In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized pr...In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.展开更多
This work proposes a novel approach for multi-type optimal placement of flexible AC transmission system(FACTS) devices so as to optimize multi-objective voltage stability problem. The current study discusses a way for...This work proposes a novel approach for multi-type optimal placement of flexible AC transmission system(FACTS) devices so as to optimize multi-objective voltage stability problem. The current study discusses a way for locating and setting of thyristor controlled series capacitor(TCSC) and static var compensator(SVC) using the multi-objective optimization approach named strength pareto multi-objective evolutionary algorithm(SPMOEA). Maximization of the static voltage stability margin(SVSM) and minimizations of real power losses(RPL) and load voltage deviation(LVD) are taken as the goals or three objective functions, when optimally locating multi-type FACTS devices. The performance and effectiveness of the proposed approach has been validated by the simulation results of the IEEE 30-bus and IEEE 118-bus test systems. The proposed approach is compared with non-dominated sorting particle swarm optimization(NSPSO) algorithm. This comparison confirms the usefulness of the multi-objective proposed technique that makes it promising for determination of combinatorial problems of FACTS devices location and setting in large scale power systems.展开更多
The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly...The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.展开更多
Unlike the shortest path problem that has only one optimal solution and can be solved in polynomial time, the muhi-objective shortest path problem （ MSPP ） has a set of pareto optimal solutions and cannot be solved ...Unlike the shortest path problem that has only one optimal solution and can be solved in polynomial time, the muhi-objective shortest path problem （ MSPP ） has a set of pareto optimal solutions and cannot be solved in polynomial time. The present algorithms focused mainly on how to obtain a precisely pareto optimal solution for MSPP resulting in a long time to obtain multiple pareto optimal solutions with them. In order to obtain a set of satisfied solutions for MSPP in reasonable time to meet the demand of a decision maker, a genetic algo- rithm MSPP-GA is presented to solve the MSPP with typically competing objectives, cost and time, in this pa- per. The encoding of the solution and the operators such as crossover, mutation and selection are developed. The algorithm introduced pareto domination tournament and sharing based selection operator, which can not only directly search the pareto optimal frontier but also maintain the diversity of populations in the process of evolutionary computation. Experimental results show that MSPP-GA can obtain most efficient solutions distributed all along the pareto frontier in less time than an exact algorithm. The algorithm proposed in this paper provides a new and effective method of how to obtain the set of pareto optimal solutions for other multiple objective optimization problems in a short time.展开更多
A competitive co-evolutionary Multi-Objective Genetic Algorithm (cc-MOGA) was used to approximate a Pareto front of efficient silvicultural regimes for Eucalyptus fastigata. The three objectives to be maximised includ...A competitive co-evolutionary Multi-Objective Genetic Algorithm (cc-MOGA) was used to approximate a Pareto front of efficient silvicultural regimes for Eucalyptus fastigata. The three objectives to be maximised included, sawlog, pulpwood and carbon sequestration payment. Three carbon price scenarios (3CPS), i.e. NZ $25, NZ $50 and NZ $100 for a tonne of CO2 sequestered, were used to assess the impact on silvicultural regimes, against a fourth non-carbon Pareto set of efficient regimes (nonCPS), determined from a cc-MOGA with two objectives, i.e. competing sawlog and pulpwood productions. Carbon prices included in stand valuation were found to influence the silvicultural regimes by increasing the rotation length and lowering the final crop number before clearfell. However, there were no significant changes in the frequency, timing, and intensity of thinning operations amongst all the four Pareto sets of solutions. However, the 3CPS were not significantly different from each other, which meant that these silvicultural regimes were insensitive to the price of carbon. This was because maximising carbon sequestration was directly related to the biological growth rate. As such an optimal mix of frequency, intensity, and timing of thinning maintained maximum growth rate for as long as possible for any one rotation.展开更多
Exploring optimal operational schemes for synergistic development is crucial for sustainable management in river basins.This study introduces a multi-objective synergistic optimization framework aimed at analyzing the...Exploring optimal operational schemes for synergistic development is crucial for sustainable management in river basins.This study introduces a multi-objective synergistic optimization framework aimed at analyzing the interplay among flood control,ecological integrity,and desilting objectives under varying watersediment conditions.The framework encompasses multi-objective reservoir optimal operation,scheme decision,and trade-off analysis among competing objectives.To address the optimization model,an elite mutation-based multiobjective particle swarm optimization(MOPSO)algorithm that integrates genetic algorithms(GA)is developed.The coupling coordination degree is employed for optimal scheme decision-making,allowing for the adjustment of weight ratios to investigate the trade-offs between objectives.This research focuses on the Sanmenxia and Xiaolangdi cascade reservoirs in the Yellow River,utilizing