Chaotic bat swarm optimisation (CBSO)

Bat swarm optimisation (BSO) is a novel heuristic optimisation algorithm that is being used for solving different global optimisation problems. The paramount problem in BSO is that it severely suffers from premature convergence problem, that is, BSO is easily trapped in local optima. In this paper, chaotic-based strategies are incorporated into BSO to mitigate this problem. Ergodicity and non-repetitious nature of chaotic functions can diversify the bats and mitigate premature convergence problem. Eleven different chaotic map functions along with various chaotic BSO strategies are investigated experimentally and the best one is chosen as the suitable chaotic strategy for BSO. The results of applying the proposed chaotic BSO to different benchmark functions vividly show that premature convergence problem has been mitigated efficiently. Actually, chaotic-based BSO significantly outperforms conventional BSO, cuckoo search optimisation (CSO), big bang-big crunch algorithm (BBBC), gravitational search algorithm (GSA) and genetic algorithm (GA).     

A chaotic-based big bang–big crunch algorithm for solving global optimisation problems

Big bang–big crunch (BBBC) algorithm is a fairly novel gradient-free optimisation algorithm. It is based on theories of evolution of the universe, namely the big bang and big crunch theory. The big challenge in BBBC is that it is easily trapped in local optima. In this paper, chaotic-based strategies are incorporated into BBBC to tackle this challenge. Five various chaotic-based BBBC strategies with three different chaotic map functions are investigated and the best one is selected as the proposed chaotic strategy for BBBC. The results of applying the proposed chaotic BBBC to different unimodal and multimodal benchmark functions vividly show that chaotic-based BBBC yields quality solutions. It significantly outperforms conventional BBBC, cuckoo search optimisation and gravitational search algorithm.     

A new effective operator for the hybrid algorithm for solving global optimisation problems

Hybrid algorithms have been recently used to solve complex single-objective optimisation problems. The ultimate goal is to find an optimised global solution by using these algorithms. Based on the existing algorithms (HP_CRO, PSO, RCCRO), this study proposes a new hybrid algorithm called MPC (Mean-PSO-CRO), which utilises a new Mean-Search Operator. By employing this new operator, the proposed algorithm improves the search ability on areas of the solution space that the other operators of previous algorithms do not explore. Specifically, the Mean-Search Operator helps find the better solutions in comparison with other algorithms. Moreover, the authors have proposed two parameters for balancing local and global search and between various types of local search, as well. In addition, three versions of this operator, which use different constraints, are introduced. The experimental results on 23 benchmark functions, which are used in previous works, show that our framework can find better optimal or close-to-optimal solutions with faster convergence speed for most of the benchmark functions, especially the high-dimensional functions. Thus, the proposed algorithm is more effective in solving single-objective optimisation problems than the other existing algorithms.     

An improved particle swarm optimiser based on swarm success rate for global optimisation problems

Inertia weight is one of the control parameters that influences the performance of particle swarm optimisation (PSO) in the course of solving global optimisation problems, by striking a balance between exploration and exploitation. Among many inertia weight strategies that have been proposed in literature are chaotic descending inertia weight (CDIW) and chaotic random inertia weight (CRIW). These two strategies have been claimed to perform better than linear descending inertia weight (LDIW) and random inertia weight (RIW). Despite these successes, a closer look at their results reveals that the common problem of premature convergence associated with PSO algorithm still lingers. Motivated by the better performances of CDIW and CRIW, this paper proposed two new inertia weight strategies namely: swarm success rate descending inertia weight (SSRDIW) and swarm success rate random inertia weight (SSRRIW). These two strategies use swarm success rates as a feedback parameter. Efforts were made using the proposed inertia weight strategies with PSO to further improve the effectiveness of the algorithm in terms of convergence speed, global search ability and improved solution accuracy. The proposed PSO variants, SSRDIW_PSO and SSRRIW_PSO were validated using several benchmark unconstrained global optimisation test problems and their performances compared with LDIW-PSO, CDIW-PSO, RIW-PSO, CRIW-PSO and some other existing PSO variants. Empirical results showed that the proposed variants are more efficient.     

