. Applications Applications Applications Design optimization: structural engineering, product design ... Scheduling, routing and planning: discrete, combinatorial problems ... Image processing and data Mining: image segmentation, feature selection ... Applications in almost all areas (e.g., ﬁnance, economics, engineering, industry, ...) 10 Examples in Science and Engineering Xin-She Yang Nature-Inspired Computation ICHSA2017 24 / 54
25. 25. Applications Pressure Vessel Design Optimization (Example 1) Pressure Vessel Design Optimization (Example 1) r d1 r L d2 Xin-She Yang Nature-Inspired Computation ICHSA2017 25 / 54
26. 26. Applications Pressure Vessel Design Pressure Vessel Design This is a well-known test problem for optimization (e.g., see Cagnina et al. 2008) and it can be written as minimize f (x) = 0.6224d1rL + 1.7781d2r2 + 3.1661d2 1 L + 19.84d2 1 r, subject to    g1(x) = −d1 + 0.0193r ≤ 0 g2(x) = −d2 + 0.00954r ≤ 0 g3(x) = −πr2L − 4π 3 r3 + 1296000 ≤ 0 g4(x) = L − 240 ≤ 0. The simple bounds are 0.0625 ≤ d1, d2 ≤ 99 × 0.0625, 10.0 ≤ r, L ≤ 200.0. The best solution (Yang, 2010; Gandomi and Yang, 2011) f∗ = 6059.714, x∗ = (0.8125, 0.4375, 42.0984, 176.6366). Now we have a set of analytical solutions (Yang et al., 2013). Xin-She Yang Nature-Inspired Computation ICHSA2017 26 / 54
27. 27. Applications Speed Reducer/Gear Box Design (Example 2) Speed Reducer/Gear Box Design (Example 2) Mixed-Integer Programming: Continuous variables and integers. Xin-She Yang Nature-Inspired Computation ICHSA2017 27 / 54
28. 28. Applications f (x1, x2, x3, x4, x5, x6, x7) = 0.7854x1x2 2 (3.3333x2 3 + 14.9334x3 − 43.0934) −1.508x1(x2 6 + x2 7 ) + 7.4777(x3 6 + x3 7 ) + 0.7854(x4x2 6 + x5x2 7 ), subject to g1 = 27 x1x2 2 x3 − 1 ≤ 0, g2 = 397.5 x1x2 2 x2 3 − 1 ≤ 0, g3 = 1.93x3 4 x2x3d4 1 − 1 ≤ 0, g4 = 1.93x3 5 x2x3d4 2 − 1 ≤ 0, g5 = 1 110x3 6 (745x4 hx3 )2 + 16.9 × 106 − 1 ≤ 0, g6 = 1 85x3 7 (745x5 hx3 )2 + 157.5 × 106 − 1 ≤ 0, g7 = x2x3 40 − 1 ≤ 0, g8 = 5x2 x1 − 1 ≤ 0, g9 = x1 12x2 − 1 ≤ 0, g10 = 1.5x6+1.9 x4 − 1 ≤ 0, g11 = 1.1x7+1.9 x5 − 1 ≤ 0. Simple bounds are 2.6 ≤ x1 ≤ 3.6, 0.7 ≤ h ≤ 0.8, 17 ≤ x3 ≤ 28, 7.3 ≤ x4 ≤ 8.3, 7.8 ≤ x5 ≤ 8.3, 2.9 ≤ x6 ≤ 3.9, and 5.0 ≤ x7 ≤ 5.5. z must be integers. Xin-She Yang Nature-Inspired Computation ICHSA2017 28 / 54
29. 29. Applications Dome Design (Example 3) Dome Design (Example 3) 120-bar dome: Divided into 7 groups, 120 design elements, about 200 constraints (Gandomi and Yang 2011; Yang et al. 2012). Xin-She Yang Nature-Inspired Computation ICHSA2017 29 / 54
30. 30. Applications Tower Design (Example 4) Tower Design (Example 4) 26-storey tower: 942 design elements, 244 nodal links, 59 groups/types, > 4000 nonlinear constraints (Yang et al. 2011; Gandomi & Yang 2012). Xin-She Yang Nature-Inspired Computation ICHSA2017 30 / 54
31. 31. Applications Car Door Design (Example 5) Car Door Design (Example 5) Design better, safer and energy-eﬃcient cars Minimize weight, low crash deﬂection (< 32 mm), lower impact force (< 4 kN), .... Even a side barrier has 11 design variables! Xin-She Yang Nature-Inspired Computation ICHSA2017 31 / 54
32. 32. Applications Scheduling(Example 6) Scheduling(Example 6) MK Marichelvam, T Prabaharan, XS Yang, Improved cuckoo search algorithm for hybrid ﬂow shop scheduling problems to minimize makespan, Applied Soft Computing, vol. 19, no. 1,pp. 93-101 (2014). Xin-She Yang Nature-Inspired Computation ICHSA2017 32 / 54
33. 33. Applications Soft Testing and Path Generation Soft Testing and Path Generation Srivastava, Mallikarjun, Yang (2013). Optimal test sequence generation using ﬁreﬂy algorithm, Swarm and Evolutionary Computation, 8(2013) 44-53. Xin-She Yang Nature-Inspired Computation ICHSA2017 33 / 54
