Enhanced Multi-Strategy Particle Swarm Optimization for Constrained Problems with an Evolutionary-Strategies-Based Unfeasible Local Search Operator

Nowadays, optimization problems are solved through meta-heuristic algorithms based on stochastic search approaches borrowed from mimicking natural phenomena. Notwithstanding their successful capability to handle complex problems, the No-Free Lunch Theorem by Wolpert and Macready (1997) states that there is no ideal algorithm to deal with any kind of problem. This issue arises because of the nature of these algorithms that are not properly mathematics-based, and the convergence is not ensured. In the present study, a variant of the well-known swarm-based algorithm, the Particle Swarm Optimization (PSO), is developed to solve constrained problems with a different approach to the classical penalty function technique. State-of-art improvements and suggestions are also adopted in the current implementation (inertia weight, neighbourhood). Furthermore, a new local search operator has been implemented to help localize the feasible region in challenging optimization problems. This operator is based on hybridization with another milestone meta-heuristic algorithm, the Evolutionary Strategy (ES). The self-adaptive variant has been adopted because of its advantage of not requiring any other arbitrary parameter to be tuned. This approach automatically determines the parameters’ values that govern the Evolutionary Strategy simultaneously during the optimization process. This enhanced multi-strategy PSO is eventually tested on some benchmark constrained numerical problems from the literature. The obtained results are compared in terms of the optimal solutions with two other PSO implementations, which rely on a classic penalty function approach as a constraint-handling method

Chaotic coyote algorithm applied to truss optimization problems

The optimization of truss structures is a complex computing problem with many local minima, while metaheuristics are naturally suited to deal with multimodal problems without the need of gradient information. The Coyote Optimization Algorithm (COA) is a population-based nature-inspired metaheuristic of the swarm intelligence field for global optimization that considers the social relations of the coyote proposed to single-objective optimization. Unlike most widespread algorithms, its population is subdivided in packs and the internal social influences are designed. The COA requires a few control hyperparameters including the number of packs, the population size, and the number maximum of generations. In this paper, a modified COA (MCOA) approach based on chaotic sequences generated by Tinkerbell map to scatter and association probabilities tuning and an adaptive procedure of updating parameters related to social condition is proposed. It is then validated by four benchmark problems of structures optimization including planar 52-bar truss, spatial 72-bar truss, 120-bar dome truss and planar 200 bar-truss with discrete design variables and focus in minimization of the structure weight under the required constraints. Simulation results collected in the mentioned problems demonstrate that the proposed MCOA presented competitive solutions when compared with other state-of-the-art metaheuristic algorithms in terms of results quality

Chaotically Enhanced Meta-Heuristic Algorithms for Optimal Design of Truss Structures with Frequency Constraints

The natural frequencies of any structure contain useful information about the dynamic behavior of that structure, and by controlling these frequencies, the destructive effects of dynamic loads, including the resonance phenomenon, can be minimized. Truss optimization by applying dynamic constraints has been widely welcomed by researchers in recent decades and has been presented as a challenging topic. The main reason for this choice is quick access to dynamic information by examining natural frequencies. Also, frequency constraint relations are highly nonlinear and non-convex and have implicit variables, so using mathematical and derivative methods will be very difficult and time consuming. In this regard, the use of meta-heuristic algorithms in truss weight optimization with frequency constraints has good results, but with the introduction of form variables, these algorithms trap at local optima. In this research, by applying chaos map in meta-heuristic algorithms, suitable conditions have been provided to escape from local optima and access to global optimums. These algorithms include Chaotic Cyclical Parthenogenesis Algorithms (CCPA), Chaotic Biogeography-Based Optimization (CBBO), Chaotic Teaching-Learning-Based Optimization (CTLBO) and Chaotic Particle Swarm Optimization (CPSO), respectively. Also, by using different scenarios, a good balance has been achieved between the exploration and exploitation of the algorithms

Chaotic biogeography algorithm for size and shape optimization of truss structures with frequency constraints

Size and shape optimization of truss structures with natural frequency constraints is inherently nonlinear dynamic optimization problem with  several local optima. Therefore theoptimization method should be sagacious enough to avoid being trapped in local optima and in this way to reduce premature convergence. To address this problem, we develop a Chaotic Biogeography-Based Optimization (CBBO) algorithm which combines the chaos theory and the biogeography-based optimization (BBO) to achieve an ecient optimization method. In this method, new chaotic migration and mutation operators are proposed to enhance the exploration ability of BBO. The performance of the method is demonstrated through five benchmark design examples with size and shape variables associated by multiply frequency constraints. The results show the eciency and robustness of proposed method and in most cases, CBBO finds a relatively lighter structural weight than those previously reported results in the literature

Structural optimization in steel structures, algorithms and applications

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A cultural algorithm for optimal design of truss structures

Peer reviewedPublisher PD