three representative hydrological years:1967,1969,and 2002.The findings reveal that:(1)the proposed model effectively generates Pareto fronts for multi-objective operations,facilitating the recommendation of optimal schemes based on coupling coordination degrees;(2)as water-sediment conditions shift from flooding to drought,competition intensifies between the flood control and desilting objectives.While flood control and ecological objectives compete during flood and dry years,they demonstrate synergies in normal years(r=0.22);conversely,ecological and desilting objectives are consistently competitive across all three typical years,with the strongest competition observed in the normal year(r=-0.95);(3)the advantages conferred to ecological objectives increase as water-sediment conditions shift from flooding to drought.However,the promotion of the desilting objective requires more complex trade-offs.This study provides a model and methodological approach for the multi-objective optimization of flood control,sediment management,and ecological considerations in reservoir clusters.Moreover,the methodologies presented herein can be extended to other water resource systems for multi-objective optimization and decision-making.展开更多
Reinsurance is an effective risk management tool for insurers to stabilize their profitability. In a typical reinsurance treaty, an insurer cedes part of the loss to a reinsurer. As the insurer faces an increasing num...Reinsurance is an effective risk management tool for insurers to stabilize their profitability. In a typical reinsurance treaty, an insurer cedes part of the loss to a reinsurer. As the insurer faces an increasing number of total losses in the insurance market, the insurer might expect the reinsurer to bear an increasing proportion of the total loss, that is the insurer might expect the reinsurer to pay an increasing proportion of the total claim amount when he faces an increasing number of total claims in the insurance market. Motivated by this, we study the optimal reinsurance problem under the Vajda condition. To prevent moral hazard and reflect the spirit of reinsurance, we assume that the retained loss function is increasing and the ceded loss function satisfies the Vajda condition. We derive the explicit expression of the optimal reinsurance under the TVaR risk measure and TVaR premium principle from the perspective of both an insurer and a reinsurer. Our results show that the explicit expression of the optimal reinsurance is in the form of two or three interconnected line segments. Under an additional mild constraint, we get the optimal parameters and find the optimal reinsurance strategy is full reinsurance, no reinsurance, stop loss reinsurance, or quota-share reinsurance. Finally, we gave an example to analyze the impact of the weighting factor on optimal reinsurance.展开更多
文摘In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.
文摘This work proposes a novel approach for multi-type optimal placement of flexible AC transmission system(FACTS) devices so as to optimize multi-objective voltage stability problem. The current study discusses a way for locating and setting of thyristor controlled series capacitor(TCSC) and static var compensator(SVC) using the multi-objective optimization approach named strength pareto multi-objective evolutionary algorithm(SPMOEA). Maximization of the static voltage stability margin(SVSM) and minimizations of real power losses(RPL) and load voltage deviation(LVD) are taken as the goals or three objective functions, when optimally locating multi-type FACTS devices. The performance and effectiveness of the proposed approach has been validated by the simulation results of the IEEE 30-bus and IEEE 118-bus test systems. The proposed approach is compared with non-dominated sorting particle swarm optimization(NSPSO) algorithm. This comparison confirms the usefulness of the multi-objective proposed technique that makes it promising for determination of combinatorial problems of FACTS devices location and setting in large scale power systems.
基金the Liaoning Province Nature Fundation Project(2022-MS-291)the National Programme for Foreign Expert Projects(G2022006008L)+2 种基金the Basic Research Projects of Liaoning Provincial Department of Education(LJKMZ20220781,LJKMZ20220783,LJKQZ20222457)King Saud University funded this study through theResearcher Support Program Number(RSPD2023R704)King Saud University,Riyadh,Saudi Arabia.
文摘The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.
文摘Unlike the shortest path problem that has only one optimal solution and can be solved in polynomial time, the muhi-objective shortest path problem （ MSPP ） has a set of pareto optimal solutions and cannot be solved in polynomial time. The present algorithms focused mainly on how to obtain a precisely pareto optimal solution for MSPP resulting in a long time to obtain multiple pareto optimal solutions with them. In order to obtain a set of satisfied solutions for MSPP in reasonable time to meet the demand of a decision maker, a genetic algo- rithm MSPP-GA is presented to solve the MSPP with typically competing objectives, cost and time, in this pa- per. The encoding of the solution and the operators such as crossover, mutation and selection are developed. The algorithm introduced pareto domination tournament and sharing based selection operator, which can not only directly search the pareto optimal frontier but also maintain the diversity of populations in the process of evolutionary computation. Experimental results show that MSPP-GA can obtain most efficient solutions distributed all along the pareto frontier in less time than an exact algorithm. The algorithm proposed in this paper provides a new and effective method of how to obtain the set of pareto optimal solutions for other multiple objective optimization problems in a short time.
