The differences lie in that the and are replaced by personal best for the th particle in the high-quality group and the optimal particle for th particle sub-population, respectively. If multiple particles exist, they will be further compared to locate the optimal particle with the largest crowding distance.
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In this section, we conduct simulation experiments to demonstrate the superiority of the proposed IMOPSO with several testing functions. A total of 30 independent simulations are conducted to offset randomness effect. The IGD is an indicator for assessing convergence and solution diversity. Therefore, the IMOPSO is verified to have advantages on solution quality and stable performance compared with other methods selected. In this section, simulation is conducted to analyze the sensitivity of parameters in the method proposed. The IGD and GD indicators present a descending trend with the increase of inertia weight until the value of inertia weight is 0.
Similarly, as the population size increases, the quality of solutions becomes better. Meanwhile, more computation time will cost as the complexity of algorithm is strongly associated with population size.
Therefore, although the IGD and GD indicators are not their best when population size is , it will save a large amount of computation time compared with simulations under population sizes of and Finally, we defined the inertia weight and population size as 0. In order to verify the validity and reasonability of the GCA-TOPSIS model, the flood control operation schemes of Hongjiadu reservoir were used to make the optimal decision calculation. The sort order of schemes is consistent with that of Ma et al. However, the method in Ma et al.
As a result, the decision-making results of this method are easily influenced by the knowledge and experience of decision-makers. On the contrary, we take fully objective and subjective information into consideration using the combination weighting method based on minimum deviation.
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Furthermore, the GCA contributes to reflect the uncertain information grey information and internal connection between multi-indicators. Further comparison of the scheduling schemes shows that scheme 1 and 4 effectively utilize flood resources to increase the power generation with pre-discharge measure to control flood. Thus, the scheduling schemes 1 and 4 are optimal for the decision-maker.
However, scheme 6 and 3 take more conservative measures of flood peak mitigation to hold back the flood only at the time of flood peak arrival, failing to make the best use of flood resources. Accordingly, these schemes are incompatible with the decision-maker. The decision results coincide with practical scheduling schemes for flood control in Hongjiadu reservoir. For the cascade reservoirs in the basin, the formulation, evaluation, and optimization of the scheduling scheme is essentially a multi-objective, multi-attribute, and multi-turn decision-making problem in the same way.
In this section, multi-objective reservoir operation in Qingjiang river is chosen as one case. Qingjiang river is the largest tributary of the middle Yangtze river which flows through Enshi, Badong, Changyang, and Yidu located in Hubei province. A total of three reservoirs and hydropower stations with large installed capacity, regulating storage are located on the river. The Shuibuya reservoir with multi-year regulating storage and the largest installed capacity, is the most important reservoir of the cascade development in Qingjiang river basin.
The Geheyan reservoir is a huge water conservancy project with major functions of power generation and flood control, and is of navigational benefit. Gaobazhou reservoir, situated on the lower reaches of the Qingjiang river, plays an important role in the reverse regulation of upstream Geheyan Yang et al. The size of EAS is defined as The particle population is and sub-populations assigned M are predefined as Accordingly, the number of particles in each sub-population is The inertia weight is 0. The maximum iterations are defined as Two scheduling scenarios are proposed with the emphasis on multi-objective ecological scheduling and water supply scheduling, respectively.
The specific scenarios are described as follows. Scenario 1 : Take multiple objectives including power generation, guaranteed hydropower station and ecological water spill and shortage into account. Scenario 2 : Take multiple objectives including power generation, water supply and ecological water spill and shortage into account. Scenario 1 : Multi-objective ecological scheduling MOES : For this scenario, the maximum power generation and guaranteed hydropower output and minimum ecological water shortage and spill are considered.
The hydrologic and hydraulic constraints can be found in Zhu et al. The details of optimization objectives are listed as follows. For the input of the MOES model, we select one typical observed inflow process. Moreover, power generation of cascade reservoirs and downstream ecological benefit also shows contradictoriness and opposition.
However, with the increase of guaranteed output, decrease of ecological overflow and water shortage means increase of ecological benefit, and implies the compatibility between the cascade reservoir output and ecological benefits. For the decision-maker, they should select the suitable scheme from the solution sets to implement. The relative similarity degree and solution sorting results.
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In terms of scheme 16, the objective of power generation and guaranteed output is fully considered. Moreover, the ecological benefit obtained by this scheme outperforms most other schemes. Meanwhile, as the indicator weights calculated are 0. It should be noted that we discuss the MOES for cascade reservoirs rather than reservoir scheduling which focus on economic benefits.