34. 34. Applications Travel Salesman Problem (Example 7) Travel Salesman Problem (Example 7) Xin-She Yang Nature-Inspired Computation ICHSA2017 34 / 54
35. 35. Applications Cuckoo Search for TSP Cuckoo Search for TSP Aziz Ouaarab, Belad Ahiod, Xin-She Yang, Discrete cuckoo search algorithm for the travelling salesman problem, Neural Computing and Applications, (2013). http://link.springer.com/article/10.1007/s00521-013-1402-2. Xin-She Yang Nature-Inspired Computation ICHSA2017 35 / 54
36. 36. Applications Data Mining: Feature Selection (Example 8) Data Mining: Feature Selection (Example 8) Bat algorithm and cuckoo search are very competitive (Papa et al, 2013; 2014). Also eﬀective at dimension reduction (in terms of number of key features). Dataset # samples #features #classes Diabetes 768 8 2 DNA 2000 180 3 Mushrooms 8124 112 2 OPF BA CS FA ICS PSO0 10 20 30 40 50 60 70 80 Accuracy[%] 61 61 59 61 61 6160 61 61 62 6263 62 62 62 61 Mushrooms Baseline Binary Sigmoid Hyperbolic Tangent Xin-She Yang Nature-Inspired Computation ICHSA2017 36 / 54
37. 37. Applications Image Processing (Example 9) Image Processing (Example 9) Satellite images and ﬂooding estimates (Senthilnath & Yang, 2014) Xin-She Yang Nature-Inspired Computation ICHSA2017 37 / 54
38. 38. Applications Satellite images Satellite images Three methods are compared, and FA obtained the best results. Algorithms Optimal Worst Mean GA 0.8044 0.7528 0.7824 PSO 0.8057 0.8009 0.8051 FA 0.8126 0.8019 0.8076 Also, Senthilnath et al. compared 14 diﬀerent algorithms for classiﬁcations, and they found that the ﬁreﬂy algorithm seems to be most eﬃcient among 14 diﬀerent classiﬁcation methods. Xin-She Yang Nature-Inspired Computation ICHSA2017 38 / 54
39. 39. Applications Classiﬁcations and Clustering (Example 10) Classiﬁcations and Clustering (Example 10) K-means clustering with nature-inspired algorithms can produce far better results than K-means methods (Fong, Deb, Yang, Zhang, 2014). Xin-She Yang Nature-Inspired Computation ICHSA2017 39 / 54
40. 40. Applications Theoretical Analysis Theoretical Analysis Though it still lacks a solid mathematical framework, theoretical studies start to emerge: Dynamic system theory Bayesian statistics Intermit search theory Markov chain Monte Carlo Self-organization theory Convergence analysis Exploration and exploitation Xin-She Yang Nature-Inspired Computation ICHSA2017 40 / 54
41. 41. Applications Self-Organization Self-Organization Self-organizing systems are everywhere, physical, chemical, biological, social, artiﬁcial ... Xin-She Yang Nature-Inspired Computation ICHSA2017 41 / 54
42. 42. Applications Similarities Between Self-Organization and Optimization Similarities Between Self-Organization and Optimization Self-organization: High degrees of freedom, a suﬃcient number of states. Noise, perturbation =⇒ diversity. Selection mechanism =⇒ structure. Far-from-equilibrium and large perturbation =⇒ potentially faster to re-organize. Optimization Algorithms: A suﬃcient larger population. Randomization, stochastic components, exploration =⇒ to escape local optima. Selection and exploitation =⇒ convergence & optimal solutions. High-degrees of randomization =⇒ more likely to reach global optimality (but may be slow). Xin-She Yang Nature-Inspired Computation ICHSA2017 42 / 54
