Individual Objective Functions Research Articles

Multicriteria optimization of molecular force fields by Pareto approach

Molecular force fields are widely used for simulating thermodynamic properties of fluids. In developing such force fields, usually some of their parameters are adjusted to experimental data sets, which are often of different type. The adjustment is commonly carried out by minimizing a single objective function which represents the deviations between the model and the data. In the present work, a different approach is explored. Individual objective functions are defined for each data set and a multicriteria optimization task is solved. It is explicitly acknowledged that the different objectives are usually conflicting. The multicriteria optimization problem is solved by determining the Pareto set. By definition this set includes all solutions for which no further improvement in one objective can be achieved without having to accept a decline in at least one other objective and, hence, contains best compromises. The user can then choose out of these solutions one which is particularly suited for his application. The procedure is illustrated using the parameterization of the Lennard-Jones model for argon and methane as examples. Six different objective functions are included in the optimization. They represent the deviations between the model and the following properties at boiling conditions over a wide temperature range: (a) liquid density, (b) vapor pressure, (c) enthalpy of vaporization, (d) liquid shear viscosity, (e) liquid thermal conductivity, and (f) surface tension. First single objective fits are carried out for all properties. Then Pareto sets are determined for two triples of objectives namely, (a, b, c) on one side and (d, e, f) on the other side. An unexpected topology of the Pareto set is observed and explained. Then the full Pareto set for all six properties is determined and all results are compared. They show that good results can be achieved with the simple Lennard-Jones model for the two studied fluids, even when the goal is to simultaneously describe many different thermodynamic properties. The work also illustrates the benefits of using Pareto optimization for developing force fields, and, more generally thermodynamic models.

Finite-state model predictive control of NPC inverter using multi-criteria fuzzy decision-making

Summary In this paper, the multiple objectives optimization problem in a finite-state model predictive control (FS-MPC) is formulated using fuzzy multi-criteria decision-making. Conventionally, to optimize the multiple objectives in a FS-MPC, the aggregate objective function or a single cost function is constructed, which requires the weighting factor tuning to select the appropriate switching state. Determination of these weighting factors for a particular objective function is a complex and time-consuming task as no systematic procedure is available in literature. The main aim of this paper is to replace the time-consuming task of weighting factor tuning by a simple and systematic procedure, which relies on the relative importance of the individual objective functions. The relative importance of objective functions derived from the expert's knowledge and the desired control objectives is used for appropriate switching state selection. The method is validated with the help of simulation results of a neutral point clamped inverter for the multiple objectives viz. reference current tracking, capacitor voltage balance and switching frequency minimization. The result outcomes of the proposed methodology are compared with the conventional FS-MPC and space vector pulse width modulation based current control schemes. Copyright © 2014 John Wiley & Sons, Ltd.

Social Identity Strategies in Recent Economics

This paper reviews three distinct strategies in recent economics for using the concept of social identity in the explanation of individual behavior: Akerlof and Kranton's neoclassical approach, Sen's commitment approach, and Kirman et al.'s complexity approach. The primary focus is the multiple selves problem and the difficulties associated with failing to explain social identity and personal identity together. The argument of the paper is that too narrow a scope for reflexivity in individual decision-making renders the problem intractable, but that enlarging this scope makes it possible to explain personal and social identity together in connection with an individual behavior termed comparative value-objective evaluation. The paper concludes with recommendations for treating the individual objective function as a production function.

Game theoretic approach for fertilizer application: looking for the propensity to cooperate

This paper continues the research implemented in previous work of (Schreider et al. in Environ. Model. Assess. 15(4):223–238, 2010) where a game theoretic model for optimal fertilizer application in the Hopkins River catchment was formulated, implemented and solved for its optimal strategies. In that work, the authors considered farmers from this catchment as individual players whose objective is to maximize their objective functions which are constituted from two components: economic gain associated with the application of fertilizers which contain phosphorus to the soil and environmental harms associated with this application. The environmental losses are associated with the blue-green algae blooming of the coastal waterways due to phosphorus exported from upstream areas of the catchment. In the previous paper, all agents are considered as rational players and two types of equilibria were considered: fully non-cooperative Nash equilibrium and cooperative Pareto optimum solutions. Among the plethora of Pareto optima, the solution corresponding to the equally weighted individual objective functions were selected. In this paper, the cooperative game approach involving the formation of coalitions and modeling of characteristic value function will be applied and Shapley values for the players obtained. A significant contribution of this approach is the construction of a characteristic function which incorporates both the Nash and Pareto equilibria, showing that it is superadditive. It will be shown that this approach will allow each players to obtain payoffs which strictly dominate their payoffs obtained from their Nash equilibria.

