Diversity-Based Evolutionary Population Dynamics: A New Operator for Grey Wolf Optimizer

Evolutionary Population Dynamics (EPD) refers to eliminating poor individuals in nature, which is the opposite of survival of the fittest. Although this method can improve the median of the whole population of the meta-heuristic algorithms, it suffers from poor exploration capability to handle high-dimensional problems. This paper proposes a novel EPD operator to improve the search process. In other words, as the primary EPD mainly improves the fitness of the worst individuals in the population, and hence we name it the Fitness-Based EPD (FB-EPD), our proposed EPD mainly improves the diversity of the best individuals, and hence we name it the Diversity-Based EPD (DB-EPD). The proposed method is applied to the Grey Wolf Optimizer (GWO) and named DB-GWO-EPD. In this algorithm, the three most diversified individuals are first identified at each iteration, and then half of the best-fitted individuals are forced to be eliminated and repositioned around these diversified agents with equal probability. This process can free the merged best individuals located in a closed populated region and transfer them to the diversified and, thus, less-densely populated regions in the search space. This approach is frequently employed to make the search agents explore the whole search space. The proposed DB-GWO-EPD is tested on 13 high-dimensional and shifted classical benchmark functions as well as 29 test problems included in the CEC2017 test suite, and four constrained engineering problems. The results obtained by the proposal upon implemented on the classical test problems are compared to GWO, FB-GWO-EPD, and four other popular and newly proposed optimization algorithms, including Aquila Optimizer (AO), Flow Direction Algorithm (FDA), Arithmetic Optimization Algorithm (AOA), and Gradient-based Optimizer (GBO). The experiments demonstrate the significant superiority of the proposed algorithm when applied to a majority of the test functions, recommending the application of the proposed EPD operator to any other meta-heuristic whenever decided to ameliorate their performance.

GMO: Geometric Mean Optimizer for Solving Engineering Problems.. [DOI: 10.21203/rs.3.rs-2052464/v1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

This paper introduces a new meta-heuristic technique, named Geometric Mean Optimizer (GMO) that emulates the unique properties of the geometric mean operator in mathematics. This operator can simultaneously evaluate the fitness and diversity of the search agents in the search space. In GMO, the geometric mean of the scaled objective values of a certain agent’s opposites is assigned to that agent as its weight representing its overall eligibility to guide the other agents in the search process when solving an optimization problem. Furthermore, the GMO has no parameter to tune, contributing its results to be highly reliable. The competence of the GMO in solving optimization problems is verified via implementation on 52 standard benchmark test problems including 23 classical test functions, 29 CEC2017 test functions as well as nine constrained engineering problems. The results presented by the GMO are then compared with those offered by several newly-proposed and popular meta-heuristic algorithms. The results demonstrate that the GMO significantly outperforms its competitors on a vast range of the problems.

An improved MOPSO algorithm for multi-objective optimization of reservoir operation under climate change

Gradually, the previously proposed water resource management schemes and reservoir operating policies adjusted to the historically experienced climatic conditions are losing their validity and efficacy, urging building up the models compatible with the likely climatic change conditions at the future. This paper aims at optimizing the reservoir operation under climate change conditions targeting the objectives including (1) minimizing the shortages in meeting the reservoir downstream water demands and (2) maximizing the sustainability of the reservoir storage. For evaluating the effects of the climate change, six general circulation models (GCMs) built up under the representative concentration pathway (RCP4.5) emission scenario are adopted and utilized to predict the climate variables over a 30-year planning period. To solve this problem, an improved version of our recently proposed fuzzy multi-objective particle swarm optimization (f-MOPSO) algorithm, named f-MOPSO-II, is proposed. The f-MOPSO takes a novel approach to handle multi-objective nature of the optimization problems. In this approach, the common concept of "diversity" is replaced with "extremity," to choose the better guides of the search agents in the algorithm. The f-MOPSO-II is based on the f-MOPSO. However, it is aimed at simultaneously mitigating the f-MOPSO computational complexity and enhancing the quality of the final results presented by this algorithm. The results obtained by the f-MOPSO-II were then compared with those yielded by the popular non-dominated sorting genetic algorithm-II (NSGA-II). As the results suggest, the f-MOPSO-II is capable of simultaneously meeting the water demands and holding the reservoir storage sustainable, much better than the NSGA-II.

