scholarly journals Optimal Claim Settlement Strategies under Constraint of Cap on Claim Loss

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3284
Author(s):  
Hong Mao ◽  
Krzysztof Ostaszewski
Keyword(s):  
Numerical Analysis ◽  
Objective Function ◽  
Expected Loss ◽  
Objective Functions ◽  
Net Benefit ◽  
Insurance Claim ◽  
Optimal Insurance ◽  
Settlement Strategies

In this paper, we examine the question of how to devise an optimal insurance claim settlement scheme under the constraint of a cap on the amount of the claim payment. We establish objective functions to maximize the net benefit due to exaggerated claims while at the same time maximizing the total expected wealth of the insured. Then, we establish a dual objective function to minimize the total expected loss, including the perspective of the insurer. Finally, we illustrate applications of our work and provide numerical analysis of it along with an example.

Scalable Computing Architecture for Time-Dependent Transportation Optimization Problems Based on High-Performance Computing Techniques

2019 ◽  
Vol 2673 (4) ◽  
pp. 205-216 ◽  
Author(s):  
Pengfei (Taylor) Li ◽  
Peirong (Slade) Wang ◽  
Farzana Chowdhury ◽  
Li Zhang
Keyword(s):  
Objective Function ◽  
High Performance Computing ◽  
High Performance ◽  
Optimization Problems ◽  
Dynamic Network ◽  
Alternative Formulation ◽  
High Fidelity ◽  
Objective Functions ◽  
Performance Computing ◽  
Transportation Optimization

Traditional formulations for transportation optimization problems mostly build complicating attributes into constraints while keeping the succinctness of objective functions. A popular solution is the Lagrangian decomposition by relaxing complicating constraints and then solving iteratively. Although this approach is effective for many problems, it generates intractability in other problems. To address this issue, this paper presents an alternative formulation for transportation optimization problems in which the complicating attributes of target problems are partially or entirely built into the objective function instead of into the constraints. Many mathematical complicating constraints in transportation problems can be efficiently modeled in dynamic network loading (DNL) models based on the demand–supply equilibrium, such as the various road or vehicle capacity constraints or “IF–THEN” type constraints. After “pre-building” complicating constraints into the objective functions, the objective function can be approximated well with customized high-fidelity DNL models. Three types of computing benefits can be achieved in the alternative formulation: ( a) the original problem will be kept the same; ( b) computing complexity of the new formulation may be significantly reduced because of the disappearance of hard constraints; ( c) efficiency loss on the objective function side can be mitigated via multiple high-performance computing techniques. Under this new framework, high-fidelity and problem-specific DNL models will be critical to maintain the attributes of original problems. Therefore, the authors’ recent efforts in enhancing the DNL’s fidelity and computing efficiency are also described in the second part of this paper. Finally, a demonstration case study is conducted to validate the new approach.

scholarly journals Intramax and other objective functions: The case of Slovenia

2016 ◽  
Vol 24 (2) ◽  
pp. 12-25 ◽  
Author(s):  
Samo Drobne ◽  
Mitja Lakner
Keyword(s):  
Objective Function ◽  
The Other ◽  
Objective Functions ◽  
Interaction Index ◽  
Functional Regions ◽  
Hierarchical Aggregation ◽  
Administrative Units

Abstract The use of different objective functions in hierarchical aggregation procedures is examined in this paper. Specifically, we analyse the use of the original Intramax objective function, the sum-of-flows objective function, the sum-of-proportions-to-intra-regional-flows objective function, Smart’s weighted interaction index, the first and second CURDS weighted interaction indices, and Tolbert and Killian’s interaction index. The results of the functional regionalisation have been evaluated by self-containment statistics, and they show that the use of the original Intramax procedure tends to delineate operationally the most persuasive and balanced regions that, regarding the intra-regional flows, homogeneously cover the analysed territory. The other objective functions give statistically better but operationally less suitable results. Functional regions modelled using the original Intramax procedure were compared to the regions at NUTS 2 and NUTS 3 levels, as well as to administrative units in Slovenia. We conclude that there are some promising directions for further research on functional regionalisation using hierarchical aggregation procedures.