A memetic particle swarm optimisation algorithm for dynamic multi-modal optimisation problems

Many real-world optimisation problems are both dynamic and multi-modal, which require an optimisation algorithm not only to find as many optima under a specific environment as possible, but also to track their moving trajectory over dynamic environments. To address this requirement, this article investigates a memetic computing approach based on particle swarm optimisation for dynamic multi-modal optimisation problems (DMMOPs). Within the framework of the proposed algorithm, a new speciation method is employed to locate and track multiple peaks and an adaptive local search method is also hybridised to accelerate the exploitation of species generated by the speciation method. In addition, a memory-based re-initialisation scheme is introduced into the proposed algorithm in order to further enhance its performance in dynamic multi-modal environments. Based on the moving peaks benchmark problems, experiments are carried out to investigate the performance of the proposed algorithm in comparison with several state-of-the-art algorithms taken from the literature. The experimental results show the efficiency of the proposed algorithm for DMMOPs.     

Improved butterfly optimisation algorithm based on guiding weight and population restart

ABSTRACT

Butterfly Optimisation Algorithm (BOA) is a kind of meta-heuristic swarm intelligence algorithm based on butterfly foraging strategy, but it still needs to be improved in the aspects of convergence speed and accuracy when solving with high-dimensional optimisation problems. In this paper, an improved butterfly optimisation algorithm is proposed, in which guiding weight and population restart strategy are applied to the original algorithm. By adding guiding weight to the global search equation, the convergence speed and accuracy of the algorithm are improved, and the possibility of jumping out of the local optimal solution is increased by the population restart strategy. In order to verify the performance of the proposed algorithm, 24 benchmark functions commonly used for optimisation algorithm experiments are applied in this paper, including 12 unimodal functions and 12 multimodal functions. Experimental results show that the proposed algorithm improves the convergence speed, accuracy and the ability to jump out of the local optimal solution.     

Cauchy Grey Wolf Optimiser for continuous optimisation problems

ABSTRACT

Grey Wolf Optimiser (GWO) is a recently developed optimisation approach to solve complex non-linear optimisation problems. It is relatively simple and leadership-hierarchy based approach in the class of Swarm Intelligence based algorithms. For solving complex real-world non-linear optimisation problems, the search equation provided in GWO is not of sufficient explorative behaviour. Therefore, in the present paper, an attempt has been made to increase the exploration capability along with the exploitation of a search space by proposing an improved version of classical GWO. The proposed algorithm is named as Cauchy-GWO. In Cauchy-GWO Cauchy operator has been integrated in which first two new wolves are generated with the help of Cauchy distributed random numbers and then another new wolf is generated by taking the convex combination of these new wolves. The performance of Cauchy-GWO is exhibited on standard IEEE CEC 2014 benchmark problem set. Statistical analysis of the results on CEC 2014 benchmark set and popular evaluation criteria, Performance Index (PI) proves that Cauchy-GWO outperforms GWO in terms of error values defined in IEEE CEC 2014 benchmarks collection. Later on in the paper, GWO and Cauchy-GWO algorithms have been used to solve three well-known engineering application problems and two problems of reliability. From the analysis conducted in the present paper, it can be concluded that the proposed algorithm, Cauchy-GWO is reliable and efficient algorithm to solve continuous benchmark test problems, as well as real-life applications problems.     