43. 43. Applications But there are signiﬁcant diﬀerences! But there are signiﬁcant diﬀerences! Self-Organization: Avenues to self-organization may be unclear. Time may not be important. Optimization (especially metaheuristics): How to make an algorithm converge is very important. Speed of convergence is crucial (to reach truly global optimality with the minimum computing eﬀorts). However, we lack good theories to understand either self-organization or metaheuristic optimization. Xin-She Yang Nature-Inspired Computation ICHSA2017 43 / 54
44. 44. Applications Multi-Agent System (Swarm Intelligence?) Multi-Agent System (Swarm Intelligence?) For a multi-agent system or a swarm, an algorithm can be considered as a set of interacting Markov chain or a complex dynamical system      x1 x2 ... xn      t+1 = A[x1, ..., xn; ǫ1, ..., ǫm; p1(t), ..., pk (t)]      x1 x2 ... xn      t . A population of solutions xt+1 i (i = 1, ..., n) are generated from xt i , controlled by k parameters and m random numbers. In principle, the behaviour of an algorithm is controlled by the eigenvalues of A, but in practice, it is almost impossible to ﬁgure out the eigenvalues (apart from very simple/rare cases). Xin-She Yang Nature-Inspired Computation ICHSA2017 44 / 54
45. 45. Exploration & Exploitation Key Components in All Metaheuristics Key Components in All Metaheuristics So many algorithms – what are the common characteristics? What are the key components? How to use and balance diﬀerent components? What controls the overall behaviour of an algorithm? Xin-She Yang Nature-Inspired Computation ICHSA2017 45 / 54
46. 46. Exploration & Exploitation Exploration and Exploitation Exploration and Exploitation Characteristics of Metaheuristics Exploration and Exploitation, or Diversiﬁcation and Intensiﬁcation. Exploitation/Intensiﬁcation Intensive local search, exploiting local information. E.g., hill-climbing. Exploration/Diversiﬁcation Exploratory global search, using randomization/stochastic components. E.g., hill-climbing with random restart. Xin-She Yang Nature-Inspired Computation ICHSA2017 46 / 54
47. 47. Exploration & Exploitation Summary Summary Exploitation Exploration uniform search steepest descent Tabu Nelder-Mead CS PSO/FAEP/ES SA Ant/Bee Genetic algorithms Newton- Raphson Best? Free lunch? Xin-She Yang Nature-Inspired Computation ICHSA2017 47 / 54
48. 48. The Future – Some Open Problems (Swarm Intelligence) The Future – Some Open Problems (Swarm Intelligence) The Future – Some Open Problems (Swarm Intelligence) Origin of Swarm Intelligence: What are the main mechanisms to produce collective intelligence from seemingly simple local rules? Any theory for the rise of swarm intelligence? Mathematical Analysis: A uniﬁed mathematical framework (e.g., Markov chain theory, dynamical systems) is needed. Comparison: What are the best/fair performance measures? Parameter tuning: How to tune the algorithm-dependent parameters so that an algorithm can achieve the best performance? Is there a general framework for this? Scalability: Can the algorithms that work for small-scale problems be directly applied to large-scale/high-dimensional problems (for d > 1000) ? Intelligence: Smart algorithms may be a buzz word, but can truly intelligent algorithms be developed? Xin-She Yang Nature-Inspired Computation ICHSA2017 48 / 54
49. 49. The Future – Some Open Problems (Swarm Intelligence) Intelligent Algorithms? Intelligent Algorithms? Xin-She Yang Nature-Inspired Computation ICHSA2017 49 / 54
