A simulated weed colony system with subregional differential evolution for multimodal optimization

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.

The optimal hydropower operation of reservoir systems is known as a complex nonlinear nonconvex optimization problem. This paper presents the application of invasive weed optimization (IWO) algorithm, which is a novel evolutionary algorithm inspired from colonizing weeds, for optimal operation of hydropower reservoir systems. The IWO algorithm is used to optimally solve the hydropower operation problems for both cases of single reservoir and multi reservoir systems, over short, medium and long term operation periods, and the results are compared with the existing results obtained by the two most commonly used evolutionary algorithms, namely, particle swam optimization (PSO) and genetic algorithm (GA). The results show that the IWO is more efficient and effective than PSO and GA for both single reservoir and multi reservoir hydropower operation problems.

In artificial intelligence, evolutionary algorithms (EAs) have shown to be effective and robust in solving difficult optimization problems. EAs are generic populationbased metaheuristic optimization algorithms. The mechanisms used in EAs are inspired by biological evolution: reproduction, mutation, recombination, and selection. The development of EAs can be classified into two categories: single objective and multi-objective optimization. In this thesis, both single objective and multi-objective evolutionary algorithms have been studied. For single objective optimization, various niching techniques are integrated with differential evolution (DE) and particle swarm optimization (PSO) for multi-modal optimization. Multi-modal optimization deals with optimization tasks that involve finding all or most of the global/local peaks in one single run. EAs in their original forms are usually designed for locating one single global solution. To promote and maintain formation of multiple stable subpopulations within a single population, we introduced a neighborhood mutation technique to enhance DE with ability of handling multi-modal problems. We also proposed a locally informed PSO to tackle multi-modal optimization. Beside these, several existing niching techniques from the literature were modified and improved by us.

In this paper, a novel hybrid Invasive Weed Optimization (IWO) and Cuckoo Search (CS) algorithm (IWO/CS) is presented for phase-only pattern synthesis of large array antenna. The hybrid IWO/CS algorithm embeds the Levy flight of CS algorithm into IWO algorithm as a global guide, thereby enhancing the global search ability of the algorithm. At the same time, in order to avoid trapping into the local optimal solution, mutation operator is introduced to enhance search ability of the algorithm. Finally, competitive exclusion operation is improved to maintain the diversity of population. The hybrid algorithm is applied to phase-only beam shaping to achieve main lobe broadening and side lobe depression. Simulation results demonstrate the superiority of the hybrid IWO and CS algorithm.

Differential evolution (DE) is undoubtedly one of the most powerful stochastic searching optimization algorithms. However, solving a specific problem using DE crucially depends on appropriately choosing of trial vector generation strategies and their associated control parameters. At the same time, multimodal optimization refers to locating not only one optimum but a set of optimal solutions. Niching is a useful technique to solve multi-modal optimization problems. Discovering multiple niches is the key capability of niching algorithms. In this paper, we propose a Strategy Adaptive Memetci Crowding DE (SAMCDE), which incorporate Crowding DE (CDE) with strategies and control parameter self-adaptation technique as well as fine search technique to handle multi-modal optimization problems. The algorithm is tested on 10 benchmark multi-modal functions and compared with the original CDE as well as several popular multimodal optimization algorithms in literature. As shown by the experimental results, the proposed algorithm is able to generate superior performance on the tested functions.

Some problems exist in classical optimization algorithms to solve multi-modal optimization problems and other complex systems. A Dynamic Niches-based Improved Hybrid Breeding Optimization (DNIHBO) algorithm is proposed to address the multi-modal optimization problem in the paper. By dynamically adjusting the niche scale, it effectively addresses the issue of niche parameter sensitivity. The structure of the algorithm includes three distinct groups: maintainer, restorer, and sterile lines for updating operations. However, the maintainer individuals often stagnate, leading to the risk of the local optima. To overcome this, neighborhood search and elite mutation strategies are incorporated, enhancing the balance between exploration and exploitation. To further improve individual utilization within niches, a niche restart strategy is introduced, ensuring sustained population diversity. The efficacy of DNIHBO is validated through simulations on 16 multi-modal test functions, followed by comparative analyses with various multi-modal optimization algorithms. The results convincingly demonstrate that DNIHBO not only effectively locates multiple global optima but also consistently outperforms other algorithms on test functions. These findings underscore the superiority of DNIHBO as a high-performing solution for multi-modal optimization.

In this paper, fitness euclidean-distance ratio (FER) is incorprated into differential evolution to solve multimodal optimization problems. The prime target of multi-modal optimization is to finding multiple global and local optima of a problem in one single run. Though variants of differential evolution (DE) are highly effective in locating single global optimum, few DE algorithms perform well when solving multi-optima problems. This work uses the FER technique to enhance the DE’s ability of locating and maintaining multiple peaks. The proposed algorithm is tested on a number of benchmark test function and the experimental results show that the proposed simple algorithm performs better comparing with a number of state-of-the-art multimodal optimization approaches.Keywordsmultimodal optimizationniching algorithmdifferential evolutionfitness euclidean-distance ratio

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.

A novel scalable test problem suite for multimodal multiobjective optimization

Trajectory planning algorithm based on MIWO used for nondestructive testing of EAST divertor

A ring-hierarchy-based evolutionary algorithm for multimodal multi-objective optimization

In this paper, a modified invasive weed optimization (IWO) algorithm is presented for optimization of multiobjective flexible job shop scheduling problems (FJSSPs) with the criteria to minimize the maximum completion time (makespan), the total workload of machines and the workload of the critical machine. IWO is a bio-inspired metaheuristic that mimics the ecological behaviour of weeds in colonizing and finding suitable place for growth and reproduction. IWO is developed to solve continuous optimization problems that’s why the heuristic rule the Smallest Position Value (SPV) is used to convert the continuous position values to the discrete job sequences. The computational experiments show that the proposed algorithm is highly competitive to the state-of-the-art methods in the literature since it is able to find the optimal and best-known solutions on the instances studied.

We compared two floating-point-encoded evolutionary algorithms (EA) – differential evolution (DE) and the generalized generation gap (G3) – using a set of problems with different characteristics. G3 is reported to offer superior performance with unimodal functions, which are, however, often solved more efficiently using derivative-based optimization for example and it is interesting to know, how these algorithms perform in multimodal global optimization problems. Our results suggest that G3 converges fast but is prone to converge prematurely rather than finding the global optimum in high-dimensional multimodal problems. DE, in contrast, appears to handle multimodal problems better but cannot match convergence speed of G3 in unimodal problems.

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.

Novel benchmark functions for continuous multimodal optimization with comparative results