Fusion-based framework for meteorological drought modeling using remotely sensed datasets under climate change scenarios: Resilience, vulnerability, and frequency analysis

Severe drought events in recent decades and their catastrophic effects have called for drought prediction and monitoring needed for developing drought readiness plans and mitigation measures. This study used a fusion-based framework for meteorological drought modeling for the historical (1983-2016) and future (2020-2050) periods using remotely sensed datasets versus ground-based observations and climate change scenarios. To this aim, high-resolution remotely sensed precipitation datasets, including PERSIANN-CDR and CHIRPS (multi-source products), ERA5 (reanalysis datasets), and GPCC (gauge-interpolated datasets), were employed to estimate non-parametric SPI (nSPI) as a meteorological drought index against local observations. For more accurate drought evaluation, all stations were classified into different clusters using the K-means clustering algorithm based on ground-based nSPI. Then, four Individual Artificial Intelligence (IAI) models, including Adaptive Neuro-Fuzzy Inference System (ANFIS), Group Method of Data Handling (GMDH), Multi-Layer Perceptron (MLP), and General Regression Neural Network (GRNN), were developed for drought modeling within each cluster. Finally, two advanced fusion-based methods, including Multi-Model Super Ensemble (MMSE) as a linear weighted model and a nonlinear model called machine learning Random Forest (RF), combined results by IAI models using different remotely sensed datasets. The proposed framework was implemented to simulate each remotely sensed precipitation data for the future based on CORDEX regional climate models (RCMs) under RCP4.5 and RCP8.5 scenarios for drought projection. The efficiency of IAI and fusion models was evaluated using statistical error metrics, including the coefficient of determination (R²), Mean Absolute Error (MAE), Mean Square Error (MSE), and Root Mean Square Error (RMSE). The proposed methodology was employed in the Gavkhooni basin of Iran, and results showed that the RF model with the lowest estimation error (RMSE of 0.391 and R² of 0.810) had performed well compared to all other models. Finally, the resilience, vulnerability, and frequency of probability metrics indicated that the 12-month time scale of drought affected the basin more severely than other time scales.

Multi-objective optimization for optimal extraction of groundwater from a nitrate-contaminated aquifer considering economic-environmental issues: A case study

This paper focuses on the multi-objective optimization of the groundwater extraction scheme in the Bouein-Myandasht aquifer (Iran) in order to reduce the concentration of nitrate, originating from agricultural activities and wastewater absorbent wells. A simulation-optimization model coupling an artificial neural network (ANN) as the simulator with the non-dominated sorting genetic algorithm-type II (NSGA-II) as the optimizer, are employed. The simulator is trained by help of data generated by process-based simulation models for groundwater flow (MODFLOW) and solute transport (MT3D). The optimization objectives include (1) minimizing the contamination concentration and (2) maximizing the net benefit of the agricultural activities. The outcome of the simulation-optimization model is an optimized management strategy formed by the optimal values of the optimization parameters searched and obtained consisting of (1) seasonal groundwater extraction volume; (2) the ratio of the wastewater which should be treated before being leached into the groundwater through the absorbent wells; (3) the ratio of the fertilizers consumption; and (4) the cultivated area for each of the main crops in the study area. The results of the model suggest a groundwater extraction policy fulfilling the objectives of the optimization. The optimal operating policy also indicates that a partly conflicting relation exists between minimizing the risk of groundwater contamination and maximizing the net benefits of the agricultural activities. Hence, the focus of this paper is at finding the better and better Pareto-fronts in the objective space while dealing with the parts of the objective functions with less conflict to reach the optimal Pareto-front on which the full conflict between the objectives is held. Then, an entropy-based trade-off reflected in designating a couple of weights assigned to the couple of objectives calculated for each solution in the bi-objective space is held over the solutions lying on the optimal Pareto-front and finally, the favorite solution minimizing the weighted-distance to the ideal point in the objective space is achieved using the TOPSIS method. With this policy the regional nitrate concentration will be decreased by 36.7%, 20.45% and 21.6% in the first, second and third study sub-areas, respectively, as compared to those in the actual operation. Furthermore, the model suggests 15%, 12% and 9% wastewater treatment and also 9%, 6% and 7% decrease in the fertilizer use in the first, second, and third study sub-areas, respectively.

Assessment of the management scenarios for groundwater quality remediation of a nitrate-contaminated aquifer

Nitrate contaminant degrades groundwater quality and threatens the health of the humans, livestock, and the environment. Damaneh-Daran aquifer is located at upstream of the Zayandehrood reservoir in west-central Iran. This aquifer has been highly contaminated by nitrate and is still rapidly being contaminated. Thus, its quality needs to be remediated. This paper is focused on the quantity-quality modeling to predict the average nitrate concentration of the aquifer. Several remediation scenarios are presented in a period beginning from fall 2019, ending in spring 2024. These scenarios address several ways to mitigate the injection of the major sources of contamination in the region, such as equipping the urban regions with wastewater collection and treatment plants and reducing the fertilizers' use. The decreased use of the fertilizers may be achieved through two strategies: directly reducing the amount of the fertilizers by several specific and predefined rates of reduction and indirectly decreasing the amount of the fertilizers used by crop pattern modification. The latter strategy is evaluated to replace all or a part of the areas allocated to the more fertilizer-demanding crops with those of the less fertilizer-demanding crops. Furthermore, some of these scenarios are hybridized to more mitigate groundwater quality degradation. The results of performing the proposed scenarios are once compared together and then compared with the trend scenario letting current case study conditions and facilities be held in the future. The results suggest that the scenario hybridizing the effects of the wastewater treatment plants-equipping scenario with those of the quality-enhancing crop pattern modification scenario is evaluated as the most effective and best-performing scenario, implementation of which offers 20% and 30% reduction of the nitrate concentration for the agricultural and urban areas, respectively.