Characterization of feedback Nash equilibria for multi-channel systems via a set of non-fragile stabilizing state-feedback solutions and dissipativity inequalities

We consider the problem of state-feedback stabilization for a multi-channel system in a game-theoretic framework, where the class of admissible strategies for the players is induced from a solution set of the individual objective functions that are associated with certain dissipativity properties of the system. In such a framework, we characterize the feedback Nash equilibria via a set of non-fragile stabilizing state-feedback solutions corresponding to a family of perturbed multi-channel systems. Moreover, we show that the existence of a weak-optimal solution to a set of constrained dissipativity problems is a sufficient condition for the existence of a feedback Nash equilibrium, whereas the set of non-fragile stabilizing state-feedbacks solutions is described in terms of a set of dilated linear matrix inequalities.

Hidden Insurance in a Moral Hazard Economy

We consider an economy where individuals privately choose effort and trade competitively priced securities that pay off with effort-determined probability. We show that if insurance against a negative shock is sufficiently incomplete, then standard functional form restrictions ensure that individual objective functions are optimized by an effort and insurance combination that is unique and satisfies first- and second-order conditions. Modeling insurance incompleteness in terms of costly production of private insurance services, we characterize the constrained inefficiency arising in general equilibrium from competitive pricing of nonexclusive financial contracts.

Multiobjective daily Volt/VAr control in distribution systems with distributed generation using binary ant colony optimization

This paper presents a multiobjective daily voltage and reactive power control (Volt/VAr) in radial distribution systems, including distributed generation units. The main purpose is to determine optimum dispatch schedules for on-load tap changer (OLTC) settings at substations, substation-switched capacitors, and feeder-switched capacitors based on the day-ahead load forecast. The objectives are selected to minimize the voltage deviation on the secondary bus of the main transformer, total electrical energy losses, the number of OLTCs, and capacitor operation and voltage fluctuations in distribution systems for the next day. Since this model is the weighted sum of individual objective functions, an analytic hierarchy process is adopted to determine the weights. In order to simplify the control actions for OLTC at substations, a time interval-based control strategy is used for decomposition of a daily load forecast into several sequential load levels. A binary ant colony optimization (BACO) method is used to solve the daily voltage and reactive control, which is a nonlinear mixed-integer problem. To illustrate the effectiveness of the proposed method, the Volt/VAr control is performed in IEEE 33-bus and 69-bus distribution systems and its performance is compared with the genetic, hybrid binary genetic, and particle swarm optimization algorithms. The simulation results verify that the BACO algorithm gives better performances than other algorithms.

Fuzzy Multi-Objective Optimization for Die Structures Design in Sheet Metal Forming

Abstract: Finite element analysis and fuzzy multi-objective optimization technique have been integrated to solve the die structure design of sheet metal forming by transforming fuzzy multi-objective problem into a normal optimization problem. A mathematical model of fuzzy optimization for bending die was established. A fuzzy goal set was constructed. The fuzziness of multi-objective functions and constraints were defined. The optimal solution and optimal constraint value of individual objective function in the feasible field were found using the genetic algorithms. An electronic part bending case shows that this approach is more effective and accurate than traditional finite element analysis method and the ‘trial and error’ procedure.

Rapid Sample Size Calculations for a Defined Likelihood Ratio Test-Based Power in Mixed-Effects Models

Efficient power calculation methods have previously been suggested for Wald test-based inference in mixed-effects models but the only available alternative for Likelihood ratio test-based hypothesis testing has been to perform computer-intensive multiple simulations and re-estimations. The proposed Monte Carlo Mapped Power (MCMP) method is based on the use of the difference in individual objective function values (ΔiOFV) derived from a large dataset simulated from a full model and subsequently re-estimated with the full and reduced models. The ΔiOFV is sampled and summed (∑ΔiOFVs) for each study at each sample size of interest to study, and the percentage of ∑ΔiOFVs greater than the significance criterion is taken as the power. The power versus sample size relationship established via the MCMP method was compared to traditional assessment of model-based power for six different pharmacokinetic and pharmacodynamic models and designs. In each case, 1,000 simulated datasets were analysed with the full and reduced models. There was concordance in power between the traditional and MCMP methods such that for 90% power, the difference in required sample size was in most investigated cases less than 10%. The MCMP method was able to provide relevant power information for a representative pharmacometric model at less than 1% of the run-time of an SSE. The suggested MCMP method provides a fast and accurate prediction of the power and sample size relationship.

A new class of distributed optimization algorithms: application to regression of distributed data

In a distributed optimization problem, the complete problem information is not available at a single location but is rather distributed among different agents in a multi-agent system. In the problems studied in the literature, each agent has an objective function and the network goal is to minimize the sum of the agents’ objective functions over a constraint set that is globally known. In this paper, we study a generalization of the above distributed optimization problem. In particular, the network objective is to minimize a function of the sum of the individual objective functions over the constraint set. The ‘outer’ function and the constraint set are known to all the agents. We discuss an algorithm and prove its convergence, and then discuss extensions to more general and complex distributed optimization problems. We provide a motivation for our algorithms through the example of distributed regression of distributed data.

