The Efficiency of Setting Parameters in a Modified Shuffled Frog Leaping Algorithm Applied to Optimizing Water Distribution Networks

Due to the need of correct diseases analysis, MR image segmentation remains till now a challenging problem, especially in the presence of random noise. This paper proposes a new meta-heuristic algorithm for MR brain image segmentation, named Modified Shuffled Frog Leaping Algorithm (MSFLA), based on the technique of Shuffled Frog Leaping Algorithm (SFLA). In this new paradigm, there is no need to filter the original image. The new fitness function proposed in our algorithm helps to evaluate quickly the particle frogs in order to arrange them in descending order. The proposed approach has been compared with other meta-heuristics such as 3D-Otsu thresholding with SFLA and Genetic Algorithm (GA) and also with the algorithm of segmentation using the Rician Classifier (RiCE). Experimental results show that the proposed MSFLA is able to achieve better segmentation quality and execution time than the latest methods.

This paper presents cross entropy (CE) optimization for optimal design of water distribution networks (WDN) under demand uncertainty. In design of WDNs, it is desired to achieve a minimum cost WDN that provides higher reliability in meeting the demands. To achieve these goals, an optimization model is formulated for design of WDNs with an objective of minimizing the total cost of WDN subject to meeting the nodal demands at a specified system reliability, mass conservation and other physical constraints. The uncertainty in future water demands is modeled using the theory of fuzzy random variable (FRV). The water demand at each node is assumed to be following a normal distribution with a fuzzy mean, and 10 % (or 20 %) of the fuzzy mean as its standard deviation. The water demand is represented as a triangular fuzzy number with the random demand as its kernel, and the interval of ±5 % (or ±10 %) variation of the random demand as its support for two scenarios. The fuzzy random system reliability (R) of WDNs is defined on the basis of necessity measure to assess system performance under fuzzy random demands and crisp head requirements. The latin hypercube sampling method is adopted for sampling of uncertain demands. The methodology is applied to two WDNs, and optimization models are solved through cross entropy optimization for different levels of reliability, and generated tradeoffs between the cost and R. On comparing the solutions obtained with the proposed methodology with earlier reported solutions, it is noted that the proposed method is very effective in producing robust optimal solutions. On analyzing the tradeoffs between reliability and costs, the results show that negligence of uncertainty can lead to under design of the WDNs, and the cost increases steeply at higher levels of reliability. The results of the two case studies demonstrate that the presented CE based methodology is effective for fuzzy-probabilistic design of WDNs.

A transmission loss minimum re-scheduling method by genetic algorithm and modified shuffled frog leaping algorithm are proposed. The problem is a complex mixed integer programming problem. A genetic algorithm (GA) is a search or optimization algorithm based on the mechanics of natural selection and natural genetics where modified shuffled frog-leaping algorithm (MSFLA), which is an improved version of memetic algorithm, is a relatively new evolutionary method where local search is applied during the evolutionary cycle. Since GA and MSFLA both are suitable to solve combinatorial optimization problems, it can be successfully applied to problems of loss minimum in transmission system. The proposed methodology depicts the information related to the optimization status of total system loss without installing external device to minimize the investment cost using only different re-dispatching scheduling. IEEE 30 bus system is used to demonstrate the effectiveness of the method.

Water distribution networks (WDNs) evolve continuously over time. Changes in water demands and pipe deterioration require construction upgrades to be performed on the network during its entire lifecycle. However, strategically planning WDNs, especially for the long term, is a challenging task. This is because parameters that are essential for the description of WDNs in the future, such as climate, population and demand transitions, are characterized by deep uncertainty. To cope with future uncertainty, and avoid overdesign or costly unplanned and reactive interventions, research is moving away from the static design of WDNs. Dynamic design approaches, aim to make water networks adaptive to changing conditions over long planning horizons. A promising, dynamic design approach is the staged design of WDNs, in which the planning horizon is divided into construction phases. This approach allows short-term interventions to be made, while simultaneously considering the expected long-term network growth outcomes. The aim of this paper is to summarize the current state of the art in staged design of water distribution networks. To achieve that, we critically examined relevant publications and classified them according to their shared key characteristics, such as the nature of the design problem (new or existing network design, expansion, strengthening, and rehabilitation), problem formulation (objective functions, length of planning horizon), optimization method, and uncertainty considerations. In the process, we discuss the latest findings in the literature, highlight the major contributions of staged design on water distribution networks, and suggest future research directions.

