Pareto Optimality Theory Research Articles

Multi-sensor multi-objective optimization deployment on complex terrain based on Pareto optimal theory

Multiple optimization objectives are often taken into account during the process of sensor deployment. Aiming at the problem of multi-sensor deployment in complex environment, a novel multi-sensor deployment method based on the multi-objective intelligent search algorithm is proposed. First, the complex terrain is modeled by the multi-attribute grid technology to reduce the computational complexity, and a truncation probability sensing model is presented. Two strategies, the local mutation operation and parameter adaptive operation, are introduced to improve the optimization ability of quantum particle swarm optimization (QPSO) algorithm, and then an improved multi-objective intelligent search algorithm based on QPSO is put forward to get the Pareto optimal front. Then, considering the multi-objective deployment requirements, a novel multi-sensor deployment method based on the multi-objective optimization theory is built. Simulation results show that the proposed method can effectively deal with the problem of multi-sensor deployment and provide more deployment schemes at once. Compared with the traditional algorithms, the Pareto optimal fronts achieved by the improved multi-objective search algorithm perform better on both convergence time and solution diversity aspects.

Evolutionary Multi-Objective Cost and Privacy Driven Load Morphing in Smart Electricity Grid Partition

Utilization of digital connectivity tools is the driving force behind the transformation of the power distribution system into a smart grid. This paper places itself in the smart grid domain where consumers exploit digital connectivity to form partitions within the grid. Every partition, which is independent but connected to the grid, has a set of goals associated with the consumption of electric energy. In this work, we consider that each partition aims at morphing the initial anticipated partition consumption in order to concurrently minimize the cost of consumption and ensure the privacy of its consumers. These goals are formulated as two objectives functions, i.e., a single objective for each goal, and subsequently determining a multi-objective problem. The solution to the problem is sought via an evolutionary algorithm, and more specifically, the non-dominated sorting genetic algorithm-II (NSGA-II). NSGA-II is able to locate an optimal solution by utilizing the Pareto optimality theory. The proposed load morphing methodology is tested on a set of real-world smart meter data put together to comprise partitions of various numbers of consumers. Results demonstrate the efficiency of the proposed morphing methodology as a mechanism to attain low cost and privacy for the overall grid partition.

Noise-precision tradeoff in predicting combinations of mutations and drugs.

Many biological problems involve the response to multiple perturbations. Examples include response to combinations of many drugs, and the effects of combinations of many mutations. Such problems have an exponentially large space of combinations, which makes it infeasible to cover the entire space experimentally. To overcome this problem, several formulae that predict the effect of drug combinations or fitness landscape values have been proposed. These formulae use the effects of single perturbations and pairs of perturbations to predict triplets and higher order combinations. Interestingly, different formulae perform best on different datasets. Here we use Pareto optimality theory to quantitatively explain why no formula is optimal for all datasets, due to an inherent bias-variance (noise-precision) tradeoff. We calculate the Pareto front of log-linear formulae and find that the optimal formula depends on properties of the dataset: the typical interaction strength and the experimental noise. This study provides an approach to choose a suitable prediction formula for a given dataset, in order to best overcome the combinatorial explosion problem.

A multicriterial analysis of the efficiency of conservative information security systems

The paper addresses the task on a multicriterial analysis of the effectiveness of conservative information security systems whose structure and components do not change over a certain period of time. The principal scheme of such systems includes a protected object, vulnerabilities ‒ channels for attacks, threats, and protection tools. Based on the assumption about the independence of attacks and protection tools, we have developed a discrete probabilistic model of damage to a protected object. For a random variable of the amount of damage over a fixed period of time, we have derived a representation in the form of a sum of binomially-distributed random variables, dependent on the parameters for attacks and protection. We have described in a similar manner the random variables for economic losses, recovery time, as well as recovery costs, for which mathematical expectations and variances have been obtained in the analytical form. To ensure the high statistical confidence, it has been proposed to determine the risk indicators using a Cantelli’s inequality. On this basis, we have defined performance indicators for a protection system, which characterize the probability of protected object’s safety, residual losses, conditionally saved costs, survivability, and the cost of recovery. By using a Pareto optimality theory, we have devised a procedure for multi-criteria analysis and rational design of conservative systems of information protection. Verification has been carried out for the audio information protection systems. A Pareto frontier has been investigated according to the criteria of economic benefit and investment costs for 66 variants of protection. We have examined the influence of protection level on the Cantelli’s measure for conditional savings, as well as the contribution of various types of protection devices to it. The research results have confirmed the saturation law by Gordon-Loeb for the case when over-protection does not improve the effectiveness of protection systems.

