Combined Objective Function Research Articles

Parameter uncertainty and identifiability of a conceptual semi-distributed model to simulate hydrological processes in a small headwater catchment in Northwest China

Abstract Introduction Conceptual hydrological models are useful tools to support catchment water management. However, the identifiability of parameters and structural uncertainties in conceptual rainfall-runoff modeling prove to be a difficult task. Here, we aim to evaluate the performance of a conceptual semi-distributed rainfall-runoff model, HBV-light, with emphasis on parameter identifiability, uncertainty, and model structural validity. Results The results of a regional sensitivity analysis (RSA) show that most of the model parameters are highly sensitive when runoff signatures or combinations of different objective functions are used. Results based on the generalized likelihood uncertainty estimation (GLUE) method further show that most of the model parameters are well constrained, showing higher parameter identifiability and lower model uncertainty when runoff signatures or combined objective functions are used. Finally, the dynamic identifiability analysis (DYNIA) shows different types of parameter behavior and reveals that model parameters have a higher identifiability in periods where they play a crucial role in representing the predicted runoff. Conclusions The HBV-light model is generally able to simulate the runoff in the Pailugou catchment with an acceptable accuracy. Model parameter sensitivity is largely dependent upon the objective function used for the model evaluation in the sensitivity analysis. More frequent runoff observations would substantially increase the knowledge on the rainfall-runoff transformation in the catchment and, specifically, improve the distinction of fast surface-near runoff and interflow components in their contribution to the total catchment runoff. Our results highlight the importance of identifying the periods when intensive monitoring is critical for deriving parameter values of reduced uncertainty.

Optimization of Damper Top Mount Characteristics to Improve Vehicle Ride Comfort and Harshness

A novel optimization technique for optimizing the damper top mount characteristics to improve vehicle ride comfort and harshness is developed. The proposed optimization technique employs a new combined objective function based on ride comfort, harshness, and impact harshness evaluation. A detailed and accurate damper top mount mathematical model is implemented inside a validated quarter vehicle model to provide a realistic simulation environment for the optimization study. The ride comfort and harshness of the quarter vehicle are evaluated by analyzing the body acceleration in different frequency ranges. In addition, the top mount deformation is considered as a penalty factor for the system performance. The influence of the ride comfort and harshness weighting parameters of the proposed objective function on the optimal damper top mount characteristics is studied. The dynamic stiffness of the damper top mount is used to describe the optimum damper top mount characteristics for different optimization case studies. The proposed optimization routine is able to find the optimum characteristics of the damper top mount which improve the ride comfort and the harshness performances together.

Damage identification using combined transient power flow balance and acceleration matching technique

This paper presents a multiobjective optimization formulation to detect and quantify crack damage in beam structures at variable locations. It is implemented at the substructure level where the concept is to balance the instantaneous power flow by equating the input power to the dissipated power and the time rate of change of kinetic and strain energies and power transferred to adjacent substructures. This imbalance is reduced to zero to identify the structural parameters or damages. For improved results, the power balance method is combined with conventional acceleration matching method where the objective is to minimize the deviation between measured and estimated accelerations—no additional sensors are required to incorporate the extra power flow balance criteria. Numerical simulations are performed for a lumped mass system, a planar truss structure, and a cantilever beam of 20 elements with multiple damages to evaluate the accuracy of the proposed method. Effects of noise are also taken into account by contaminating the measured responses with 3%, 5%, and 10% Gaussian noise. The particle swarm optimization is used as the optimization algorithm, and normalized fitness functions are defined for both power flow and acceleration components with weighted aggregation multiobjective optimization technique. The effects of various weighting factors for the combined objective function are also studied. The results demonstrate that improvement in accuracy of damage detection is achieved by the combined method, when compared with previous acceleration only matching method as well as other methods. Copyright © 2013 John Wiley & Sons, Ltd.