文摘A competitive co-evolutionary Multi-Objective Genetic Algorithm (cc-MOGA) was used to approximate a Pareto front of efficient silvicultural regimes for Eucalyptus fastigata. The three objectives to be maximised included, sawlog, pulpwood and carbon sequestration payment. Three carbon price scenarios (3CPS), i.e. NZ $25, NZ $50 and NZ $100 for a tonne of CO2 sequestered, were used to assess the impact on silvicultural regimes, against a fourth non-carbon Pareto set of efficient regimes (nonCPS), determined from a cc-MOGA with two objectives, i.e. competing sawlog and pulpwood productions. Carbon prices included in stand valuation were found to influence the silvicultural regimes by increasing the rotation length and lowering the final crop number before clearfell. However, there were no significant changes in the frequency, timing, and intensity of thinning operations amongst all the four Pareto sets of solutions. However, the 3CPS were not significantly different from each other, which meant that these silvicultural regimes were insensitive to the price of carbon. This was because maximising carbon sequestration was directly related to the biological growth rate. As such an optimal mix of frequency, intensity, and timing of thinning maintained maximum growth rate for as long as possible for any one rotation.
基金National Natural Science Foundation of China,Grant/Award Number:U2243228The Belt and Road Special Foundation of the National Key Laboratory of Water Disaster Prevention,Grant/Award Number:2022nkms04+1 种基金MOE(Ministry of Education in China)Liberal Arts and Social Sciences Foundation,Grant/Award Number:23YJCZH332Natural Science Foundation of Anhui Province,Grant/Award Numbers:2208085US03,2308085US13。
文摘Exploring optimal operational schemes for synergistic development is crucial for sustainable management in river basins.This study introduces a multi-objective synergistic optimization framework aimed at analyzing the interplay among flood control,ecological integrity,and desilting objectives under varying watersediment conditions.The framework encompasses multi-objective reservoir optimal operation,scheme decision,and trade-off analysis among competing objectives.To address the optimization model,an elite mutation-based multiobjective particle swarm optimization(MOPSO)algorithm that integrates genetic algorithms(GA)is developed.The coupling coordination degree is employed for optimal scheme decision-making,allowing for the adjustment of weight ratios to investigate the trade-offs between objectives.This research focuses on the Sanmenxia and Xiaolangdi cascade reservoirs in the Yellow River,utilizing three representative hydrological years:1967,1969,and 2002.The findings reveal that:(1)the proposed model effectively generates Pareto fronts for multi-objective operations,facilitating the recommendation of optimal schemes based on coupling coordination degrees;(2)as water-sediment conditions shift from flooding to drought,competition intensifies between the flood control and desilting objectives.While flood control and ecological objectives compete during flood and dry years,they demonstrate synergies in normal years(r=0.22);conversely,ecological and desilting objectives are consistently competitive across all three typical years,with the strongest competition observed in the normal year(r=-0.95);(3)the advantages conferred to ecological objectives increase as water-sediment conditions shift from flooding to drought.However,the promotion of the desilting objective requires more complex trade-offs.This study provides a model and methodological approach for the multi-objective optimization of flood control,sediment management,and ecological considerations in reservoir clusters.Moreover,the methodologies presented herein can be extended to other water resource systems for multi-objective optimization and decision-making.
文摘Reinsurance is an effective risk management tool for insurers to stabilize their profitability. In a typical reinsurance treaty, an insurer cedes part of the loss to a reinsurer. As the insurer faces an increasing number of total losses in the insurance market, the insurer might expect the reinsurer to bear an increasing proportion of the total loss, that is the insurer might expect the reinsurer to pay an increasing proportion of the total claim amount when he faces an increasing number of total claims in the insurance market. Motivated by this, we study the optimal reinsurance problem under the Vajda condition. To prevent moral hazard and reflect the spirit of reinsurance, we assume that the retained loss function is increasing and the ceded loss function satisfies the Vajda condition. We derive the explicit expression of the optimal reinsurance under the TVaR risk measure and TVaR premium principle from the perspective of both an insurer and a reinsurer. Our results show that the explicit expression of the optimal reinsurance is in the form of two or three interconnected line segments. Under an additional mild constraint, we get the optimal parameters and find the optimal reinsurance strategy is full reinsurance, no reinsurance, stop loss reinsurance, or quota-share reinsurance. Finally, we gave an example to analyze the impact of the weighting factor on optimal reinsurance.