Archetypes of human cognition defined by time preference for reward and their brain correlates: An evolutionary trade-off approach

Biological systems carry out multiple tasks in their lifetime, which, in the course of evolution, may lead to trade-offs. In fact phenotypes (different species, individuals within a species, circuits, bacteria, proteins, etc.) cannot be optimal at all tasks, and, according to Pareto optimality theory, lay into a well-defined geometrical distribution (polygons and/or polyhedrons) in the space of traits. The vertices of this distribution contain archetypes, namely phenotypes that are specialists at one of the tasks, whereas phenotypes toward the center of the geometrical distribution show average performance across tasks.We applied this theory to the variability of cognitive and behavioral scores measured in 1206 individuals from the Human Connectome Project. Among all possible combinations of pairs of traits, we found the best fit to Pareto optimality when individuals were plotted in the trait-space of time preferences for reward, evaluated with the Delay Discounting Task (DDT). The DDT measures subjects' preference in choosing either immediate smaller rewards or delayed larger rewards. Time preference for reward was described by a triangular distribution in which each of the three vertices included individuals who used a particular strategy to discount reward. These archetypes accounted for variability on many cognitive, personality, and socioeconomic status variables, as well as differences in brain structure and functional connectivity, with only a weak influence of genetics. In summary, time preference for reward reflects a core variable that biases human phenotypes via natural and cultural selection.

Coordinated pitch & torque control of large-scale wind turbine based on Pareto efficiency analysis

For the existing pitch and torque control of the wind turbine generator system (WTGS), further development on coordinated control is necessary to improve effectiveness for practical applications. In this paper, the WTGS is modeled as a coupling combination of two subsystems: the generator torque control subsystem and blade pitch control subsystem. Then, the pole positions in each control subsystem are adjusted coordinately to evaluate the controller participation and used as the objective of optimization. A two-level parameters-controllers coordinated optimization scheme is proposed and applied to optimize the controller coordination based on the Pareto optimization theory. Three solutions are obtained through optimization, which includes the optimal torque solution, optimal power solution, and satisfactory solution. Detailed comparisons evaluate the performance of the three selected solutions and provide the optimized controller coordination suggestions according to different requirements.

An Optimal Driving Strategy for the Ride Comfort Performance of Intelligent Vehicles on Uneven Roads

This paper proposes an optimal driving strategy to improve the ride comfort performance of intelligent vehicles, which is different from the general researches that focus on the driving safety. Firstly, based on the establishment of a 7-DOF vehicle model and a road excitation model, the relationship between vehicle velocity and the comfort index is analyzed and described by a non-monotonic polynomial. Then, a velocity control requirement considering driving performance and comfort performance is constructed and transformed into a multi-objective optimization problem. By using the Pareto optimization theory, a set of Pareto optimal solutions is obtained. Finally, to choose a velocity from the Pareto optimal set, a strategy considering the subjective and objective comfort indexes from ISO2631 is given. This strategy can be applied to the velocity planning of intelligent vehicles on uneven roads. The simulation results show that the proposed strategy is effective and feasible.