A Performance Study of Real Coded Genetic Algorithm on Gear Design Optimization

he major problem that deals with practical engineers is the mechanical design and creativeness. Mechanical design can be defined as the choice of materials and geometry, which satisfies, specified functional requirements of that design. A good design has to minimize the most significant adverse result and to maximize the most significant desirable result. An evolutionary algorithm offers efficient ways of creating and comparing a new design solution in order to complete an optimal design. In this paper a type of Genetic Algorithm, Real Coded Genetic Algorithm (RCGA) is used to optimize the design of helical gear pair and a combined objective function with maximizes the Power, Efficiency and minimizes the overall Weight, Centre distance. The performance of the proposed algorithms is validated through LINGO Software and the comparative results are analyzed.

Particle swarm optimization of artificial-neural-network-based on-line trained speed controller for battery electric vehicle

Abstract The paper presents implementation of PSO (Particle Swarm Optimization) to ANN-based speed controller tuning. Selected learning parameters are optimized according to the control objective function. A battery electric vehicle is considered as a potential plant for an adaptive speed controller. The need for adaptivity in the control algorithm is justified by variations of a total weight of the vehicle. A sizable section of the paper deals with selection of a combined objective function able to effectively evaluate the quality of a solution.

Effective Minimization of Ill-conditioned Functions

The problem of minimization of ill-conditioned functions is considered. These functions are motivated by the limit analysis problem for dielectrics in powerful electric fields. From computing point of view a minimization of these functions is not following by standard methods because they are nonsmooth. Distinct ravine of objective function in combination with a high dimension variables requires a smooth regularisation of finite-dimensional problem. Convergence of heave-ball method in relation to it's internal parameters and optimization parameters are studied in numerical computing environment and fourth-generation programming language Matlab.

Integrated Watershed Management with Multiobjective Land-Use Optimizations under Uncertainty

Integrated watershed management plays an important role in the environment and ecosystem. This paper analyzes multiobjective optimizations of agricultural land-use management problems with uncertainty involved. For each trial land-use scenario, multiple objective functions are constructed based on coupled simulation of the AnnAGNPS watershed model and the CCHE1D channel network model. To account for parameter uncertainties and uncertainties in numerical model results, the combined objective function is calculated using a fuzzy logic system based on interval computations to obtain a membership function, which yields not only a crisp value but also a range of variations. The proposed approach is tested with a land-use management study for the Goodwin Creek Experimental Watershed in northern Mississippi. The results show that it is a convenient way to introduce uncertainty-related considerations into an optimization framework, and it can incorporate various model parameters that are difficult or impossible for other uncertainty analysis techniques to consider. More importantly, this approach allows for the development of a complex system of estimating the responses between management goals and miscellaneous environmental factors under uncertainty.

Constraining saturated hydraulic transmissivity values by means of maximum saturated area mapping and maximum subsurface discharge: long‐term simulation in the Amazon basin

AbstractAlthough saturated hydraulic conductivity (K0) and saturated hydraulic transmissivity (T0) are physically based parameters, quite often, their calibrated values lie out of the physically based range, driving modellers to increased K0 values in some orders of magnitude, from field measured values, in order to fit observed discharge data. Therefore, calibration is a necessary process in hydrological modelling. Within a hydrological model, K0 or T0 plays an important role. They allow the model to represent the hydrograph separation through estimates of subsurface discharges. Simulating different flow components in hydrological modelling is an increasing need for basin management and water quality predictions. The present study has the objective to develop two criteria to constrain T0 values using a TOPMODEL multi‐velocity approach in order to represent the hydrograph separation in a more realistic way. The method was (i) applied to three sub‐basins in the Amazon basin (the Óbidos, the Humaita and Santo Antônio basins), (ii) evaluated by means of a combined objective function and uncertainty bounds and (iii) validated in a long‐term simulation. Because the constraint criteria were applied, it has verified a significant reduction in subsurface uncertainty for all the basins. The constraint criteria reduced the number of simulations to 11%, 42% and 23% for the Óbidos basin, the Humaita basin and the Santo Antônio basin, respectively. This means that a large number of simulations were rejected in the sense they represented unrealistic hydrograph separation. Copyright © 2012 John Wiley & Sons, Ltd.

