An improved memetic algorithm using ring neighborhood topology for constrained optimization

The constrained optimization problem (COP) is converted into a biobjective optimization problem first, and then a new memetic differential evolution algorithm with dynamic preference is proposed for solving the converted problem. In the memetic algorithm, the global search, which uses differential evolution (DE) as the search scheme, is guided by a novel fitness function based on achievement scalarizing function (ASF). The novel fitness function constructed by a reference point and a weighting vector adjusts preference dynamically towards different objectives during evolution, in which the reference point and weighting vector are determined adapting to the current population. In the local search procedure, simplex crossover (SPX) is used as the search engine, which concentrates on the neighborhood embraced by both the best feasible and infeasible individuals and guides the search approaching the optimal solution from both sides of the boundary of the feasible region. As a result, the search can efficiently explore and exploit the search space. Numerical experiments on 22 well-known benchmark functions are executed, and comparisons with five state-of-the-art algorithms are made. The results illustrate that the proposed algorithm is competitive with and in some cases superior to the compared ones in terms of the quality, efficiency, and the robustness of the obtained results.

In view of the traditional numerical method to solve the nonlinear equations exist is sensitive to initial value and the higher accuracy of defects. This paper presents an invasive weed optimization (IWO) algorithm which has population diversity with the heuristic global search of differential evolution (DE) algorithm. In the iterative process, the global exploration ability of invasive weed optimization algorithm provides effective search area for differential evolution; at the same time, the heuristic search ability of differential evolution algorithm provides a reliable guide for invasive weed optimization. Based on the test of several typical nonlinear equations and a circle packing problem, the results show that the differential evolution invasive weed optimization (DEIWO) algorithm has a higher accuracy and speed of convergence, which is an efficient and feasible algorithm for solving nonlinear systems of equations.

An ecologically inspired optimization algorithm, called invasive weed optimization (IWO), is presented for the design of non-uniform, planar, and circular antenna arrays that can achieve minimum side lobe levels for a specific first null beamwidth while avoiding the mutual coupling effects simultaneously. IWO recently emerged as a derivative-free real parameter optimizer that mimics the ecological behavior of colonizing weeds. For the present application, classical IWO has been modified by introducing a more explorative routine of changing the standard deviation of the seed population (equivalent to mutation step-size in evolutionary algorithms) of the algorithm. Simulation results over three significant instances of the circular array design problem have been presented to illustrate the effectiveness of the modified IWO algorithm. The design results obtained with modified IWO have been shown to comfortably beat those obtained with other state-of-the-art metaheuristics like genetic algorithm (GA), particle swarm optimization (PSO), original IWO and differential evolution (DE) in a statistically meaningful way.

This article proposes a two-stage hybrid multimodal optimizer based on invasive weed optimization (IWO) and differential evolution (DE) algorithms for locating and preserving multiple optima of a real-parameter functional landscape in a single run. Both IWO and DE have been modified from their original forms to meet the demands of the multimodal problems used in this work. A p-best crossover operation is introduced in the subregional DEs to improve their exploitative behaviour. The performance of the proposed algorithm is compared with a number of state-of-the-art multimodal optimization algorithms over a benchmark suite comprising 21 basic multimodal problems and seven composite multimodal problems. Experimental results suggest that the proposed technique is able to provide better and more consistent performance over the existing well-known multimodal algorithms for the majority of test problems without incurring any serious computational burden.

MEMPSODE: A global optimization software based on hybridization of population-based algorithms and local searches

This paper presents a novel method for optimizing a planar elliptical dipole antenna with elliptical slots, for ultrawideband electromagnetic compatibility applications. The antenna is required to achieve minimum return loss and boresight realized gain with an adequate gain flatness across the frequency range of 1-5 GHz. Such an antenna is a powerful tool for electromagnetic measurements, due to its very compact size and its wide operating bandwidth. The main optimization method used in this paper is the invasive weed optimization (IWO), which is a nature-inspired metaheuristic evolutionary algorithm. The conventional and a modified version of IWO are compared to other prior-art evolutionary algorithms, such as the particle swarm optimization and differential evolution. The comparison is performed by applying all the methods on a set of mathematical test functions and also on the specific antenna design problem presented in this paper. The comparative results demonstrate the superiority of the modified IWO over the other optimization methods.