Research and application of ensemble forecasting based on a novel multi-objective optimization algorithm for wind-speed forecasting

Wind energy is rapidly emerging as an appealing energy option because it is both abundant and environmentally friendly. Because of the stochastic nature and intrinsic complexity of wind speed, precise and reliable wind-speed prediction is vital for wind-farm planning and the operational planning of power grids. To improve wind-speed forecasting accuracy or stability, many forecasting approaches have been proposed. However, these models usually only consider one criterion (accuracy or stability) and have limitations associated with using individual models. In this paper, an ensemble method optimized by a novel multi-objective optimization algorithm is introduced. With respect to ensemble weight coefficients, a bias-variance framework, which is formulated by a multi-objective optimization problem, is used to assess model accuracy and stability. A novel hybrid flower pollination with bat search algorithm is proposed to search for the optimal weight coefficients based on the previous step, while Pareto optimality theory provides the necessary conditions to identify an optimal solution. In addition, data decomposition and de-noising are also incorporated into the data pre-processing stage. To evaluate the forecasting ability of the proposed model, a case study of 12 wind-speed datasets from two wind farms in the eastern coastal areas of China was completed. The experimental results of this study indicate that the developed ensemble model is superior to other comparison models in terms of the high precision and stability of wind-speed prediction.

Bending of beams of arbitrary cross sections - optimal design by analytical formulae

The paper deals with the conceptual design of a beam under bending. The common problem of designing a beam in a state of pure bending is discussed in the framework of Pareto-optimality theory. The analytical formulation of the Pareto-optimal set is derived by using a procedure based on the reformulation of the Fritz John Pareto-optimality conditions. The shape of the cross section of the beam is defined by a number of design variables pertaining to the optimization process by means of efficiency factors. Such efficiency factors are able to describe the bending properties of any beam cross section and can be used to derive analytical formulae. Design performance is determined by the combination of cross section shape, material and process. Simple expressions for the Pareto-optimal set of a beam of arbitrary cross section shape under bending are derived. This expression can be used at the very early stage of the design to choose a possible cross section shape and material for the beam among optimal solutions.

The Mass-Longevity Triangle: Pareto Optimality and the Geometry of Life-History Trait Space.

When organisms need to perform multiple tasks they face a fundamental tradeoff: no phenotype can be optimal at all tasks. This situation was recently analyzed using Pareto optimality, showing that tradeoffs between tasks lead to phenotypes distributed on low dimensional polygons in trait space. The vertices of these polygons are archetypes—phenotypes optimal at a single task. This theory was applied to examples from animal morphology and gene expression. Here we ask whether Pareto optimality theory can apply to life history traits, which include longevity, fecundity and mass. To comprehensively explore the geometry of life history trait space, we analyze a dataset of life history traits of 2105 endothermic species. We find that, to a first approximation, life history traits fall on a triangle in log-mass log-longevity space. The vertices of the triangle suggest three archetypal strategies, exemplified by bats, shrews and whales, with specialists near the vertices and generalists in the middle of the triangle. To a second approximation, the data lies in a tetrahedron, whose extra vertex above the mass-longevity triangle suggests a fourth strategy related to carnivory. Each animal species can thus be placed in a coordinate system according to its distance from the archetypes, which may be useful for genome-scale comparative studies of mammalian aging and other biological aspects. We further demonstrate that Pareto optimality can explain a range of previous studies which found animal and plant phenotypes which lie in triangles in trait space. This study demonstrates the applicability of multi-objective optimization principles to understand life history traits and to infer archetypal strategies that suggest why some mammalian species live much longer than others of similar mass.

Evolutionary tradeoffs, Pareto optimality and the morphology of ammonite shells.

BackgroundOrganisms that need to perform multiple tasks face a fundamental tradeoff: no design can be optimal at all tasks at once. Recent theory based on Pareto optimality showed that such tradeoffs lead to a highly defined range of phenotypes, which lie in low-dimensional polyhedra in the space of traits. The vertices of these polyhedra are called archetypes- the phenotypes that are optimal at a single task. To rigorously test this theory requires measurements of thousands of species over hundreds of millions of years of evolution. Ammonoid fossil shells provide an excellent model system for this purpose. Ammonoids have a well-defined geometry that can be parameterized using three dimensionless features of their logarithmic-spiral-shaped shells. Their evolutionary history includes repeated mass extinctions.ResultsWe find that ammonoids fill out a pyramid in morphospace, suggesting five specific tasks - one for each vertex of the pyramid. After mass extinctions, surviving species evolve to refill essentially the same pyramid, suggesting that the tasks are unchanging. We infer putative tasks for each archetype, related to economy of shell material, rapid shell growth, hydrodynamics and compactness.ConclusionsThese results support Pareto optimality theory as an approach to study evolutionary tradeoffs, and demonstrate how this approach can be used to infer the putative tasks that may shape the natural selection of phenotypes.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-015-0149-z) contains supplementary material, which is available to authorized users.