Hierarchical Deployment Optimization for Wireless Sensor Networks

Sensor nodes deployment is very crucial for wireless sensor networks (WSNs). Current methods are apt to enlarge the coverage by achieving a nearly even deployment with similar density in the whole network. However, in some specific applications, the even distribution may not satisfy the sensing requirements. This paper proposes a virtual force directed coevolutionary particle swarm optimization (VFCPSO) algorithm, which uses a combined objective function to achieve the tradeoff of coverage and energy consumption. By considering deployment as an optimization problem, VFCPSO is more reliable and flexible for WSNs, since it can satisfy the combined requirements instead of only enlarging coverage. For investigating the performance of different paradigms, centralized VFCPSO is extended to distributed VFCPSO, heterogeneous hierarchical VFCPSO and homogeneous hierarchical VFCPSO (Homo-H-VFCPSO), and the solution of preferential deployment in interested region is also analyzed. Simulation results show that the Homo-H-VFCPSO has the best performance, i.e., it is more efficient than other three VFCPSO algorithms and the VF-style algorithms in terms of computation time, coverage and efficient moving energy consumption. It is obvious that the Homo-H-VFCPSO has good global searching ability and scalability, and it can rapidly and effectively achieve the sensor nodes deployment in WSNs.

Design optimisation of bevel gear pair

In this paper, an attempt has been made to optimise bevel gear pair design using a non-linear programming optimising software LINGO and meta-heuristics such as real coded genetic algorithm, ant colony optimisation and particle swarm optimisation algorithms. A combined objective function which maximises the power, efficiency and minimises the overall weight, centre distance has been considered in this model. The efficiency of the proposed algorithms is validated through gear design problems and the comparative results are studied.

Parametric spectrum estimation of flight vehicle vibration time series based on TVARMA model

To solve the problem of spectral deviation for Time-Varied Auto-Regressive Moving Average (TVARMA) parametric spectrum estimation, a TVARMA parameter estimation method based on Genetic Algorithm (GA) and combined objective function was proposed and then used for estimating the spectrum of flight vibration time series. Firstly, an initial estimation of the model parameters was acquired by the long time-varied auto-regressive and augmented Least-Square (LS) method; secondly, through extremum condition of continuous function, a constraint equation of model parameters was derived and a combined objective function was constructed based on the punishment function idea; lastly, the GA was used to optimize the initial parameters and the optimum parameters were the ones that made the combined objective function be the least. The experimental results demonstrate that the new method can overcome the spectrum deviation and improve the model precision both in time domain and frequency domain.

Multi-period multi-objective electricity generation expansion planning problem with Monte-Carlo simulation

A new approach to the electricity generation expansion problem is proposed to minimize simultaneously multiple objectives, such as cost and air emissions, including CO 2 and NO x , over a long term planning horizon. In this problem, system expansion decisions are made to select the type of power generation, such as coal, nuclear, wind, etc., where the new generation asset should be located, and at which time period expansion should take place. We are able to find a Pareto front for the multi-objective generation expansion planning problem that explicitly considers availability of the system components over the planning horizon and operational dispatching decisions. Monte-Carlo simulation is used to generate numerous scenarios based on the component availabilities and anticipated demand for energy. The problem is then formulated as a mixed integer linear program, and optimal solutions are found based on the simulated scenarios with a combined objective function considering the multiple problem objectives. The different objectives are combined using dimensionless weights and a Pareto front can be determined by varying these weights. The mathematical model is demonstrated on an example problem with interesting results indicating how expansion decisions vary depending on whether minimizing cost or minimizing greenhouse gas emissions or pollutants is given higher priority.

Technical note: allocation of optimal tolerances in a mechanical assembly using DE and NSGA-II

This paper discusses a general methodology based on evolutionary algorithms (Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and Differential Evolution (DE)) for allocation of optimal tolerance for an over-running clutch assembly. New hybrid models are developed for obtaining the manufacturing costs of hub, rollers and cage. The aim of this paper is to find optimal tolerances values that give minimum combined objective function value, minimum Manufacturing Cost (MC), minimum Quality Loss (QL) function and maximum Number of Standard Deviations (ZNSD) by satisfying stack-up conditions using non-traditional optimisation techniques. The results obtained from various techniques are compared and analysed.