Multiobjective optimization with ϵ-constrained method for solving real-parameter constrained optimization problems

Memetic algorithms (MAs) are widely recognized to have better convergence capability than their conventional counterparts. Due to its good robustness and universality, differential evolution (DE) has been frequently used as the global search method in MAs. However, on account of the limited performance of the conventional local search operators, the performance of previous DE-related MAs still needs further improvement. In this paper, we implement more efficient evolutionary algorithms (EAs) as the local search techniques in an adaptive MA framework to form two MA(DE-LS) variants, and investigate their impacts. In order to comprehensively show the effectiveness and efficiency of MA(DE-LS), we experimentally compare it with state-of-the-art EAs, DE-based MAs and other MAs.

Niching is an important technique for multimodal optimization. Most existing niching methods require specification of certain niching parameters in order to perform well. These niching parameters, often used to inform a niching algorithm how far apart between two closest optima or the number of optima in the search space, are typically difficult to set as they are problem dependent. This paper describes a simple yet effective niching algorithm, a particle swarm optimization (PSO) algorithm using a ring neighborhood topology, which does not require any niching parameters. A PSO algorithm using the ring topology can operate as a niching algorithm by using individual particles' <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">local memories</i> to form a stable network retaining the best positions found so far, while these particles explore the search space more broadly. Given a reasonably large population uniformly distributed in the search space, PSO algorithms using the ring topology are able to form stable niches across different local neighborhoods, eventually locating multiple global/local optima. The complexity of these niching algorithms is only <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> ), where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> is the population size. Experimental results suggest that PSO algorithms using the ring topology are able to provide superior and more consistent performance over some existing PSO niching algorithms that require niching parameters.

An improved teaching–learning-based optimization with neighborhood search for applications of ANN

Recommender systems intend to help users find their interested items from among a large number of items. We continue our previous work that emphasizes on approach as an effective approach to increase the quality of the recommendations. Prioritized user-profile is an approach that tries to implement more personalized recommendation by assigning different priority importance to each of the features of the user-profile for different users. In order to find the optimal priorities for each user an optimization algorithm is needed. In this paper, we employ a new optimization algorithm namely invasive weed optimization (IWO) for this purpose. IWO is a relatively new and simple algorithm inspired from the invasive habits of growth of weeds in nature. Experimental results showed that IWO achieved the best accuracy in predicting users' interests compared to two other prioritized approaches which were based on genetic algorithm (GA) and particle swarm optimization (PSO) and to standard user-based Pearson algorithm on a movie dataset.

Particle Swarm Optimization or Differential Evolution—A comparison

Differential evolution (DE) is a novel evolutionary approach capable of handling non-differentiable, nonlinear and multi-modal objective functions. Previous studies have shown that DE is an efficient, effective and robust evolutionary algorithm, but usually it takes large computational time for optimizing the computationally expensive objective function, therefore it is necessary to find a trade-off between convergence speed and robustness. For this purpose, in this paper, a new DE based on uniform design is presented for solving nonlinear constrained optimization problems. Constraints are handled by embodying them in an augmented Lagrangian function, where the penalty parameters and multipliers are adapted as the execution of the algorithm proceeds. The efficiency of the proposed methodology is illustrated by solving numerous constrained optimization problems that can be found in the literature

Time modulated antenna arrays attracted the attention of researchers for the synthesis of low/ultra-low side lobes in recent past. In this article we propose an improved variant of a recently developed ecologically inspired metaheuristic, well-known as Invasive Weed Optimization (IWO), to solve the real parameter optimization problem related to the design of time-modulated linear antenna arrays with ultra low Side Lobe Level (SLL), Side Band Level (SBL) and Main Lobe Beam Width (BWFN). We improvise the classical IWO by introducing two parallel populations and a more explorative routine of changing the mutation step-size with iterations. Experimental results indicate that the proposed algorithm achieves better performance over the design problem as compared to the conventional Taylor Series based method and the only known metaheuristic approach based on the Differential Evolution (DE) algorithm.

The objective of this research is to determine the optimum order quantity such that the expected total profit will be maximised while some constraints such as the service level and stochastic storage space will be satisfied in the gardener problem. The main contribution is to utilise the emergency order in case of shortage, in order to achieve more profits where the demand is more than the on hand inventory. In this case, the vendor should pay the cost of customer waiting time to receive the required products either purchasing the products or losing the sale condition. As the proposed problem is NP-hard, using meta-heuristic method is our methodology for solving. Two meta-heuristic algorithms, namely differential evolution and invasive weed optimisation, are utilised to solve the problem in which their parameters are tuned. Finally, some numerical experiments and statistical comparisons are performed to evaluate the applicability of both proposed model and the algorithms. The computational results show that the proposed differential evolution has a desirable performance in favour of the expected total profits.