A Novel Algorithm for Solving Structural Optimization Problems

In the past few decades, metaheuristic optimization methods have emerged as an effective approach for addressing structural design problems. Structural optimization methods are based on mathematical algorithms that are population-based techniques. Optimization methods use technology development to employ algorithms to search through complex solution space to find the minimum. In this paper, a simple algorithm inspired by hurricane chaos is proposed for solving structural optimization problems. In general, optimization algorithms use equations that employ the global best solution that might cause the algorithm to get trapped in a local minimum. Hence, this methodology is avoided in this work. The algorithm was tested on several common truss examples from the literature and proved efficient in finding lower weights for the test problems

Incremental approximation of nonlinear constraint functions for evolutionary constrained optimization

This paper proposes an alternative approach to efficient solving of nonlinear constrained optimization problems using evolutionary algorithms. It is assumed that the separate-ness of the feasible regions, which imposes big difficulties for evolutionary search, is partially resulted from the complexity of the nonlinear constraint functions. Based on this hypothesis, an approximate model is built for each constraint function with an increasing accuracy, starting from a simple linear approximation. As a result, the feasible region based on the approximate constraint functions will be much simpler, and the isolated feasible regions will become more likely connected. As the evolutionary search goes on, the approximated feasible regions should gradually change back to the original one by increasing the accuracy of the approximate models to ensure that the optimum found by the evolutionary algorithm does not violate any of the original constraints. Empirical studies have been performed on 13 test problems and four engineering design optimization problems. Simulation results suggest that the proposed method is competitive compared to the state-of-the-art techniques for solving nonlinear constrained optimization problems

A spring search algorithm applied to engineering optimization problems

At present, optimization algorithms are used extensively. One particular type of such algorithms includes random-based heuristic population optimization algorithms, which may be created by modeling scientific phenomena, like, for example, physical processes. The present article proposes a novel optimization algorithm based on Hooke’s law, called the spring search algorithm (SSA), which aims to solve single-objective constrained optimization problems. In the SSA, search agents are weights joined through springs, which, as Hooke’s law states, possess a force that corresponds to its length. The mathematics behind the algorithm are presented in the text. In order to test its functionality, it is executed on 38 established benchmark test functions and weighed against eight other optimization algorithms: a genetic algorithm (GA), a gravitational search algorithm (GSA), a grasshopper optimization algorithm (GOA), particle swarm optimization (PSO), teaching–learning-based optimization (TLBO), a grey wolf optimizer (GWO), a spotted hyena optimizer (SHO), as well as an emperor penguin optimizer (EPO). To test the SSA’s usability, it is employed on five engineering optimization problems. The SSA delivered better fitting results than the other algorithms in unimodal objective function, multimodal objective functions, CEC 2015, in addition to the optimization problems in engineering

Constrained stochastic blackbox optimization using a progressive barrier and probabilistic estimates

This work introduces the StoMADS-PB algorithm for constrained stochastic blackbox optimization, which is an extension of the mesh adaptive direct-search (MADS) method originally developed for deterministic blackbox optimization under general constraints. The values of the objective and constraint functions are provided by a noisy blackbox, i.e., they can only be computed with random noise whose distribution is unknown. As in MADS, constraint violations are aggregated into a single constraint violation function. Since all functions values are numerically unavailable, StoMADS-PB uses estimates and introduces so-called probabilistic bounds for the violation. Such estimates and bounds obtained from stochastic observations are required to be accurate and reliable with high but fixed probabilities. The proposed method, which allows intermediate infeasible iterates, accepts new points using sufficient decrease conditions and imposing a threshold on the probabilistic bounds. Using Clarke nonsmooth calculus and martingale theory, Clarke stationarity convergence results for the objective and the violation function are derived with probability one