Pareto-optimal clustering scheme using data aggregation for wireless sensor networks

The presence of cluster heads (CHs) in a clustered wireless sensor network (WSN) leads to improved data aggregation and enhanced network lifetime. Thus, the selection of appropriate CHs in WSNs is a challenging task, which needs to be addressed. A multicriterion decision-making approach for the selection of CHs is presented using Pareto-optimal theory and technique for order preference by similarity to ideal solution (TOPSIS) methods. CHs are selected using three criteria including energy, cluster density and distance from the sink. The overall network lifetime in this method with 50% data aggregation after simulations is 81% higher than that of distributed hierarchical agglomerative clustering in similar environment and with same set of parameters. Optimum number of clusters is estimated using TOPSIS technique and found to be 9–11 for effective energy usage in WSNs.

The Optimal Configuration of Feeder Switches in DAS Based on Pareto Optimality Solution

In urban radial networks, the feeder is often complex with a main line, branches and even sub-branches. It is necessary to optimize the configuration of automation switching devices in distribution automation system (DAS) to reduce the impact range of power outage and improve the power supply reliability. The interruption frequency and the space-time relationship among the switching devices were ignored in the most of researches. This paper presents a new reliability planning scheme of switching devices in DAS which involves three types of circuit breakers and three types of load switches. The model which target is to get the minimal cost, the lowest average annual interruption frequency and the least interruption duration is built thereby. The constraint is the availability rate of electricity supply of load node. Based on the Pareto optimality theory, the multi-objective differential evolution algorithm is adopted to solve the Pareto front efficiently. The proposed algorithm can provide many optional choices and the final scheme can be chosen based on the situation. Finally, a practical example is used to illustrate the developed scheme.

Stable families of coalitions for network resource allocation problems

A very common question appearing in resource management is: what is the optimal way of behaviour of the agents and distribution of limited resources. Is any form of cooperation more preferable strategy than pure competition? How cooperation can be treated in the game theoretic framework: just as one of a set of Pareto optimal solutions or cooperative game theory is a more promising approach? This research is based on results proving the existence of a non-empty K -core, that is, the set of allocations acceptable for the family K of all feasible coalitions, for the case when this family is a set of subtrees of a tree. A wide range of real situations in resource management, which include optimal water, gas and electricity allocation problems, can be modeled using this class of games. Thus, the present research is pursuing two goals: 1. optimality and 2. stability.Firstly, we suggest to players to unify their resources and then we optimize the total payoff using some standard LP technique. The same unification and optimization can be done for any coalition of players, not only for the total one. However, players may object unification of resources. It may happen when a feasible coalition can guarantee a better result for every coalitionist. Here we obtain some stability conditions which ensure that this cannot happen for some family K. Such families were characterized by Boros, Gurvich and Vasin [4] as Berge’s normal hypergraphs. Thus, we obtain a solution which is optimal and stable. From practical point of view, we suggest a distribution of profit that would cause no conflict between players.

Stable families of coalitions for network resource allocation problems

A very common question appearing in resource management is: what is the optimal way of behaviour of the agents and distribution of limited resources. Is any form of cooperation more preferable strategy than pure competition? How cooperation can be treated in the game theoretic framework: just as one of a set of Pareto optimal solutions or cooperative game theory is a more promising approach? This research is based on results proving the existence of a non-empty K -core, that is, the set of allocations acceptable for the family K of all feasible coalitions, for the case when this family is a set of subtrees of a tree. A wide range of real situations in resource management, which include optimal water, gas and electricity allocation problems, can be modeled using this class of games. Thus, the present research is pursuing two goals: 1. optimality and 2. stability.Firstly, we suggest to players to unify their resources and then we optimize the total payoff using some standard LP technique. The same unification and optimization can be done for any coalition of players, not only for the total one. However, players may object unification of resources. It may happen when a feasible coalition can guarantee a better result for every coalitionist. Here we obtain some stability conditions which ensure that this cannot happen for some family K. Such families were characterized by Boros, Gurvich and Vasin [4] as Berge’s normal hypergraphs. Thus, we obtain a solution which is optimal and stable. From practical point of view, we suggest a distribution of profit that would cause no conflict between players.