Development of a Stepped Calibration Approach for XAJ Hydrological Model

2013 ◽  
Vol 405-408 ◽  
pp. 2222-2225
Author(s):  
Qian Li ◽  
Wei Min Bao ◽  
Jing Lin Qian
Keyword(s):  
Root Mean Square Error ◽  
Objective Function ◽  
Traditional Method ◽  
Hydrological Model ◽  
Model Performance ◽  
Layer By Layer ◽  
Mean Square ◽  
Objective Functions ◽  
Single Objective ◽  
Calibration Approach

This paper discusses the conceptual stepped calibration approach (SCA) which has been developed for the Xinanjiang (XAJ) model. Multi-layer and multi-objective functions which can make optimization work simpler and more effective are introduced in this procedure. In all eight parameters were considered, they were divided into four layers according to the structure of XAJ model, and then calibrated layer by layer. The SCA procedure tends to improve the performance of the traditional method of calibration (thus, using a single objective function, such as root mean square error RMSE). The compared results demonstrate that the SCA yield better model performance than RMSE.

scholarly journals Lane-deviation penalty formulation and analysis for autonomous vehicle avoidance maneuvers

2021 ◽  
pp. 095440702110079
Author(s):  
Pavel Anistratov ◽  
Björn Olofsson ◽  
Lars Nielsen
Keyword(s):  
Objective Function ◽  
Traffic Safety ◽  
Autonomous Vehicles ◽  
Autonomous Vehicle ◽  
Emergency Situation ◽  
Change Scenario ◽  
Initial Speed ◽  
Objective Functions ◽  
Double Lane Change ◽  
Tire Friction

Autonomous vehicles hold promise for increased vehicle and traffic safety, and there are several developments in the field where one example is an avoidance maneuver. There it is dangerous for the vehicle to be in the opposing lane, but it is safe to drive in the original lane again after the obstacle. To capture this basic observation, a lane-deviation penalty (LDP) objective function is devised. Based on this objective function, a formulation is developed utilizing optimal all-wheel braking and steering at the limit of road–tire friction. This method is evaluated for a double lane-change scenario by computing the resulting behavior for several interesting cases, where parameters of the emergency situation such as the initial speed of the vehicle and the size and placement of the obstacle are varied, and it performs well. A comparison with maneuvers obtained by minimum-time and other lateral-penalty objective functions shows that the use of the considered penalty function decreases the time that the vehicle spends in the opposing lane.

A new representation for a robot grasping quality measure

Robotica ◽  
1995 ◽  
Vol 13 (3) ◽  
pp. 287-295 ◽  
Author(s):  
Venugopal K. Varma ◽  
Uri Tasch
Keyword(s):  
Objective Function ◽  
Material Properties ◽  
Graphical Representation ◽  
Contact Forces ◽  
Geometric Constraints ◽  
Objective Functions ◽  
Finger Force ◽  
Finger Forces ◽  
Robot Grasping ◽  
Selection Of

SummaryWhen an object is held by a multi-fingered hand, the values of the contact forces can be multivalued. An objective function, when used in conjunction with the frictional and geometric constraints of the grasp, can however, give a unique set of finger force values. The selection of the objective function in determining the finger forces is dependent on the type of grasp required, the material properties of the object, and the limitations of the röbot fingers. In this paper several optimization functions are studied and their merits highlighted. The paper introduces a graphical representation of the finger force values and the objective functions that enable one to select and compare various grasping configurations. The impending motion of the object at different torque and finger force values are determined by observing the normalized coefficient of friction plots.