A study of search neighbourhood in the bees algorithm

The Bees Algorithm, a heuristic optimisation procedure that mimics bees foraging behaviour, is becoming more popular among swarm intelligence researchers. The algorithm involves neighbourhood and global search and is able to find promising solutions to complex multimodal optimisation problems. The purpose of neighbourhood search is to intensify the search effort around promising solutions, while global search is to enable avoidance of local optima. Despite numerous studies aimed at enhancing the Bees Algorithm, there have not been many attempts at studying neighbourhood search. This research investigated different kinds of neighbourhoods and their effects on neighbourhood search. First, the adaptive enlargement of the search neighbourhood was proposed. This idea was implemented in the Bees Algorithm and tested on a set of mathematical benchmarks. The modified algorithm was also tested on single objective engineering design problems. The experimental results obtained confirmed that the adaptive enlargement of the search neighbourhood improved the performance of the proposed algorithm. Normally, a symmetrical search neighbourhood is employed in the Bees Algorithm. As opposed to this practice, an asymmetrical search neighbourhood was tried in this work to determine the significance of neighbourhood symmetry. In addition to the mathematical benchmarks, the algorithm with an asymmetrical search neighbourhood was also tested on an engineering design problem. The analysis verified that under certain measurements of asymmetry, the proposed ii algorithm produced a similar performance as that of the Bees Algorithm. For this reason, it was concluded that users were free to employ either a symmetrical or an asymmetrical search neighbourhood in the Bees Algorithm. Finally, the combination of adaptive enlargement and reduction of the search neighbourhood was presented. In addition to the above mathematical benchmarks and engineering design problems, a multi-objective design optimisation exercise with constraints was selected to demonstrate the performance of the modified algorithm. The experimental results obtained showed that this combination was beneficial to the proposed algorithm.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Enhancement of bees algorithm for global optimisation

This research focuses on the improvement of the Bees Algorithm, a swarm-based nature-inspired optimisation algorithm that mimics the foraging behaviour of honeybees. The algorithm consists of exploitation and exploration, the two key elements of optimisation techniques that help to find the global optimum in optimisation problems. This thesis presents three new approaches to the Bees Algorithm in a pursuit to improve its convergence speed and accuracy. The first proposed algorithm focuses on intensifying the local search area by incorporating Hooke and Jeeves’ method in its exploitation mechanism. This direct search method contains a pattern move that works well in the new variant named “Bees Algorithm with Hooke and Jeeves” (BA-HJ). The second proposed algorithm replaces the randomly generated recruited bees deployment method with chaotic sequences using a well-known logistic map. This new variant called “Bees Algorithm with Chaos” (ChaosBA) was intended to use the characteristic of chaotic sequences to escape from local optima and at the same time maintain the diversity of the population. The third improvement uses the information of the current best solutions to create new candidate solutions probabilistically using the Estimation Distribution Algorithm (EDA) approach. This new version is called Bees Algorithm with Estimation Distribution (BAED). Simulation results show that these proposed algorithms perform better than the standard BA, SPSO2011 and qABC in terms of convergence for the majority of the tested benchmark functions. The BA-HJ outperformed the standard BA in thirteen out of fifteen benchmark functions and is more effective in eleven out of fifteen benchmark functions when compared to SPSO2011 and qABC. In the case of the ChaosBA, the algorithm outperformed the standard BA in twelve out of fifteen benchmark functions and significantly better in eleven out of fifteen test functions compared to qABC and SPSO2011. BAED discovered the optimal solution with the least number of evaluations in fourteen out of fifteen cases compared to the standard BA, and eleven out of fifteen functions compared to SPSO2011 and qABC. Furthermore, the results on a set of constrained mechanical design problems also show that the performance of the proposed algorithms is comparable to those of the standard BA and other swarm-based algorithms from the literature