The design of water distribution networks (WDNs) is addressed by using a variant of the particle swarm optimization (PSO) algorithm. This variant, which makes use of a discrete version of PSO already considered by the authors, overcomes one of the PSO's main drawbacks, namely its difficulty in maintaining acceptable levels of population diversity and in balancing local and global searches. The performance of the variant proposed here is investigated by applying the model to solve two standard benchmark problems: the Hanoi new water distribution network and the New York Tunnel water supply system. The results obtained show considerable improvements in both convergence characteristics and the quality of the final solutions, and near-optimal results are consistently achieved at reduced computational cost.

We developed a hybrid algorithm for multi-objective design of water distribution networks (WDNs) in the present study. The proposed algorithm combines the global search schemes of differential evolution (DE) with the local search capabilities of harmony search (HS) to enhance the search proficiency of evolutionary algorithms. This method was compared with other multi-objective evolutionary algorithms (MOEAs) including NSGA2, SPEA2, MOEA/D and extended versions of DE and HS combined with non-dominance criteria using several metrics. We tested the compared algorithms on four benchmark WDN design problems with two objective functions, (i) the minimization of cost and (ii) the maximization of resiliency as reliability measure. The results showed that the proposed hybrid method provided better optimal solutions and outperformed the other algorithms. It also exhibited significant improvement over previous MOEAs. The hybrid algorithm generated new optimal solutions for a case study that dominated the best-known Pareto-optimal solutions in the literature

Water distribution network (WDN) design problems generally consider minimising network costs while meeting minimum allowable pressure under specified demand patterns. However, extension and renovation of networks based on assessment of demand uncertainty causes an increase in efficiency of the system and monetary savings. Attention to uncertain changes in pattern and the value of nodal demands in an operational period can thus show the effect of uncertainties in the network's efficiency. Using Monte Carlo simulation and shuffled frog leaping algorithm optimisation, this paper analyses the efficiency of a designed network based on nodal demand uncertainty during the operational period. Assessment of a network efficiency index according to a probabilistic normal distribution for nodal demand in an operational period shows that a network design that does not consider nodal demand uncertainty decreases network efficiency, especially at the end of the operational period. Moreover, an increase in demand uncertainty decreases network efficiency. The results of the proposed model for a benchmark WDN show that a network designed deterministically for a 30-year operational period is unable to secure nodal demands with suitable pressure after 10 years. In addition, the minimum required pressure considered in network design is met in approximately the first 18 years of the operational period.

Shuffled Frog Leaping Algorithm (SFLA) is a meta-heuristic for solving discrete optimization problems. Here it is applied to determine optimal discrete pipe sizes for new pipe networks and for network expansions. SFLA is a population based, cooperative search metaphor inspired by natural memetics. The algorithm uses memetic evolution in the form of infection of ideas from one individual to another in a local search. The local search is similar in concept to particle swarm optimization. A shuffling strategy allows for the exchange of information between local searches to move toward a global optimum. This paper summarizes the development of SFLANET, a computer model that links SFLA and the hydraulic simulation software EPANET and its library functions. Application of SFLANET to literature network design problems is then described. Although the algorithm is in its initial stages of development, promising results were obtained.

This study presents an innovative data-driven approach to optimally design water distribution networks (WDNs). The methodology comprises five key stages: Generation of 600 synthetic WDNs with diverse properties, optimized to determine optimal component diameters; Extraction of 80 topological and hydraulic features from the optimized WDNs using graph theory; preprocessing and preparing the extracted features using established data science methods; Application of six feature selection methods (Variance Threshold, k-best, chi-squared, Light Gradient-Boosting Machine, Permutation, and Extreme Gradient Boosting) to identify the most relevant features for describing optimal diameters; and Integration of the selected features with four machine learning models (Random Forest, Support Vector Machine, Bootstrap Aggregating, and Light Gradient-Boosting Machine), resulting in 24 ensemble models. The Extreme Gradient Boosting-Light Gradient-Boosting Machine (Xg-LGB) model emerged as the optimal choice, achieving R2, MAE, and RMSE values of 0.98, 0.017, and 0.02, respectively. When applied to a benchmark WDN, this model accurately predicted optimal diameters, with R2, MAE, and RMSE values of 0.94, 0.054, and 0.06, respectively. These results highlight the developed model’s potential for the accurate and efficient optimal design of WDNs.