Application of Multi Objective Fuzzy Linear Programming in Supply Production Planning Problem

The objective of this paper is to establish the usefulness of modified s-curve membership function in a limited supply production planning problem with continuous variables. In this respect, fuzzy parameters of linear programming are modeled by non-linear membership functions such as s-curve function. This paper begins with an introduction and construction of the modified s-curve membership function. A numerical real life example of supply production planning problem is then presented. The computational results show the usefulness of the modified s-curve membership function with fuzzy linear programming technique in optimising individual objective functions, compared to non-fuzzy linear programming approach. Futhermore, the optimal solution helps to conclude that by incorporating fuzziness in a linear programming model through the objective function and constraints, a better level of satisfactory solution will be provided in respect to vagueness, compared to non-fuzzy linear programming.

Clustering Parts Based on the Design and Manufacturing Similarities Using a Genetic Algorithm

The part family (PF) formation in a cellular manufacturing has been a key issue for the successful implementation of Group Technology (GT). Basically, a part has two different attributes; i.e., design and manufacturing. The respective similarity in both attributes is often conflicting each other. However, the two attributes should be taken into account appropriately in order for the PF to maximize the benefits of the GT implementation. This paper proposes a clustering algorithm which considers the two attributes simultaneously based on pareto optimal theory. The similarity in each attribute can be represented as two individual objective functions. Then, the resulting two objective functions are properly combined into a pareto fitness function which assigns a single fitness value to each solution based on the two objective functions. A GA is used to find the pareto optimal set of solutions based on the fitness function. A set of hypothetical parts are grouped using the proposed system. The results show that the proposed system is very promising in clustering with multiple objectives.

The Worst-Case Efficiency of Cost Sharing Methods in Resource Allocation Games

Resource allocation problems play a key role in many applications, including traffic networks, telecommunication networks, and economics. In most applications, the allocation of resources is determined by a finite number of independent players, each optimizing an individual objective function. An important question in all these applications is the degree of suboptimality caused by selfish resource allocation. We consider the worst-case efficiency of cost sharing methods in resource allocation games in terms of the ratio of the minimum guaranteed surplus of a Nash equilibrium and the maximal surplus. Our main technical result is an upper bound on the efficiency loss that depends on the class of allowable cost functions and the class of allowable cost sharing methods. We demonstrate the power of this bound by evaluating the worst-case efficiency loss for three well-known cost sharing methods: incremental cost sharing, marginal cost pricing, and average cost sharing.

Estimating crustal seismic anisotropy with a joint analysis of radial and transverse receiver function data

SUMMARY We developed an integrated technique for estimating crustal anisotropy with a horizontal axis using radial (R) and transverse (T) receiver functions. The technique includes computing three individual and one joint objective function (JOF) and a reliability analysis of the estimated anisotropy. The individual objective functions (IOFs) are designed to: (1) maximize the peak energy of the stacked R receiver function after a cosine moveout correction in the Ps arrival time; (2) to maximize the correlation of the radial receiver functions after a full correction of anisotropy or (3) to minimize the total energy of transverse receiver functions stacked after a removal of crustal anisotropy. The JOF was computed by a weighted average of the three IOFs, and the reliability analysis uses the principle that stacking coherent signals can lead to an increase of signal-to-noise ratio. We applied the technique to synthetic receiver functions generated with 30–60 per cent white noise from a variety of anisotropic and heterogeneous models. The synthetic tests indicate that the proposed technique has good capability to recover the input models. Despite the presence of random and other coherent noises, such as those caused by inhomogeneous structures, in the data, the technique can always provide accurate estimates of crustal anisotropy. We applied the technique to two permanent seismic stations in western China and found significant crustal anisotropy beneath one station located at the northern edge of the Tibetan plateau. The observed fast polarization direction at this station follows the direction of the maximum horizontal tensile stress, suggesting that the observed seismic anisotropy is likely caused by mineral alignment in the lower crust. The station situated in the Sichuan basin, on the other hand, shows little to no seismic anisotropy, which may suggest that the crust beneath the basin is nearly rigid with very little deformation. The developed technique can be applied to any broadband seismic stations that have a good backazimuthal coverage of teleseismic events.