Therefore, scheduling schemes are not just ranked in descending order as the power generation increases. The ecological objective also has a non-negligible and significant influence on scheme evaluation and decision. On the other hand, as the decision process tends to ecological benefit, corresponding indicator weights are 0. It is evident that scheme sorting results under this situation are basically consistent with variation tendency of ecological water spill and shortage.
The medium and worst schemes are added as comparison. Due to the flood control task undertaken by Qingjiang cascade reservoirs in the flood season, the flood control benefit becomes the main factor. Instead, the differences between schemes are mainly reflected in the dry season.
Multi-objective Decision Analysis: Managing Trade-offs and Uncertainty
Power generation efficiency requires the reservoir to operate at a high-water head, consequently, the variation range of flow rate is increased, and natural runoff will be changed, to a large extent, which produces obvious competition between power generation and ecological benefits. Meanwhile, guaranteed output benefit needs to maintain stability of power generation flow under the condition of certain amount of water.
The ecological flow in dry season is simultaneously beneficial to hydropower output effect because the differences between schemes exist in this season. Therefore, the compatibility between ecological and guaranteed hydropower output benefits is remarkable. Accordingly, it increases corresponding reservoir discharge in the dry season in order to protect the stability of guaranteed output and downstream ecological flow to a certain extent.
In comparison, scheme 22 outperforms on total power generation and makes full use of high-water head effect; however, its guaranteed output is relatively lower than that of scheme 16 due to large variation of hydropower output. The large variation of output also implies instability of reservoir discharge which impairs the ecological benefit. In terms of scheme 13, which tends to achieve the ecological benefit, the ecological water spill and shortage in the initial stage of the flood season is larger than other schemes. However, with a small growth rate, the total amount of ecological spill and shortage is small, and the stable variation is more beneficial to ecological benefit.
In the meantime, the hydropower output is also outstanding as discharge in the flood season increases. Scenario 2 : Multi-objective water supply scheduling MOWSS : In this scenario, optimization goals are adjusted so that the water supply benefit is added, and ecological benefit is described in the form of ecological flow guarantee rate.
Similarly, the water supply guarantee rate is used for representing water supply benefit.
Moreover, power generation benefit described above is also considered. The details are shown as follows. Accordingly, improving power generation will bring about the violation of water supply and ecological benefits and vice versa. This may be explained by the increase of AWSGR needs larger reservoir discharge, which is also beneficial for maintaining downstream ecological health.
As a result, it will bring about an adverse effect on power generation and ecological benefits. The medium and worst schemes are used as a comparison. As the indicator weights calculated are 0. Thus, the sorting result of the optimal scheme to that of the worst scheme is basically consistent with the variation trend of water supply guarantee rate. Scheme 2 increases reservoir discharge and produces water stage drawdown to guarantee the water supply task during the dry season. Meanwhile, the larger quantity of water discharge is beneficial to alleviate ecological water shortage at the dry season stage.
Thus, the compatibility relationship between water supply and ecological protection is presented. On the other hand, although the hydropower output outperforms other schemes in the initial stage of the dry season, high-water head is not efficiently utilized to guarantee total power generation. In terms of scheme 24, it focuses more energy on the power generation benefit.
To this end, reservoir water discharge is cut down to operate at higher-water head and concentrate drawdown before the arrival of the flood season. As a result, high-water head effect is fully used to play the power generation benefit. However, the smaller discharge in the early stage of the dry period will alleviate the benefit of AWSGR and AEFGR, and great fluctuation of reservoir discharge is harmful to maintain stability of water supply and ecological health.
It can quickly and reasonably select the most ideal scheme of comprehensive benefits under different decision-making scenarios for the reservoir decision-makers. In terms of the MCDM model, the GCA contributes to reflecting the difference between the change trend in the scheduling scheme sets and ideal scheme, while the TOPSIS can reflect the overall similarity between alternative and ideal schemes.
The combination of GCA and TOPSIS can take uncertainty factors and grey characteristics in the multi-objective decision process fully into account, and accurately describe the comprehensive quality of alternative scheduling schemes. In summary, the decision-making method of GCA-TOPSIS shows strong applicability in solving the evaluation of multi-objective flood control, ecological and water supply scheduling schemes.
The rationality of the decision result is also illustrated and verified, which implies that the decision-making method GCA-TOPSIS can provide strong theoretical support for the implementation of multi-objective balanced scheduling decisions in complex reservoir systems. Sign In or Create an Account. Advanced Search. Sign In. Article Navigation. Close mobile search navigation Article navigation.
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