A data mining approach to evolutionary optimisation of noisy multi-objective problems

Many real world optimisation problems have opposing objective functions which are subjected to the influence of noise. Noise in the objective functions can adversely affect the stability, performance and convergence of evolutionary optimisers. This article proposes a Bayesian frequent data mining (DM) approach to identify optimal regions to guide the population amidst the presence of noise. The aggregated information provided by all the solutions helped to average out the effects of noise. This article proposes a DM crossover operator to make use of the rules mined. After implementation of this operator, a better convergence to the true Pareto front is achieved at the expense of the diversity of the solution. Consequently, an ExtremalExploration operator will be proposed in the later part of this article to help curb the loss in diversity caused by the DM operator. The result is a more directive search with a faster convergence rate. The search is effective in decision space where the Pareto set is in a tight cluster. A further investigation of the performance of the proposed algorithm in noisy and noiseless environment will also be studied with respect to non-convexity, discontinuity, multi-modality and uniformity. The proposed algorithm is evaluated on ZDT and other benchmarks problems. The results of the simulations indicate that the proposed method is effective in handling noise and is competitive against the other noise tolerant algorithms.     

Applications of particle swarm optimisation in integrated process planning and scheduling

Integration of process planning and scheduling (IPPS) is an important research issue to achieve manufacturing planning optimisation. In both process planning and scheduling, vast search spaces and complex technical constraints are significant barriers to the effectiveness of the processes. In this paper, the IPPS problem has been developed as a combinatorial optimisation model, and a modern evolutionary algorithm, i.e., the particle swarm optimisation (PSO) algorithm, has been modified and applied to solve it effectively. Initial solutions are formed and encoded into particles of the PSO algorithm. The particles “fly” intelligently in the search space to achieve the best sequence according to the optimisation strategies of the PSO algorithm. Meanwhile, to explore the search space comprehensively and to avoid being trapped into local optima, several new operators have been developed to improve the particles’ movements to form a modified PSO algorithm. Case studies have been conducted to verify the performance and efficiency of the modified PSO algorithm. A comparison has been made between the result of the modified PSO algorithm and the previous results generated by the genetic algorithm (GA) and the simulated annealing (SA) algorithm, respectively, and the different characteristics of the three algorithms are indicated. Case studies show that the developed PSO can generate satisfactory results in both applications.     

Discrete optimisation based on the combined use of reinforcement and constraint satisfaction schemes

A new approach is presented for finding near-optimal solutions to discrete optimisation problems that is based on the cooperation of two modules: an optimisation module and a constraint satisfaction module. The optimisation module must be able to search the problem state space through an iterative process of sampling and evaluating the generated samples. To evaluate a generated point, first a constraint satisfaction module is employed to map that point to another one satisfying the problem constraints, and then the cost of the new point is used as the evaluation of the original one. The scheme that we have adopted for testing the effectiveness of the method uses a reinforcement learning algorithm in the optimisation module and a general deterministic constraint satisfaction algorithm in the constraint satisfaction module. Experiments using this scheme for the solution of two optimisation problems indicate that the proposed approach is very effective in providing feasible solutions of acceptable quality.     

Power law-based local search in spider monkey optimisation for lower order system modelling

The nature-inspired algorithms (NIAs) have shown efficiency to solve many complex real-world optimisation problems. The efficiency of NIAs is measured by their ability to find adequate results within a reasonable amount of time, rather than an ability to guarantee the optimal solution. This paper presents a solution for lower order system modelling using spider monkey optimisation (SMO) algorithm to obtain a better approximation for lower order systems and reflects almost original higher order system's characteristics. Further, a local search strategy, namely, power law-based local search is incorporated with SMO. The proposed strategy is named as power law-based local search in SMO (PLSMO). The efficiency, accuracy and reliability of the proposed algorithm is tested over 20 well-known benchmark functions. Then, the PLSMO algorithm is applied to solve the lower order system modelling problem.     