A meshless Pareto-optimal method for topology optimization

Abstract A meshless Galerkin Pareto-optimal method is proposed for topology optimization of continuum structures in this paper. The compactly supported radial basis function (CSRBF) is used to create shape functions. The shape function is constructed by meshfree approximations based on a set of unstructured field nodes. Considering the Pareto-optimality theory, the initial single objective topology optimization problem is transformed into multi-objective problem. The optimum solution is traced via the Pareto-optimal frontier in a computationally effective manner. The optimal problem does not need to be solved directly. Finally, several examples are used to prove the validity and effectiveness of the proposed approach.

Pareto-Optimal Gamma Spectroscopic Radionuclide Identification Using Evolutionary Computing

Detection and identification of special nuclear materials (SNM) in measured gamma spectra is a challenge for nuclear security applications of spectroscopy. There are ongoing international efforts in industry, academia, and government to develop accurate, robust automated methods of gamma spectroscopic analysis to identify signature patterns characteristic of SNM. In this paper, we introduce a new approach for processing gamma-ray spectra measured by an NaI detector. The approach searches for radionuclide signature patterns in the measured spectrum by formulating a multiobjective optimization problem. Search in the multiobjective space is performed by an evolutionary algorithm, which identifies a solution in the context of Pareto Optimality Theory. The proposed approach is composed of two main steps: 1) signature selection, and 2) Pareto-optimal fitting. The output of the algorithm includes a list of all the identified radionuclides and their relative contributions to the gamma spectrum. The methodology is applied to a set of gamma spectra and compared to multiple linear regression fitting. Results demonstrate the superiority of the Pareto-optimal approach over multiple regression in the majority of the tested cases.

Reliability Programming of Distribution Network Feeder Switches Based on Pareto Optimality Theory

Reliability Programming of Distribution Network Feeder Switches Based on Pareto Optimality Theory

Long-Term Load Forecasting Based on a Time-Variant Ratio Multiobjective Optimization Fuzzy Time Series Model

Load forecasting problem is a complex nonlinear problem linked with economic and weather factors. Long-term load forecasting provides useful information for maintenance scheduling, adequacy assessment, and limited energy resources for electrical power systems. Fuzzy time series forecasting models can be used for long-term load forecasting. However, the interval length has been chosen arbitrarily in the implementations of known fuzzy time series forecasting models, which has an important impact on the performance of these models. In this paper, a time-variant ratio multiobjective optimization fuzzy time series model (TV-RMOP) is proposed, and its performance is tested on the prediction of enrollment at the University of Alabama. Results clearly promote the forecasting accuracy as compared to the conventional models. A genetic algorithm is used to search for the length of intervals based on the training data while Pareto optimality theory provides the necessary conditions to identify an optimal one. The TV-RMOP model is applied for the long-term load forecasting in Shanghai of China.

Evolutionary Multiobjective Optimization of Kernel-Based Very-Short-Term Load Forecasting

A useful tool for the efficient management of the electric power grid is the accurate, ahead-of-time prediction-of-load demand. A novel methodology for very-short-term load forecasting is introduced in this paper, and its performance is tested on a set of historical, demand-side, 5-min data. The approach employs an ensemble of kernel-based Gaussian processes (GPs) whose predictions constitute the terms of a linear model. Adoption of a set of cost functions assessing model accuracy allows the formulation of a multiobjective optimization problem with respect to model coefficients. A genetic algorithm (GA) is used to search for a solution based on the previous step data while Pareto optimality theory provides the necessary conditions to identify an optimal one. Thus, it is the optimized linear model that yields the final prediction over the designated time interval. The proposed methodology is examined on 5-min-interval predictions for 30-min-ahead horizon. It is compared with support vector regression (SVR) and autoregressive moving average (ARMA) models as well as the independent GP forecasters on a set of six cost functions. Results clearly promote the proposed forecasting method not only over individual GPs but also over SVR and ARMA.