Earliness—tardiness scheduling on uniform parallel machines using simulated annealing and fuzzy logic approach

Just-in-time production philosophy has led to the growing interest in scheduling problems considering both earliness and tardiness penalties. This research work considers the uniform parallel machine earliness—tardiness non-common due date sequence-dependent set-up time scheduling problem (UPETNDDSP) for jobs with varying processing times, where the objective is to minimize the sum of the absolute deviations of job completion times from their corresponding due dates. A simulated annealing (SA) —fuzzy logic approach has been proposed to select the optimal weighted earliness—tardiness combinations in a non-identical parallel machine environment. The SA algorithm identifies the best sequences for the different weighted combinations of earliness and tardiness measures for each given set of jobs. Fuzzy logic is then used to select the optimal weighted combination, which satisfies the combined objective function to a larger extent. The performance of the combined objective function and individual objective measure obtained by the proposed SA—fuzzy technique has been compared with the solutions yielded by the genetic algorithm technique known as the genetic algorithm with partially mapped cross-over operator (GA-PMX) and with those of the results reported in literature. The comparison shows that the proposed SA—fuzzy technique outperforms the existing available techniques.

Non-identical parallel-machine scheduling using genetic algorithm and fuzzy logic approach

Manufacturing industries frequently face the problem of reducing earliness and tardiness penalties, owing to the emerging concept of the just-in-time production philosophy. The problem studied in this work is the Non-identical Parallel-machine?Earliness-Tardiness Non-common Due Date?Sequence-dependent Set-up Time Scheduling Problem (NPETNDDSP) for jobs with varying processing times, where the objective is to minimise the sum of the absolute deviations of job completion times from their corresponding due dates for the different weighted earliness and tardiness combinations. A Genetic Algorithm-Fuzzy Logic Approach (GA-Fuzzy) has been proposed to select the optimal weighted earliness-tardiness combinations in a non-identical parallel-machine environment. The performance of the combined objective function obtained by the proposed GA-Fuzzy technique has been compared with the solutions yielded by the Genetic Algorithm (GA) techniques available in literature, known as GA with Partially Mapped Crossover Operator (GA-PMX) and GA with Multi-Component Uniform Order-based Crossover Generator (GA-MCUOX). The comparison shows that the proposed GA-Fuzzy technique outperforms both the GA-PMX and GA-MCUOX.

Evolutionary collision-free optimal trajectory planning for intelligent robots

This paper presents optimization procedures based on evolutionary algorithms such as the elitist non-dominated sorting genetic algorithm (NSGA-II) and differential evolution (DE) for solving the trajectory planning problem of intelligent robot manipulators with the prevalence of fixed, moving, and oscillating obstacles. The aim is the minimization of a combined objective function, with the constraints being actuator constraints, joint limits, and the obstacle avoidance constraint by considering dynamic equations of motion. Trajectories are defined by B-spline functions. This is a non-linear constrained optimization problem with six objective functions, 31 constraints, and 42 variables. The combined objective function is a weighted balance of transfer time, the mean average of actuator efforts and power, penalty for collision-free motion, singularity avoidance, joint jerks, and joint accelerations. The obstacles are present in the workspace of the robot. The distance between potentially colliding parts is expressed as obstacle avoidance. Further, the motion is represented using translational and rotational matrices. The proposed optimization techniques are explained by applying them to an industrial robot (PUMA 560 robot). Also, the results obtained from NSGA-II and DE are compared and analyzed. This is the first research work which considers all the decision criteria for the trajectory planning of industrial robots with obstacle avoidance. A comprehensive user-friendly general-purpose software package has been developed using VC++ to obtain the optimal solutions using the proposed DE algorithm.