A study of search neighbourhood in the bees algorithm

The Bees Algorithm, a heuristic optimisation procedure that mimics bees foraging behaviour, is becoming more popular among swarm intelligence researchers. The algorithm involves neighbourhood and global search and is able to find promising solutions to complex multimodal optimisation problems. The purpose of neighbourhood search is to intensify the search effort around promising solutions, while global search is to enable avoidance of local optima. Despite numerous studies aimed at enhancing the Bees Algorithm, there have not been many attempts at studying neighbourhood search. This research investigated different kinds of neighbourhoods and their effects on neighbourhood search. First, the adaptive enlargement of the search neighbourhood was proposed. This idea was implemented in the Bees Algorithm and tested on a set of mathematical benchmarks. The modified algorithm was also tested on single objective engineering design problems. The experimental results obtained confirmed that the adaptive enlargement of the search neighbourhood improved the performance of the proposed algorithm. Normally, a symmetrical search neighbourhood is employed in the Bees Algorithm. As opposed to this practice, an asymmetrical search neighbourhood was tried in this work to determine the significance of neighbourhood symmetry. In addition to the mathematical benchmarks, the algorithm with an asymmetrical search neighbourhood was also tested on an engineering design problem. The analysis verified that under certain measurements of asymmetry, the proposed ii algorithm produced a similar performance as that of the Bees Algorithm. For this reason, it was concluded that users were free to employ either a symmetrical or an asymmetrical search neighbourhood in the Bees Algorithm. Finally, the combination of adaptive enlargement and reduction of the search neighbourhood was presented. In addition to the above mathematical benchmarks and engineering design problems, a multi-objective design optimisation exercise with constraints was selected to demonstrate the performance of the modified algorithm. The experimental results obtained showed that this combination was beneficial to the proposed algorithm

Enhancing the Bees algorithm for global optimisation using search space manipulation

The aim of this research is to improve the ability of the Bees Algorithm to tackle global optimisation problems. The Bees Algorithm was formulated and inspired by the foraging behaviour of honeybees. The proposed enhancements target the initialisation and global search stages of the algorithm. The reason for this is that the initialisation stage could save efforts by directing the search earlier towards the more promising areas of the search space, leading to a better optimised result. Targeting during the global search is due to the researcher’s belief that the neighbourhood search depends on it and any improvement will positively affect the neighbourhood search. In this research, three enhancements were formulated based on the manipulation of the search space. The first enhancement (BAwSSR) involves continuous and gradual reduction of the search space with different scenarios that vary according to the starting point of reduction. The second enhancement (BADS) deals with the segmentation of search space into independent segments while using two sampling approaches to tackle a wide variety of problems. The third enhancement (BAOSS) also involves the segmentation of search space but divides it into independent segments to increase flexibility in handling a wider range of problems. These proposed algorithms were tested on 24 benchmark functions with a broad range of characteristics. This test involves performance comparisons with the Quick Artificial Bee Colony (qABC) and the Standard Particle Swarm Optimisation 2011 (SPSO2011) algorithms. The obtained test data indicated noticeable improvements with an adequate level of stability over the original Bees Algorithm. The results were supported by the Mann–Whitney significance test, showing the improvements are statically significant for both accuracy and speed. Additionally, the proposed algorithms were tested on two engineering problems that included a comparison with a group of competitor algorithms. However, only the first proposed algorithm (BAwSSR) showed an obvious improvement. The other two algorithms (BADS) and (BAOSS) did not reveal any improvement

Optimisation of wind turbine blade structures using a genetic algorithm

The current diminution of fossil-fuel reserves, stricter environmental guidelines and the world’s ever-growing energy needs have directed to the deployment of alternative renewable energy sources. Among the many renewable energies, wind energy is one of the most promising and the fastest growing installed alternative-energy production technology. In order to meet the production goals in the next few decades, both significant increases in wind turbine installations and operability are required, while maintaining a profitable and competitive energy cost. As the size of the wind turbine rotor increases, the structural performance and durability requirements tend to become more challenging. In this sense, solving the wind turbine design problem is an optimization problem where an optimal solution is to be found under a set of design constraints and a specific target. Seen the world evolution towards the renewable energies and the beginning of an implementation of a local wind industry in Quebec, it becomes imperative to follow the international trends in this industry. Therefore, it is necessary to supply the designers a suitable decision tool for the study and design of optimal wind turbine blades. The developed design tool is an open source code named winDesign which is capable to perform structural analysis and design of composite blades for wind turbines under various configurations in order to accelerate the preliminary design phase. The proposed tool is capable to perform a Pareto optimization where optimal decisions need to be taken in the presence of trade-offs between two conflicting objectives: the annual energy production and the weight of the blade. For a given external blade shape, winDesign is able to determine an optimal composite layup, chord and twist distributions which either minimizes blade mass or maximizes the annual energy production while simultaneously satisfying design constraints. The newly proposed graphical tool incorporates two novel VCH and KGA techniques and is validated with numerical simulation on both mono-objective and multi-objective optimization problems