Cooperative Coevolution with Formula-Based Variable Grouping for Large-Scale Global Optimization

2018 ◽  
Vol 26 (4) ◽  
pp. 569-596 ◽  
Author(s):  
Yuping Wang ◽  
Haiyan Liu ◽  
Fei Wei ◽  
Tingting Zong ◽  
Xiaodong Li
Keyword(s):  
Global Optimization ◽  
Objective Function ◽  
Real World ◽  
Large Scale ◽  
Divide And Conquer ◽  
Group Method ◽  
Objective Functions ◽  
Elementary Functions ◽  
Cooperative Coevolution ◽  
Solution Quality

For a large-scale global optimization (LSGO) problem, divide-and-conquer is usually considered an effective strategy to decompose the problem into smaller subproblems, each of which can then be solved individually. Among these decomposition methods, variable grouping is shown to be promising in recent years. Existing variable grouping methods usually assume the problem to be black-box (i.e., assuming that an analytical model of the objective function is unknown), and they attempt to learn appropriate variable grouping that would allow for a better decomposition of the problem. In such cases, these variable grouping methods do not make a direct use of the formula of the objective function. However, it can be argued that many real-world problems are white-box problems, that is, the formulas of objective functions are often known a priori. These formulas of the objective functions provide rich information which can then be used to design an effective variable group method. In this article, a formula-based grouping strategy (FBG) for white-box problems is first proposed. It groups variables directly via the formula of an objective function which usually consists of a finite number of operations (i.e., four arithmetic operations “[Formula: see text]”, “[Formula: see text]”, “[Formula: see text]”, “[Formula: see text]” and composite operations of basic elementary functions). In FBG, the operations are classified into two classes: one resulting in nonseparable variables, and the other resulting in separable variables. In FBG, variables can be automatically grouped into a suitable number of non-interacting subcomponents, with variables in each subcomponent being interdependent. FBG can easily be applied to any white-box problem and can be integrated into a cooperative coevolution framework. Based on FBG, a novel cooperative coevolution algorithm with formula-based variable grouping (so-called CCF) is proposed in this article for decomposing a large-scale white-box problem into several smaller subproblems and optimizing them respectively. To further enhance the efficiency of CCF, a new local search scheme is designed to improve the solution quality. To verify the efficiency of CCF, experiments are conducted on the standard LSGO benchmark suites of CEC'2008, CEC'2010, CEC'2013, and a real-world problem. Our results suggest that the performance of CCF is very competitive when compared with those of the state-of-the-art LSGO algorithms.

scholarly journals An evolutionary-based optimization algorithm for truss sizing design

2016 ◽  
Vol 38 (4) ◽  
pp. 307-317
Author(s):  
Pham Hoang Anh
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
The Other ◽  
Truss Structures ◽  
Benchmark Problems ◽  
Discrete Variables ◽  
Objective Functions

In this paper, the optimal sizing of truss structures is solved using a novel evolutionary-based optimization algorithm. The efficiency of the proposed method lies in the combination of global search and local search, in which the global move is applied for a set of random solutions whereas the local move is performed on the other solutions in the search population. Three truss sizing benchmark problems with discrete variables are used to examine the performance of the proposed algorithm. Objective functions of the optimization problems are minimum weights of the whole truss structures and constraints are stress in members and displacement at nodes. Here, the constraints and objective function are treated separately so that both function and constraint evaluations can be saved. The results show that the new algorithm can find optimal solution effectively and it is competitive with some recent metaheuristic algorithms in terms of number of structural analyses required.

scholarly journals Performance of Static Iot Networks using RPL Objective Functions

2019 ◽  
Vol 8 (4) ◽  
pp. 8972-8977 ◽  
Keyword(s):  
Objective Function ◽  
Routing Protocol ◽  
Routing Algorithms ◽  
Transmission Protocol ◽  
Objective Functions ◽  
Lossy Networks ◽  
Hop Count ◽  
Efficient Data ◽  
Selection Of ◽  
Better Than

Internet of Things, abbreviated as IoT is a network used mainly for the communication where different devices are connected for the retrieval, examination and execution of the necessary task. One of IoT’s biggest challenge is that, they are resource-constrained. Hence, it is essential to use an efficient data transmission protocol for routing. An effective routing protocol for static IoT network is the Routing protocol for Low Power and Lossy Networks (RPL). It is essential to assess the effectiveness of the RPL with the selection of best objective function for different static model. In this paper, the performance of different routing algorithms is compared in connection with different static topologies. Hence, the objective function’s performance is compared for different topologies i.e., Butterfly, Ring and Umbrella topologies. We consider two objective functions: namely Minimum Rank with Hysteresis Objective Function (MRHOF) and Objective Function Zero (OF0). MRHOF considers Expected Transmission Count (ETX) as its metric and the metric considered under OF0 is hop count. It is observed that the objective function OF0 performs better than MRHOF for the metric of energy and successful receiving of data.

