Then, an improved multi-objective particle swarm optimization algorithm of solving the above model is developed. Evolutionary algorithms are used widely in optimization studies on water distribution networks. Within the chapters, the reader will find different studies about specialized subjects, such as: special mechanisms to focus the search on the boundaries of the feasible region, the relevance of infeasible solutions in the search process, parameter control in constrained optimization, the combination of mathematical programming techniques and evolutionary algorithms in constrained search spaces and the adaptation of novel nature-inspired algorithms for numerical optimization with constraints. Hence, in this chapter authors have concentrated in explaining the constrained multi-objective optimization problem along with their applications. These issues are addressed in this paper by designing different tradeoff schemes during different stages of a search process to obtain an appropriate tradeoff between objective function and constraint violations. This approach is validated by the benchmark functions proposed most recently and compared with those of the state of the art from various branches of evolutionary computation paradigms.
In the first phase, the entire solution space is explored until a feasible solution is identified. The main components of the methodology included an optimizer, a hydraulic simulator and an algorithm that calculates the flow entropy for any given network configuration. To address this issue, this paper proposes a parameter-free constraint handling technique, two-archive evolutionary algorithm, for constrained multi-objective optimization. The study highlights important and commonly overlooked issues in evaluating multi-objective methods. A novel constraint handling method is introduced to ensure that a certain number of good infeasible solutions will be kept in the procedure of evolution to guide the search of the individuals. It is characterized by a storing nondominated solutions externally in a second, continuously updated population, b evaluating an individual's fitness dependent on the number of external nondominated points that domina. The presence of nonlinear mixing effects poses an important problem when attempting to provide accurate estimates of the abundance fractions of pure spectral components endmembers in a scene.
Flow entropy has been employed previously as a surrogate reliability measure. It maps individuals from a high-dimensional objective space into a 2-D polar coordinate plot while preserving Pareto dominance relationship, retaining shape and location of the Pareto front, and maintaining distribution of individuals. He also mentioned the applicability to parameter optimization whic. To utilize the useful information contained in infeasible individuals, this paper uses infeasible weights to maintain a number of well-diversified infeasible individuals. The main goal of evolving infeasible solutions in the search process is to use the information they carry. In addition, an overview of the most commonly used test functions, performance measures and statistical tests is presented. Aiming at robot path planning in an environment with danger sources, a global path planning approach based on multi-objective particle swarm optimization is presented in this paper.
Three popular types of multiobjective evolutionary algorithms, i. It is shown that the method is able to find the optimum solutions. The results obtained in the computational experiments are used to compare the proposal with another well known constraint handling scheme in the literature. Expenses are decreased through the reduction in components design time as well as through savings in manufacturing costs and inventory. Each subpopulation focuses on only optimizing the corresponding objective which leads to a clear division of work. The performance of the method has been examined by its application to a set of eleven test cases from the specialized literature.
The proposed algorithm shows competitive results with improved diversity and convergence and demands less computational cost. As a result, many constraint-handling techniques have been proposed. It is shown that the approach applies a search towards solutions with optimal performances while taking into account high reliability. This is why existing automatic parameter estimation approaches cannot identify a unique best parameter vector. The constraint handling technique was tested on several constrained multi-objective problems and has shown superior results. This genetic algorithm is easy to implement and adapt to different settings.
The methodology comprises two main phases. The new ranking method is tested using a μ, λ evolution strategy on 13 benchmark problems. In many real-world applications, workspace of robots often involves various danger sources that robots must evade, such as fire in rescue mission, landmines and enemies in war field. In the proposed method, a different leader selection algorithm is proposed for each population. A successful application of a hydrologic model strongly depends on a good calibration. The study highlighted that the evaluation of multiobjective methods is itself a multi-objective problem. The multi-modal problems involve presence of local optima and thus conventional derivative based algorithms do not able to effectively determine the global optimum.
That is, there exist three possible combinations of two parents: both from the main population, both from the secondary population, and each from each population. Requirements such as continuity and differentiability of the cost surface add yet another conflicting element to the decision process. Moreover, the statistical analysis of the obtained results emphasize the advantages of our proposal over the original algorithm on both aspects of convergence and diversity on most test problems. Actually, the directed mating significantly contributes to improving the search performance of evolutionary constrained multi-objective optimization. The methodology developed is generic and self-adaptive, and prior setting of the reduced solution space is not required. Comprehensive experiments on a series of benchmark problems and a real-world case study fully demonstrate the competitiveness of our proposed algorithm, comparing to five state-of-the-art constrained evolutionary multi-objective optimizers. The infeasibility measure is used to form a two-stage penalty that is applied to the infeasible solutions.
These include a sequential approach, posing the search as a multi-objective problem, and posing it as a unified single-objective problem. Moreover, a constrained Pareto domination based on the degree of a path blocked by obstacles is employed to update local leaders of a particle and the two archives. Extensive computational experiments show excellent results for the first two problems, and mixed for the third. The solution with the least constraint violation is archived as the elite solution in the population. While a body of work exists for a single operating condition under steady state conditions, the effectiveness of flow entropy for systems with multiple operating conditions has received very little attention. In the study, several computational-based approaches to search for the common components are discussed, tested, and compared. The experimental results indicate that the proposed algorithm is highly competitive in solving the benchmark problems.
The principle is similar to the feasibility rules that are used to address single objective constraint problems. These novel techniques originate from the research fields of evolutionary computation and cloud computing. Niche formation techniques are used to promote diversity among preferable candidates, and progressive articulation of preferences is shown to be possible as long as the genetic algorithm can recover from abrupt changes in the cost landscape. Finally, the ranking of an arbitrary number of candidates is considered. Recently, we proposed a new threshold based penalty function.
The proposed method is compared with two other constrained multi-objective differential evolution algorithms and the results show that the proposed method is competitive. Several design examples of steerable and wideband arrays are provided to prove the flexibility and reliability of the approach. The information is used to vary the flight parameters of the Particle Swarm Optimization, to generate newer individuals and to better track dynamic and multiple optima with constraints. The objective function value modified is consisted of individuals' distance and adaptive penalty. The non-stationary penalty is a function of the generation number; as the number of generations increases so does the penalty. A set of test problems recently proposed for the evaluation of this kind of algorithm has been used in the evaluation of the algorithm presented.