Centroid Mutation Embedded Shuffled Frog-Leaping Algorithm

Water distribution networks (WDNs) play a crucial role in the well-being of human populations and economic prosperity. It is essential that they cope with abnormal operating conditions and recover functionality quickly. Traditionally, WDNs are designed using cost and reliability objectives, but there is a lack of consensus on the definition and quantification of reliability which typically is a computationally intense process. Subsequently, various reliability-like metrics, called resilience indices, have been developed and demonstrated in the design of WDNs. Few studies exist that thoroughly evaluate the performance of the previously developed resilience metrics. This paper investigates three resilience metrics by evaluating their performance on three benchmark WDNs for several simulated mechanical failure states. The metrics studied are: (a) resilience index, (b) network resilience index (NRI), and (c) modified resilience index (MRI). The metric MRI performed better overall but NRI produced cheaper designs that performed better in the case of WDN-I. It is recommended that a better metric that incorporates different dimensions of resilience, such as robustness and redundancy, should be developed in the future.

Future water demands and pipe roughness coefficients used in the design of water distribution networks (WDNs) have a high degree of uncertainty. Fuzzy analysis of WDNs provide how the uncertainties in independent or basic parameters (such as nodal demands and pipe roughness coefficients) are propagated to dependent or derived parameters (such as pipe flows, pipe velocities, and available pressure heads). Usually demand dependent analysis is used for such analysis. A WDN may be pressure deficient or may become pressure deficient because of high pipe roughness or inadequate pump pressure and may not be able to meet desired demands at all nodes. Thus, it is desirable to consider the nodal outflows as unknown and as a function of available pressure heads under pressure-deficient conditions. An approach for fuzzy analysis of a WDN that takes into account pressure-deficient condition using node flow analysis is presented in this paper. The proposed methodology is illustrated with an example network taken from literature. The methodology is useful in identifying vulnerable zones in WDNs and can be extended for reliability analysis under uncertainty of nodal demands and pipe roughness coefficients. Comparison of results with usual demand-dependent analysis shows that proposed method is better for identifying vulnerable zones.

Multi-objective meta-heuristics are used to optimize water distribution networks (WDNs) as they can achieve a near-optimal balance between cost and resilience in a unified platform. Most of these algorithms include tuning of algorithm-specific control parameters for higher optimization efficiency, leading to an increased computational effort. The current study is inspired by the desire to address the above problem. The goal is to formulate a multi-objective Rao algorithm (MORao) considering an existing modified resilience index (MRI) in the optimal design of WDNs. The model is demonstrated to attain Pareto-optimal solutions to complex WDN problems without exclusive parameter tuning. The algorithm is written in Python and is linked to a hydraulic model of a WDN implemented in EPANET 2.2 using pressure-driven demand (PDD) analysis. The method is demonstrated on three widely used networks: Two-loop, Goyang, and Fossolo. The Pareto-optimal solutions examine a tradeoff between two objectives to recognize competitive solutions. The network's resilience is increased 2.5 times by only 0.8 times increase in least-cost of Two-loop network. This research indicates that this method can achieve a satisfactory level of performance with a limited number of function evaluations.

Sampling design is often required for an appropriate assessment of monitoring points in water distribution networks to increase the effectiveness of measured data in calibrating the hydraulic model. Although many methods are available in the literature, they may be inadequate for reliable network calibration. This paper proposes a new method for the optimal collocation of monitoring points using a shortest path based approach. The monitoring points are identified by minimizing the sum of node distances from the closest sensor-node. Node distances were taken to be a weighted sum of the dimensionless arc length and the absolute head loss along arc. To ensure robustness with respect to the presence of outliers among pipe lengths and/or pressure drops, adequate reference measures were chosen for normalization. The optimization problem was solved using Mixed Integer Programming and a variant of the K-Means algorithm. Alternative formulations considering different path blending and distance norms were also analyzed. Numerical experiments carried out on both theoretical and real water distribution networks showed the reliability of the proposed approach and a greater effectiveness compared to similar methods available in the literature.

Global performance of metaheuristic optimization tools for water distribution networks