f-MOPSO/Div: an improved extreme-point-based multi-objective PSO algorithm applied to a socio-economic-environmental conjunctive water use problem

In this paper, a new version of the multi-objective particle swarm optimizer named the Diversity-enhanced fuzzy multi-objective particle swarm optimization (f-MOPSO/Div) algorithm is proposed. This algorithm is an improved version of our recently proposed f-MOPSO. In the proposed algorithm, a new characteristic of the particles in the objective space, which we named the "extremity," is also evaluated, along with the Pareto dominance, to appoint proper guides for the particles in the search space. Three improvements are applied to the f-MOPSO to mitigate its shortcomings, generating f-MOPSO/Div: (1) selecting the global best solution based on the diversity of the extreme solutions, (2) impeding the particles to be trapped in the local optima using a mutation scheme based on the dynamic probability, and (3) removing the pre-optimization process. To validate f-MOPSO/Div, it was compared with some other popular multi-objective algorithms on 14 standard low- and high-dimensional test problem suites. After the comparative results indicated the outperformance of the proposal, the f-MOPSO/Div was applied to solve an optimal conjunctive water use management problem, in a semi-arid study area in west-central Iran, over a 13-year long-term planning period with two main objectives: (1) maximizing the aquifer sustainability as an environmental goal, and (2) maximizing the crop yields as a socio-economic goal. As the results suggest, the cumulative groundwater level drawdown is considerably decreased over the whole planning period to make the aquifer sustainable, while the water productivity is held at a desirable level, demonstrating the superiority of the f-MOPSO/Div when also applied to solve a large-scale real-world optimization problem.

Prediction and assessment of drought effects on surface water quality using artificial neural networks: case study of Zayandehrud River, Iran

Although drought impacts on water quantity are widely recognized, the impacts on water quality are less known. The Zayandehrud River basin in the west-central part of Iran plateau witnessed an increased contamination during the recent droughts and low flows. The river has been receiving wastewater and effluents from the villages, a number of small and large industries, and irrigation drainage systems along its course. What makes the situation even worse is the drought period the river basin has been going through over the last decade. Therefore, a river quality management model is required to include the adverse effects of industrial development in the region and the destructive effects of droughts which affect the river's water quality and its surrounding environment. Developing such a model naturally presupposes investigations into pollution effects in terms of both quality and quantity to be used in such management tools as mathematical models to predict the water quality of the river and to prevent pollution escalation in the environment. The present study aims to investigate electrical conductivity of the Zayandehrud River as a water quality parameter and to evaluate the effect of this parameter under drought conditions. For this purpose, artificial neural networks are used as a modeling tool to derive the relationship between electrical conductivity and the hydrological parameters of the Zayandehrud River. The models used in this research include multi-layer perceptron and radial basis function. Finally, these two models are compared in terms of their performance using the time series of electrical conductivity at eight monitoring-hydrometric stations during drought periods between the years 1997-2012. Results show that artificial neural networks can be used for modeling the relationship between electrical conductivity and hydrological parameters under drought conditions. It is further shown that radial basis function works better for the upstream stretches of the river while multi-layer perceptron is more efficient for the downstream stretches.

Groundwater vulnerability assessment using fuzzy logic: a case study in the Zayandehrood aquifers, Iran

Groundwater is an important source of water, especially in arid and semi-arid regions where surface water is scarce. Groundwater pollution in these regions is consequently a major concern, especially as pollution control and removal in these resources are not only expensive but at times impossible. It is, therefore, essential to prevent their contamination in the first place by properly identifying vulnerable zones. One method most commonly used for evaluating groundwater pollution is the DRASTIC method, in which the Boolean logic is used to rank and classify the parameters involved. Problems arise, however, in the application of the Boolean logic. In this paper, the fuzzy logic has been used to avoid the problems. For this purpose, three critical cases of minimum, maximum, and mean values have been considered for the net recharge parameter. The process has been performed on the Zayandehrood river basin aquifers. The fuzzy-DRASTIC vulnerability map thus obtained indicates that the western areas of the basin generally have the maximum pollution potential followed by the areas located in the east. The central parts of the study area are found to have a low pollution potential. Finally, two sensitivity analyses are performed to show the significance of each value of the net recharge parameter in the calculation of vulnerability index.