Pareto-Optimal Reinsurance Based on TVaR Premium Principle and Vajda Condition

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.

A predictive equation for residual strength using a hybrid of subset selection of maximum dissimilarity method with Pareto optimal multi-gene genetic programming

More accurate and reliable estimation of residual strength friction angle(/r)of clay is crucial in many geotechnical engineering applications,including riverbank stability analysis,design,and assessment of earthen dam slope stabilities.However,a general predictive equation for/r,with applicability in a wide range of effective parameters,remains an important research gap.The goal of this study is to develop a more accurate equation for/r using the Pareto Optimal Multi-gene Genetic Programming(POMGGP)approach by evaluating a comprehensive dataset of 290 experiments compiled from published literature databases worldwide.A new framework for integrated equation derivation proposed that hybridizes the Subset Selection of Maximum Dissimilarity Method(SSMD)with Multi-gene Genetic Programming(MGP)and Pareto-optimality(PO)to find an accurate equation for/r with wide range applicability.The final predictive equation resulted from POMGGP modeling was assessed in comparison with some previously published machine learning-based equations using statistical error analysis criteria,Taylor diagram,revised discrepancy ratio(RDR),and scatter plots.Base on the results,the POMGGP has the lowest uncertainty with U95=2.25,when compared with Artificial Neural Network(ANN)(U95=2.3),Bayesian Regularization Neural Network(BRNN)(U95=2.94),Levenberg-Marquardt Neural Network(LMNN)(U95=3.3),and Differential Evolution Neural Network(DENN)(U95=2.37).The more reliable results in estimation of/r derived by POMGGP with reliability 59.3%,and resiliency 60%in comparison with ANN(reliability=30.23%,resiliency=28.33%),BRNN(reliability=10.47%,resiliency=10.39%),LMNN(reliability=19.77%,resiliency=20.29%)and DENN(reliability=27.91%,resiliency=24.19%).Besides the simplicity and ease of application of the new POMGGP equation to a broad range of conditions,using the uncertainty,reliability,and resilience analysis confirmed that the derived equation for/r significantly outperformed other existing machine learning methods,including the ANN,BRNN,LMNN,and DENN equations。

A Forward-Looking Nash Game and Its Application to Achieving Pareto-Efficient Optimization

Recognizing the fact that a player’s cognition plays a defining role in the resulting equilibrium of a game of competition, this paper provides the foundation for a Nash game with forward-looking players by presenting a formal definition of the Nash game with consideration of the players’ belief. We use a simple two-firm model to demonstrate its fundamental difference from the standard Nash and Stackelberg games. Then we show that the players’ belief functions can be regarded as the optimization parameters for directing the game towards a much more desirable equilibrium.

Improved non-dominated sorting genetic algorithm (NSGA)-II in multi-objective optimization studies of wind turbine blades

The non-dominated sorting genetic algorithm （NSGA） is improved with the controlled elitism and dynamic crowding distance. A novel multi-objective optimization algorithm is obtained for wind turbine blades. As an example, a 5 MW wind turbine blade design is presented by taking the maximum power coefficient and the minimum blade mass as the optimization objectives. The optimal results show that this algorithm has good performance in handling the multi-objective optimization of wind turbines, and it gives a Pareto-optimal solution set rather than the optimum solutions to the conventional multi objective optimization problems. The wind turbine blade optimization method presented in this paper provides a new and general algorithm for the multi-objective optimization of wind turbines.

A New Evolutionary Algorithm for Solving Multi-Objective Optimization Problems

Multi-objective optimization is a new focus of evolutionary computation research. This paper puts forward a new algorithm, which can not only converge quickly, but also keep diversity among population efficiently, in order to find the Pareto-optimal set. This new algorithm replaces the worst individual with a newly-created one by 'multi-parent crossover' , so that the population could converge near the true Pareto-optimal solutions in the end. At the same time, this new algorithm adopts niching and fitness-sharing techniques to keep the population in a good distribution. Numerical experiments show that the algorithm is rather effective in solving some Benchmarks. No matter whether the Pareto front of problems is convex or non-convex, continuous or discontinuous, and the problems are with constraints or not, the program turns out to do well.

Solving Bilevel Linear Multiobjective Programming Problems

This study addresses bilevel linear multi-objective problem issues i.e the special case of bilevel linear programming problems where each decision maker has several objective functions conflicting with each other. We introduce an artificial multi-objective linear programming problem of which resolution can permit to generate the whole feasible set of the upper level decisions. Based on this result and depending if the leader can evaluate or not his preferences for his different objective functions, two approaches for obtaining Pareto- optimal solutions are presented.

Solving A Kind of High Complexity Multi-Objective Problems by A Fast Algorithm

A fast algorithm is proposed to solve a kind of high complexity multi-objective problems in this paper. It takes advantages of both the orthogonal design method to search evenly, and the statistical optimal method to speed up the computation. It is very suitable for solving high complexity problems, and quickly yields solutions which converge to the Pareto-optimal set with high precision and uniform distribution. Some complicated multi-objective problems are solved by the algorithm and the results show that the algorithm is not only fast but also superior to other MOGAS and MOEAs, such as the currently efficient algorithm SPEA, in terms of the precision, quantity and distribution of solutions.