Alignment for Advanced Machine Learning Systems

2020 ◽  
pp. 342-382
Author(s):  
Jessica Taylor ◽  
Eliezer Yudkowsky ◽  
Patrick LaVictoire ◽  
Andrew Critch
Keyword(s):  
Machine Learning ◽  
Side Effects ◽  
Objective Function ◽  
Unintended Consequences ◽  
Learning Systems ◽  
Large Impact ◽  
Future Research ◽  
Objective Functions ◽  
Research Areas ◽  
The Right

This chapter surveys eight research areas organized around one question: As learning systems become increasingly intelligent and autonomous, what design principles can best ensure that their behavior is aligned with the interests of the operators? The chapter focuses on two major technical obstacles to AI alignment: the challenge of specifying the right kind of objective functions and the challenge of designing AI systems that avoid unintended consequences and undesirable behavior even in cases where the objective function does not line up perfectly with the intentions of the designers. The questions surveyed include the following: How can we train reinforcement learners to take actions that are more amenable to meaningful assessment by intelligent overseers? What kinds of objective functions incentivize a system to “not have an overly large impact” or “not have many side effects”? The chapter discusses these questions, related work, and potential directions for future research, with the goal of highlighting relevant research topics in machine learning that appear tractable today.

scholarly journals Evaluation Method of Multiobjective Functions’ Combination and Its Application in Hydrological Model Evaluation

2020 ◽  
Vol 2020 ◽  
pp. 1-23 ◽  
Author(s):  
Jiuyuan Huo ◽  
Liqun Liu
Keyword(s):  
Objective Function ◽  
Parameter Optimization ◽  
Optimization Problem ◽  
Hydrological Model ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Hydrological Forecasting ◽  
Model Parameter Optimization

Parameter optimization of a hydrological model is intrinsically a high dimensional, nonlinear, multivariable, combinatorial optimization problem which involves a set of different objectives. Currently, the assessment of optimization results for the hydrological model is usually made through calculations and comparisons of objective function values of simulated and observed variables. Thus, the proper selection of objective functions’ combination for model parameter optimization has an important impact on the hydrological forecasting. There exist various objective functions, and how to analyze and evaluate the objective function combinations for selecting the optimal parameters has not been studied in depth. Therefore, to select the proper objective function combination which can balance the trade-off among various design objectives and achieve the overall best benefit, a simple and convenient framework for the comparison of the influence of different objective function combinations on the optimization results is urgently needed. In this paper, various objective functions related to parameters optimization of hydrological models were collected from the literature and constructed to nine combinations. Then, a selection and evaluation framework of objective functions is proposed for hydrological model parameter optimization, in which a multiobjective artificial bee colony algorithm named RMOABC is employed to optimize the hydrological model and obtain the Pareto optimal solutions. The parameter optimization problem of the Xinanjiang hydrological model was taken as the application case for long-term runoff prediction in the Heihe River basin. Finally, the technique for order preference by similarity to ideal solution (TOPSIS) based on the entropy theory is adapted to sort the Pareto optimal solutions to compare these combinations of objective functions and obtain the comprehensive optimal objective functions’ combination. The experiments results demonstrate that the combination 2 of objective functions can provide more comprehensive and reliable dominant options (i.e., parameter sets) for practical hydrological forecasting in the study area. The entropy-based method has been proved that it is effective to analyze and evaluate the performance of different combinations of objective functions and can provide more comprehensive and impersonal decision support for hydrological forecasting.

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