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Differential equations play a noticeable role in engineering, physics, economics, and other disciplines. In this paper, a general approach is suggested to solve a wide variety of linear and nonlinear ordinary differential equations (ODEs) that are independent of their forms, orders, and given conditions. With the aid of certain fundamental concepts of mathematics, Fourier series expansion and metaheuristic methods, ODEs can be represented as an optimization problem. The target is to minimize the weighted residual function (cost function) of the ODEs. To this end, two different approaches, unit weight function and least square weight function, are examined in order to determine the appropriate method. The boundary and initial values of ODEs are considered as constraints for the optimization model. Generational distance metric is used for evaluation and assessment of the approximate solutions versus the exact solutions. Six ODEs and four mechanical problems are approximately solved and compared with their exact solutions. The optimization task is carried out using different optimizers including the particle swarm optimization, the cuckoo search, and the water cycle algorithm. The optimization results obtained show that metaheuristic algorithms can be successfully applied for approximate solving of different types of ODEs. The suggested least square weight function is slightly superior over the unit weight function in terms of accuracy and statistical results for approximate solving of ODEs. [ABSTRACT FROM AUTHOR]

This paper presents the applications of the mine blast algorithm (MBA) and the water cycle algorithm (WCA), in addition to an improved version of MBA for weight minimization of truss structures including discrete sizing variables. The MBA mimics the explosion of landmines, while the WCA is inspired by the observation of water cycle process. An improved version of MBA (IMBA), is also presented. The efficiency of the three optimization algorithms is tested using classical benchmark discrete truss design problems. Optimization results show that MBA, IMBA, and WCA offer a good degree of competitiveness against other state-of-the-art metaheuristic techniques. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new optimization technique called water cycle algorithm (WCA) which is applied to a number of constrained optimization and engineering design problems. The fundamental concepts and ideas which underlie the proposed method is inspired from nature and based on the observation of water cycle process and how rivers and streams flow to the sea in the real world. A comparative study has been carried out to show the effectiveness of the WCA over other well-known optimizers in terms of computational effort (measures as number of function evaluations) and function value (accuracy) in this paper. [Copyright &y& Elsevier]

Abstract: In this study a novel optimization method is presented, the so called mine blast algorithm (MBA). The fundamental concepts and ideas of MBA are derived from the explosion of mine bombs in real world. The efficiency of the proposed optimizer is tested via the optimization of several truss structures with discrete variables and its performance is compared with several well-known metaheuristic algorithms. The results show that MBA is able to provide faster convergence rate and also manages to achieve better optimal solutions compared to other efficient optimizers. [Copyright &y& Elsevier]

Abstract: This paper presents the application of ant colony optimization (ACO) for the multi-objective optimization of hybrid laminates for obtaining minimum weight and cost. The investigated laminate is made of glass–epoxy and graphite–epoxy plies to combine the lightness and economical attributes of the first with the high-stiffness property of the second using a modified variation of ACO so called the elitist ant system (EAS) in order to make the tradeoff between the cost and weight as the objective functions. First natural frequency was considered as a constraint. The obtained results using the EAS method including the Pareto set, optimum stacking sequences, and the number of plies made of either glass or graphite fibers were compared with those using the genetic algorithm (GA) and any colony system (ACS) reported in literature. The comparisons confirm the advantage of hybridization and showed that the EAS algorithm outperformed the GA and ACS in terms of function’s value and constraint accuracy. [Copyright &y& Elsevier]

This study addresses flexible job shop scheduling problem (FJSP) with two constraints, namely fuzzy processing time and new job insertion. The uncertainty of processing time and new job insertion are two scheduling related characteristics in remanufacturing. Fuzzy processing time is used to describe the uncertainty in processing time. Rescheduling operator is executed when new job(s) is (are) inserted into the schedule currently being executed. A two-stage artificial bee colony (TABC) algorithm with several improvements is proposed to solve FJSP with fuzzy processing time and new job insertion constraints. Also, several new solution generation methods and improvement strategies are proposed and compared with each other. The objective is to minimize maximum fuzzy completion time. Eight instances from remanufacturing are solved using the proposed TABC algorithm. The proposed improvement strategies are compared and discussed in detail. Two proposed ABC algorithms with the best performances are compared against seven existing algorithms over by five benchmark cases. The optimization results and comparisons show the competitiveness of the proposed TABC algorithm for solving FJSP. [ABSTRACT FROM AUTHOR]

Minimum cost of energy is the main goal of a wind farm layout optimization. This is achieved by maximizing the total energy while minimizing the total costs of the farm. In this study, two sizes of commercial turbines were considered to investigate the effect of a non-homogenous farm on the layout optimization process. A cost model consisting of turbines, cable, transformers, foundation, and service vehicle routes was developed. Using Genetic Algorithm and Artificial Neural Network, first the superiority of the new algorithm in turbines and cable layout was verified versus previous studies. Next, two cases were investigated, i.e. (1) a farm populated with identical turbines and (2) a farm with a random mixture of both sizes of turbines. The layouts of both cases were optimized by both single and multi-objective optimizations. In the single objective optimization, only the larger turbines remained in the optimal layout of the second case and reduced the Levelized Cost of Energy (LCOE) into half of the first case. Multi-objective optimization clarified the reason for selecting larger size turbines in the layouts when the goal of the optimization was to minimize the cost of energy. As reported in literature, non-homogenous farms produce higher output. However, they impose a higher LCOE which makes them less appealing to developers. • Single objective (cost) and multi-objective (cost & power output) optimization result in different layout. • Non-homogenous farms produce higher power output. • Non-homogenous farms impose a higher LCOE which makes them less appealing to developers. [ABSTRACT FROM AUTHOR]

• This work studies an integrated distributed flow shop scheduling and distribution problem. • A mixed integer programming model is given to describe this problem mathematically. • An enhanced brain storm optimization algorithm is designed. • Optimal solutions are obtained by using mathematical programming solvers. • State-of-the-art results are acquired by the designed approach. Production and distribution are two essential activities in supply chain management. Currently, integrated production and distribution problems receive much attention because decision-makers devote to improving the operation efficiency of both stages and try to achieve an optimal solution. This work proposes an integrated distributed production and distribution problem with consideration of time windows, in which a set of jobs (i.e., customer orders) needs to be assigned among factories and the jobs are processed on flow shop environments at their associated factories. Then, the completed jobs are delivered by capacitated vehicles to customers in different regions while satisfying given time windows as much as possible. Accordingly, to optimally solve the proposed problem, a mixed integer programming model with minimizing total weighted earliness and tardiness has been established. For the optimization task, an enhanced brain storm optimization algorithm with some particular strategies is designed to handle the considered problem. To assess the performance of the proposed optimization method, several experiments by adopting a set of benchmark test problems are performed, and state-of-the-art optimizers are chosen for comparisons. The obtained optimization results exhibit that the designed algorithm significantly outperforms its rivals and can be considered as an excellent optimizer for solving the studied problem. Besides, compared with the CPLEX solver, the designed optimizer also performs much better for solving large-size problems. [ABSTRACT FROM AUTHOR]