Automated weighting joint inversion of geoelectric data over a two dimensional geologic structure

A new L2 norm joint inversion technique is presented and combined with the series expansion inversion method applied for different simulated erroneous Vertical Electric Sounding (VES) data sets over a complicated two dimensional structure. The applied joint inversion technique takes into consideration the complete form of the likelihood function. As a result there is no need to apply input weights to the individual objective functions. The model consists of three layers with homogeneous resistivities. The first layer boundary is a horizontal plane, the other is a two dimensional laterally varying surface. For the VES inversion the exact data sets were calculated by finite difference method, one in strike direction and the other in dip direction. These data sets were contaminated with normally distributed random errors. During inversion the second layer boundary function was determined. For comparison individual and joint inversion examples were calculated for the two data sets. The best model parameter estimate result was produced by the method of automated weighting.

ポテンシャルゲーム理論的姿勢協調―同期・平衡の達成

In this paper we consider potential game theoretic attitude coordination. We especially focus on two ordered configurations: “synchronization” and “balanced circular formation”. We first show that both problems constitute potential games by employing some global and individual objective functions, and a learning algorithm called Restrictive Spatial Adaptive Play (RSAP) leads robots to the ordered configurations with high probability even in the presence of mobility constraints. We moreover show that the problem also constitutes a group-based potential game and convergence of distribution of actions to stationary one can be accelerated. Finally, the effectiveness of the schemes is demonstrated by simulation.

Experiments on the Transient Performance of an Adaptive Multi-Objective Controller for Rotating Machinery

This paper describes an experimental assessment of the transient performance of a multi-objective adaptive approach to the control of flexible rotors. This is applicable to any arrangement of controllable bearings or actuators. In the case reported here, the rotor is supported by active magnetic bearings. The theory underlying the controller is outlined. The objectives include minimization of the forces transmitted to the base while restricting rotor vibrations to a user-defined limit. A third objective is to prevent rotor contact with the auxiliary bearings, which are used to protect the active elements. These objectives are met by a two-stage weighting strategy followed by the adaptive control of two parameters that automatically and continuously adjust the weightings of individual objective functions to satisfy user-defined performance criteria.

Fuzzy Approach Based Management Model for Irrigation Planning

The objective of this paper is to develop the irrigation planning model and to apply the same in the form of Multi Objective Fuzzy Linear Programming (MOFLP) approach for crop planning in command area of Jayakwadi Project Stage I, Maharashtra State, India. To formulate MOFLP model various Linear Programming (LP) models are developed to optimize the Net Benefits (NB), Crop/Yield Production (YP), Employment Generation (EG) and Manure Utilization (MU) for which the objective function and constraints are crisp in nature. From the results of these LP models the linear membership function for each individual objective function has been developed. Considering the decision makers satisfaction level (λ), all the four objectives are maximized simultaneously. The results of the MOFLP and LP are compared. The MOFLP model concentrates on satisfying four objectives simultaneously. The present model will be helpful for the decision maker to take decision under conflicting situation when planning for different objectives simultaneously. The degree of satisfaction λ, works out to be 0.58. Compromised solution provides Net Benefits 1503.73 Million Rupees, Crop Production 319563.50 Tons, Employment Generation/Labour Requirement 29.74 Million Man days and Manure Utilization 154506.50 Tons respectively.

Reference point method with importance weighted ordered partial achievements

The Reference Point Method (RPM) is a very convenient technique for interactive analysis of the multiple criteria optimization problems. The interactive analysis is navigated with the commonly accepted control parameters expressing reference levels for the individual objective functions. The partial achievement functions quantify the DM satisfaction from the individual outcomes with respect to the given reference levels, while the final scalarizing achievement function is built as the augmented max–min aggregation of the partial achievements. In order to avoid inconsistencies caused by the regularization, the max–min solution may be regularized by the Ordered Weighted Averages (OWA) with monotonic weights which combines all the partial achievements allocating the largest weight to the worst achievement, the second largest weight to the second worst achievement, and so on. Further, following the concept of the Weighted OWA (WOWA), the importance weighting of several achievements may be incorporated into the RPM. Such a WOWA RPM approach uses importance weights to affect achievement importance by rescaling accordingly its measure within the distribution of achievements rather than by straightforward rescaling of achievement values. The recent progress in optimization methods for ordered averages allows one to implement the WOWA RPM quite effectively as extension of the original constraints and criteria with simple linear inequalities. There is shown that the OWA and WOWA RPM models meet the crucial requirements with respect to the efficiency of generated solutions as well as the controllability of interactive analysis by the reference levels.

Ising model versus normal form game

The 2-spin Ising model in statistical mechanics and the 2×2 normal form game in game theory are compared. All configurations allowed by the second are recovered by the first when the only concern is about Nash equilibria. But it holds no longer when Pareto optimum considerations are introduced as in the prisoner’s dilemma. This gap can nevertheless be filled by adding a new coupling term to the Ising model, even if that term has up to now no physical meaning. An individual complete bilinear objective function is thus found to be sufficient to reproduce all possible configurations of a 2×2 game. Using this one-to-one mapping new perspectives for future research in both fields can be envisioned.