50. 50. The Future – Some Open Problems (Swarm Intelligence) Books on Nature-Inspired Algorithms Books on Nature-Inspired Algorithms Xin-She Yang, Nature-Inspired Optimization Algorithms, Elsevier, (2014). Xin-She Yang, Cuckoo Search and Fireﬂy Algorithm, Springer, (2014). Xin-She Yang Nature-Inspired Computation ICHSA2017 50 / 54
51. 51. The Future – Some Open Problems (Swarm Intelligence) Thank you :) Any questions? Thank you :) Any questions? Xin-She Yang et al., Swarm Intelligence and Bio-Inspired Computation: Theory and Applications, Elsevier, (2013). Xin-She Yang, Artiﬁcial Intelligence, Evolutionary Computing and Metaheuristics, (2013). Xin-She Yang Nature-Inspired Computation ICHSA2017 51 / 54
52. 52. The Future – Some Open Problems (Swarm Intelligence) References References Xin-She Yang, Nature-Inspire Optimization Algorithm, Elsevier, (2014). Xin-She Yang, Gebrail Bekdas, Sinan Melih Nigdeli, Metaheuristics and Optimization in Civil Engineering, Springer, (2016). Xin-She Yang and Suash Deb, Multiobjective cuckoo search for design optimization, Computers & Operations Research, 40(6), 1616–1624 (2013). X. S. Yang and S. Deb, Cuckoo search: recent advances and applications, Neural Computing and Applications, vol. 24, no. 1, pp. 169-174 (2014). X. S. Yang and X. S. He, Bat algorithm: literature review and applications, Int. J. Bio-Inspired Computation, vol. 5, no. 3, pp. 141-149 (2013). A. H. Gandomi, S. Talatahari and X. S. Yang, S. Deb, Design optimization of truss structures using cuckoo search algorithm, Structural Design of Tall and Special Buildings, vol. 22, no. 17, pp. 1330-1340 (2013). A. H. Gandomi and X. S. Yang, Chaotic bat algorithm, Journal of Computational Science, vol. 5, no. 2, pp. 224-232 (2014). P. R. Srivastava, A. Varshney, P. Nama, X. S. Yang, Software test eﬀort estimation: a model based on cuckoo search, Int. J. Bio-Inspired Computation, vol. 4, no. 5, pp. 278-285 (2012). Xin-She Yang Nature-Inspired Computation ICHSA2017 52 / 54
53. 53. The Future – Some Open Problems (Swarm Intelligence) X. S. Yang, M. Karamanoglu, X.S. He, Flower pollination algorithm: A novel approach for multiobjective optimization, Engineering Optimization, Vol. 46, No. 9, 1222-1237 (2014). M. K. Marchelvam, T. Prabaharan, X. S. Yang, A discrete ﬁreﬂy algorithm for multi-objective hybrid ﬂowshop scheduling problems, IEEE Trans. Evolutionary Computation, vol. 18, no. 2, pp. 301-205 (2014). P. R. Srivastava, B. Millikarjun, X. S. Yang, Optimal test sequence generation using ﬁreﬂy algorithm, Swarm and Evolutionary Computation, vol. 8, no. 1, pp. 44-53 (2013). D. Rodrigues, L. A. M. Pereira, R. Y. M. Nakamura, K. A. P. Costa, X. S. Yang, A. N. Souza, J. P. Papa, A wrapper approach for feature selection and Optimum-Path Forest based on Bat Algorithm, Expert Systems with Applications, vol. 41, no. 5, pp. 2250-2258 (2014). X. S. Yang, M. Karamanoglu, X. S. He, Multi-objective ﬂower algorithm for optimization, Procedia Computer Science, Vol. 18, pp. 861-868 (2013). X. S. Yang and J. P. Papa, Bio-inspired Computation and Applications in Image Processing, Elsevier (2016). J. Senthilnath, S. Kulkarni, J. A. Benediktsson, X. S. Yang, A novel approach for multispectral satellite image classiﬁcation based on the bat algorithm, IEEE Geoscience and Remote Sensing Letters, Vol. 13, No. 4, 599-603 (2016). A. Chakri, R. Khelif, M. Benouaret, X. S. Yang, New directional bat algorithm for continuous optimization problems, Expert Systems with Applications, Vol. 69, 159-175 (2017). Xin-She Yang Nature-Inspired Computation ICHSA2017 53 / 54
54. 54. Thank you :) Any generic tool for optimization? Any generic tool for optimization? Xin-She Yang Nature-Inspired Computation ICHSA2017 54 / 54