A multi-population electromagnetic algorithm for dynamic optimisation problems

This paper is derived from an interest in the development of approaches to tackle dynamic optimisation problems. This is a very challenging research area due to the fact that any approaches utilised should be able to track the changes and simultaneously seek for global optima as the search progresses. In this research work, a multi-population electromagnetic algorithm for dynamic optimisation problems is proposed. An electromagnetic algorithm is a population based meta-heuristic method which imitates the attraction and repulsion of the sample points. In order to track the dynamic changes and to effectively explore the search space, the entire population is divided into several sub-populations (referred as multi-population that acts as diversity mechanisms) where each sub-population takes charge in exploring or exploiting the search space. In addition, further investigation are also conducted on the combination of the electromagnetic algorithm with different diversity mechanisms (i.e. random immigrants, memory mechanism and memory based immigrant schemes) with the aim of identifying the most appropriate diversity mechanism for maintaining the diversity of the population in solving dynamic optimisation problems. The proposed approach has been applied and evaluated against the latest methodologies in reviewed literature of research works with respect to the benchmark problems. This study demonstrates that the electromagnetic algorithm with a multi-population diversity mechanism performs better compared to other population diversity mechanisms investigated in our research and produces some of the best known results when tested on Moving Peak Benchmark (MPB) problems.     

A new multi-objective particle swarm optimisation algorithm based on R2 indicator selection mechanism

In recent years, Pareto-based selection mechanism has been successfully applied in dealing with complex multi-objective optimisation problems (MOPs), while indicators-based have been explored to apply in solving this problems. Therefore, a new multi-objective particle swarm optimisation algorithm based on R2 indicator selection mechanism (R2SMMOPSO) is presented in this paper. In the proposed algorithm, R2 indicator is designed as a selection mechanism for ensuring convergence and distribution of the algorithm simultaneously. In addition, an improved cosine-adjusted inertia weight balances the ability of algorithm exploitation and exploration effectively. Besides, Gaussian mutation strategy is designed to prevent particles from falling into the local optimum when the particle does not satisfy the condition of the position update formula, polynomial mutation is applied in the external archive to increase the diversity of elite solutions. The performance of the proposed algorithm is validated and compared with some state-of-the-art algorithms on a number of test problems. Experimental studies demonstrate that the proposed algorithm shows very competitive performance when dealing with complex MOPs.     

Biogeography-based optimisation with chaos

The biogeography-based optimisation (BBO) algorithm is a novel evolutionary algorithm inspired by biogeography. Similarly, to other evolutionary algorithms, entrapment in local optima and slow convergence speed are two probable problems it encounters in solving challenging real problems. Due to the novelty of this algorithm, however, there is little in the literature regarding alleviating these two problems. Chaotic maps are one of the best methods to improve the performance of evolutionary algorithms in terms of both local optima avoidance and convergence speed. In this study, we utilise ten chaotic maps to enhance the performance of the BBO algorithm. The chaotic maps are employed to define selection, emigration, and mutation probabilities. The proposed chaotic BBO algorithms are benchmarked on ten test functions. The results demonstrate that the chaotic maps (especially Gauss/mouse map) are able to significantly boost the performance of BBO. In addition, the results show that the combination of chaotic selection and emigration operators results in the highest performance.     

A hybrid approach for multi-objective combinatorial optimisation problems in ship design and shipping

Numerous real-world problems relating to ship design and shipping are characterised by combinatorially explosive alternatives as well as multiple conflicting objectives and are denoted as multi-objective combinatorial optimisation (MOCO) problems. The main problem is that the solution space is very large and therefore the set of feasible solutions cannot be enumerated one by one. Current approaches to solve these problems are multi-objective metaheuristics techniques, which fall in two categories: population-based search and trajectory-based search. This paper gives an overall view for the MOCO problems in ship design and shipping where considerable emphasis is put on evolutionary computation and the evaluation of trade-off solutions. A two-stage hybrid approach is proposed for solving a particular MOCO problem in ship design, subdivision arrangement of a ROPAX vessel. In the first stage, a multi-objective genetic algorithm method is employed to approximate the set of pareto-optimal solutions through an evolutionary optimisation process. In the subsequent stage, a higher-level decision-making approach is adopted to rank these solutions from best to worst and to determine the best solution in a deterministic environment with a single decision maker.     