Multi-objective optimization for roll shifting strategy in cross rolling campaigns of hot strip mill

A multi-objective optimization approach for the roll shifting strategy in cross rolling campaigns of hot strip mills is presented. The effect of different roll shifting strategies on roll wear contour is studied by numerical simulation, and two evaluation indexes ,namely body smoothness and edge smoothness, are proposed. The average body smoothness and average rolling edge smoothness of all strips in a rolling campaign are taken as the objective functions, the shifting positions of all wide strips as the decision variables, and the multi-objective method of NSGA-II as the optimizer. Thus a multi-objective optimization model for the roll shifting strategy is built. The simulation results show that work roll shifting can make wear contour smooth,and a dish-shaped wear contour without severe local wear can be achieved by the roll shifting strategy with varying stroke. Optimization experimentation shows that by means of NSGA-II,a good Pareto-optimal front can be obtained, which suggests a series of alternative solutions for roll shifting strategy optimization. The experimentation also shows that there is a conflict between the two objectives. Finally, application cases confirm the feasibility of the multi-objective approach, which can improve the strip profile ,reduce edge waves and extend the rolling miles of a rolling campaign.

Compactness, Contractibility and Fixed Point Properties of the Pareto Sets in Multi-Objective Programming

This paper presents the Pareto solutions in continuous multi-objective mathematical programming. We discuss the role of some assumptions on the objective functions and feasible domain, the relationship between them, and compactness, contractibility and fixed point properties of the Pareto sets. The authors have tried to remove the concavity assumptions on the objective functions which are usually used in multi-objective maximization problems. The results are based on constructing a retraction from the feasible domain onto the Pareto-optimal set.

An Application of the Maximum Theorem in Multi-Criteria Optimization, Properties of Pareto-Retract Mappings, and the Structure of Pareto Sets

In this paper we consider three problems in continuous multi-criteria optimization: An application of the Berge Maximum Theorem, properties of Pareto-retract mappings, and the structure of Pareto sets. The key goal of this work is to present the relationship between the three problems mentioned above. First, applying the Maximum Theorem we construct the Pareto-retract mappings from the feasible domain onto the Pareto-optimal solutions set if the feasible domain is compact. Next, using these mappings we analyze the structure of the Pareto sets. Some basic topological properties of the Pareto solutions sets in the general case and in the convex case are also discussed.

Visualization of Pareto Solutions by Spherical Self-Organizing Map and It’s acceleration on a GPU

In this study, we visualize Pareto-optimum solutions derived from multiple-objective optimization using spherical self-organizing maps (SOMs) that lay out SOM data in three dimensions. There have been a wide range of studies involving plane SOMs where Pareto-optimal solutions are mapped to a plane. However, plane SOMs have an issue that similar data differing in a few specific variables are often placed at far ends of the map, compromising intuitiveness of the visualization. We show in this study that spherical SOMs allow us to find similarities in data otherwise undetectable with plane SOMs. We also implement and evaluate the performance using parallel sphere processing with several GPU environments.

EMC Improvement for High Voltage Pulse Transformers by Pareto-optimal Design of a Geometry Structure Based on Parasitic Analysis and EMI Propagation

High voltage pulse transformers have an essential role in pulsed power systems and power conversion applications.Improving the electromagnetic behavior of such devices leads to better efficiency and low-level electromagnetic interference(EMI)noise propagation in systems.In this paper,a high voltage pulsed power system is considered and analyzed to improve their electromagnetic compatibility(EMC).The new generation of pulsed power systems that use SiC and GaN fast switches in capacitor charger power electronic circuits,face far more EMI challenges.Moreover,in this paper,the EMI propagation paths in the pulsed power system are realized and analyzed.The EMI noise level of the system is obtained and compared to the IEC61800-3 standard.To improve the EMC,the parasitic parameters of the transformer,as the main path of EMI circulation,are optimized to block the EMI propagation in the pulsed power system.To achieve this result,the parasitics are modeled and calculated with a novel and accurate energy distribution model.Then,by defining a cost function,the geometry structure of the transformer is optimized to lower the parasitics in the system.Three pareto-optimal techniques are investigated for the cost function optimization.The models and results are verified by the 3D-finite element method(FEM)and experimental results for several given scenarios.FEM and experimental verifications of this model,make the model suitable for any desirable design in any pulsed power system.Finally,the EMI noise level of the system after optimization is shown and compared to the IEC61800-3 standard.

Single and multi-area multi-fuel economic dispatch using a fuzzified squirrel search algorithm

Multi-Area Multi-Fuel Economic Dispatch (MAMFED) aims to allocate the best generation schedule in each area and to offer the best power transfers between different areas by minimizing the objective functions among the available fuel alternatives for each unit while satisfying various constraints in power systems. In this paper, a Fuzzified Squirrel Search Algorithm (FSSA) algorithm is proposed to solve the single-area multi-fuel economic dispatch (SAMFED) and MAMFED problems. Squirrel Search Algorithm (SSA) mimics the foraging behavior of squirrels based on the dynamic jumping and gliding strategies. In the SSA approach, predator presence behavior and a seasonal monitoring condition are employed to increase the search ability of the algorithm, and to balance the exploitation and exploration. The suggested approach considers the line losses, valve point loading impacts, multi-fuel alternatives, and tie-line limits of the power system. Because of the contradicting nature of fuel cost and pollutant emission objectives, weighted sum approach and price penalty factor are used to transfer the bi-objective function into a single objective function. Furthermore, a fuzzy decision strategy is introduced to find one of the Pareto optimal fronts as the best compromised solution. The feasibility of the FSSA is tested on a three-area test system for both the SAMFED and MAMFED problems. The results of FSSA approach are compared with other heuristic approaches in the literature. Multi-objective performance indicators such as generational distance, spacing metric and ratio of non-dominated individuals are evaluated to validate the effectiveness of FSSA. The results divulge that the FSSA is a promising approach to solve the SAMFED and MAMFED problems while providing a better compromise solution in comparison with other heuristic approaches.