Decision-making based on approximate and smoothed Pareto curves

We consider bicriteria optimization problems and investigate the relationship between two standard approaches to solving them: (i) computing the Pareto curve and (ii) the so-called decision maker’s approach in which both criteria are combined into a single (usually nonlinear) objective function. Previous work by Papadimitriou and Yannakakis showed how to efficiently approximate the Pareto curve for problems like Shortest Path, Spanning Tree, and Perfect Matching. We wish to determine for which classes of combined objective functions the approximate Pareto curve also yields an approximate solution to the decision maker’s problem. We show that an FPTAS for the Pareto curve also gives an FPTAS for the decision-maker’s problem if the combined objective function is growth bounded like a quasi-polynomial function. If the objective function, however, shows exponential growth then the decision-maker’s problem is NP-hard to approximate within any polynomial factor. In order to bypass these limitations of approximate decision making, we turn our attention to Pareto curves in the probabilistic framework of smoothed analysis. We show that in a smoothed model, we can efficiently generate the (complete and exact) Pareto curve with a small failure probability if there exists an algorithm for generating the Pareto curve whose worst-case running time is pseudopolynomial. This way, we can solve the decision-maker’s problem w.r.t. any non-decreasing objective function for randomly perturbed instances of, e.g. Shortest Path, Spanning Tree, and Perfect Matching.

Optimisation Method for Solar Heating Systems in Combination with Pellet Boilers/Stoves

In this study, an optimisation method for the design of combined solar and pellet heating systems is presented and evaluated. The paper describes the steps of the method by applying it to an example system. The objective of the optimisation was to find the design parameters that give the lowest auxiliary energy (pellet fuel + auxiliary electricity) and carbon monoxide (CO) emissions for a system with a typical load: a single family house in Sweden. Weighting factors have been used for the auxiliary energy use and CO emissions to give a combined objective function. Different weighting factors were tested. The results show that extreme weighting factors lead to their own minima. However, it was possible to find factors that ensure low values for both auxiliary energy and CO emissions, and suitable weighting factors are suggested.

Simultaneous scheduling of parts and automated guided vehicles in an FMS environment using adaptive genetic algorithm

Automated Guided Vehicles (AGVs) are among various advanced material handling techniques that are finding increasing applications today. They can be interfaced to various other production and storage equipment and controlled through an intelligent computer control system. Both the scheduling of operations on machine centers as well as the scheduling of AGVs are essential factors contributing to the efficiency of the overall flexible manufacturing system (FMS). An increase in the performance of the FMS under consideration would be expected as a result of making the scheduling of AGVs an integral part of the overall scheduling activity. In this paper, simultaneous scheduling of parts and AGVs is done for a particular type of FMS environment by using a non-traditional optimization technique called the adaptive genetic algorithm (AGA). The problem considered here is a large variety problem (16 machines and 43 parts) and combined objective function (minimizing penalty cost and minimizing machine idle time). If the parts and AGVs are properly scheduled, then the idle time of the machining center can be minimized; as such, their utilization can be maximized. Minimizing the penalty cost for not meeting the delivery date is also considered in this work. Two contradictory objectives are to be achieved simultaneously by scheduling parts and AGVs using the adaptive genetic algorithm. The results are compared to those obtained by conventional genetic algorithm.

A Bayesian integrated population dynamics model to analyze data for protected species

Managing wildlife-human interactions demands reliable information about the likely consequences of management actions. This requirement is a general one, whatever the taxonomic group. We describe a method for estimating population dynamics and decision analysis that is generally applicable, extremely flexible, uses data efficiently, and gives answers in a useful format. Our case study involves bycatch of a protected species, the Northeastern Offshore Spotted Dolphin (Stenella attenuata), in the tuna fishery of the eastern Pacific Ocean. Informed decision-making requires quantitative analyses taking all relevant information into account, assessing how bycatch affects these species and how regulations affect the fisheries, and describing the uncertainty in analyses. Bayesian analysis is an ideal framework for delivering information on uncertainty to the decision-making process. It also allows information from other populations or species or expert judgment to be included in the analysis, if appropriate. Integrated analysis attempts to include all relevant data for a population into one analysis by combining analyses, sharing parameters, and simultaneously estimating all parameters, using a combined objective function. It ensures that model assumptions and parameter estimates are consistent throughout the analysis, that uncertainty is propagated through the analysis, and that the correlations among parameters are preserved. Perhaps the most important aspect of integrated analysis is the way it both enables and forces consideration of the system as a whole, so that inconsistencies can be observed and resolved.