Enhanced leader PSO (ELPSO): A new PSO variant for solving global optimisation problems

Particle swarm optimisation (PSO) is a well-established optimisation algorithm inspired from flocking behaviour of birds. The big problem in PSO is that it suffers from premature convergence, that is, in complex optimisation problems, it may easily get trapped in local optima. In this paper, a new PSO variant, named as enhanced leader PSO (ELPSO), is proposed for mitigating premature convergence problem. ELPSO is mainly based on a five-staged successive mutation strategy which is applied to swarm leader at each iteration. The experimental results confirm that in all terms of accuracy, scalability and convergence rate, ELPSO performs well.     

Differential evolution and differential ant-stigmergy on dynamic optimisation problems

Many real-world optimisation problems are of dynamic nature, requiring an optimisation algorithm which is able to continuously track a changing optimum over time. To achieve this, we propose two population-based algorithms for solving dynamic optimisation problems (DOPs) with continuous variables: the self-adaptive differential evolution algorithm (jDE) and the differential ant-stigmergy algorithm (DASA). The performances of the jDE and the DASA are evaluated on the set of well-known benchmark problems provided for the special session on Evolutionary Computation in Dynamic and Uncertain Environments. We analyse the results for five algorithms presented by using the non-parametric statistical test procedure. The two proposed algorithms show a consistently superior performance over other recently proposed methods. The results show that both algorithms are appropriate candidates for DOPs.     

Hierarchical optimisation for non-linear dynamical systems with non-separable cost functions

In this paper the previous hierarchical optimisation algorithm of Hassan and Singh for non-linear interconnected dynamical systems with separable cost functions is extended to the case of non-linear and non-separable cost functions. This ensures that any decomposition could be used and makes the new algorithm suitable for the optimisation of general non-linear problems.     

Markerless human articulated tracking using hierarchical particle swarm optimisation

In this paper, we address markerless full-body articulated human motion tracking from multi-view video sequences acquired in a studio environment. The tracking is formulated as a multi-dimensional non-linear optimisation and solved using particle swarm optimisation (PSO), a swarm-intelligence algorithm which has gained popularity in recent years due to its ability to solve difficult non-linear optimisation problems. We show that a small number of particles achieves accuracy levels comparable with several recent algorithms. PSO initialises automatically, does not need a sequence-specific motion model and recovers from temporary tracking divergence through the use of a powerful hierarchical search algorithm (HPSO). We compare experimentally HPSO with particle filter (PF), annealed particle filter (APF) and partitioned sampling annealed particle filter (PSAPF) using the computational framework provided by Balan et al. HPSO accuracy and consistency are better than PF and compare favourably with those of APF and PSAPF, outperforming it in sequences with sudden and fast motion. We also report an extensive experimental study of HPSO over ranges of values of its parameters.     

Application of firefly algorithm and ANFIS for optimisation of functionally graded beams

Volume fraction optimisation of functionally graded beams is studied for maximising the fundamental natural frequency by applying a new meta-heuristic nature-inspired algorithm called firefly algorithm (FA) which is based on the flashing behaviour of fireflies. Nature-inspired algorithms are among the most powerful algorithms for optimisation of engineering problems. The primary optimisation variables are the three parameters in the power-law distribution. Since the search space is large, the optimisation processes becomes so complicated and too much time consuming. Thus, a suitable Adaptive Neuro-Fuzzy Inference System (ANFIS) that is based on Takagi–Sugeno fuzzy inference system is combined with FA to reproduce the behaviour of the structure in free vibration. The ANFIS improves the speed of optimisation process by a considerable amount. The results are compared with those obtained by imperialist competitive algorithm, genetic algorithm and Artificial Neural Networks proposed in our previous work. Results show that the combination of FA and ANFIS is capable of yielding better optimal solution in comparison with other available techniques. It is believed that new results are of interest to the scientific and engineering community in the area of engineering design.