Additional Objective Function Research Articles

Is Multiobjective Optimization Ready for Water Resources Practitioners? Utility’s Drought Policy Investigation

Is Multiobjective Optimization Ready for Water Resources Practitioners? Utility’s Drought Policy Investigation

ИнформационнаЯ технологиЯ управлениЯ качествоМ процессА разработкИ прОграммнОгО обеспечениЯ

В работе рассмотрена реализация моделей и алгоритмов, используемых при разработке плана программы усовершенствования процесса разработки программного обеспечения. Описана информационная технология, приведена диаграмма размещения для системы поддержки принятия решений, а также результаты исследований

Ant colony optimisation for the bi-objective due-date-setting problem in the multi-class make-to-order firm

In this study, we develop a bi-objective programming approach for due-date setting in make-to-order manufacturing with different classes of customers. We formulate the problem of quoting due-dates under the assumption that demand is dependent on lead-time and price is determined by the length of the delivery time. In addition, other parameters such as production policy, inventory holding, delivery system and capacity utilisation should be considered in due-date decisions. To this purpose, we consider additional objective function in traditional due-date management problem. So, the proposed bi-objective model attempts to maximise total profit and minimise rates of changes in capacity utilisation simultaneously. To obtain a set of Pareto solutions efficiently, we propose an algorithm based on multi-objective ant colony optimisation. The proposed algorithm is compared with a noticeable multi-objective genetic algorithm, i.e. SPEA, based on some comparison metrics with random instances.

Multi-objective Short-term Hydrothermal Generation Scheduling Using Predator–Prey Optimization

In this article, a predator–prey-based optimization technique is applied to obtain the scheduling of a hydrothermal system with cascaded reservoirs, minimizing economic and gaseous pollutants and emission objectives. These objectives are mutually conflicting and are equally important. Predator–prey optimization is a stochastic optimization technique based on the particle swarm optimization concept having an additional predator effect that helps to explore the search area more efficiently due to the fear created by the predator. A heuristic search technique is applied for generating an initial feasible solution. The direct substitution method is implemented to handle the equality constraints, whereby dependent variables are determined from the equality constraint. Inequality constraints of dependent variables are taken care by incorporating an additional objective function represented by the fuzzy membership index, and other variables are set to their limits on violation. Fuzzy methodology has been exploited for solving a decision-making problem involving the multiplicity of objectives and selection criterion for the best compromised solution. The solutions obtained from the proposed technique are compared with other existing techniques, and results are found to be satisfactory. The proposed method has the capability to escape from local optimum solutions due to its predator effect, and it is easy to implement.

Coupling of the evolution strategy algorithm and genetic algorithm with finite element mesh adaptation

PurposeThe purpose of this paper is to find a more performing and automated procedure for linking an identification algorithm implemented in a general‐purpose environment with a commercial finite‐element code for magnetic field analysis. In particular, the use of a multiprocessor computer makes it possible to perform parallel computations keeping the calculation time reasonably low.Design/methodology/approachThe method is applied to identify the B‐H curve of anisotropic magnetic laminations in the direction normal to the sheet surface. In total, three different optimization methods have been applied. First an evolution strategy algorithm for solving the identification problem was used; then genetic algorithm (GA) was applied. The results obtained using different methods were compared and discussed. The computation time is reduced by adjusting the refinement of the FEM mesh.FindingsThe key point has been the use of a derivative‐free and global‐search oriented algorithm. Even if a starting point far from the solution is chosen, a suitably large initial value of the search radius makes the convergence possible. The effect of the historical parameter of the minimization algorithm on convergence has also been investigated.Originality/valueThe main new idea presented in this paper is equipping a GA‐based identification procedure with an additional objective function describing the sensitivity of the flux density against a small perturbation in parameters. This approach gives a multiple objective problem which introduces possibility of choosing a compromise solution among many optimal solutions instead of only one, as in classical GA optimization algorithm. The paper is mainly addressed to readers interested in the efficient use of GA‐based identification.

Global tolerances in the problems of combinatorial optimization with an additive objective function

It is known that by means of minimal values of tolerances one can obtain necessary and sufficient conditions for the uniqueness of the optimal solution of a combinatorial optimization problem (COP) with an additive objective function and the set of nonembedded feasible solutions. Moreover, the notion of a tolerance is defined locally, i.e., with respect to a chosen optimal solution. In this paper we introduce the notion of a global tolerance with respect to the whole set of optimal solutions and prove that the nonembeddedness assumption on the set of feasible solutions of the COP can be relaxed, which generalizes the well known relations for the extremal values of the tolerances. In particular, we formulate a new criterion for the uniqueness of the optimal solution of the COP with an additive objective function, which is based on certain equalities between locally and globally defined tolerances.

A Multi-Objective Stochastic Model for a Green Supply Chain planning

In this study we develop a stochastic multi-objective stochastic programming approach to deal with a supply chain planning under uncertainty. Supply chain cost parameters such as transportation cost, inventory holding cost, shortage cost, production cost in addition to some respects as employment, dismissal, workers productivity and training are all considered. Due to the important role of the lead time especially in supplying, the lead time between suppliers and factories and between factories and customer zones is assumed to be a function of transportation mode. Cost parameters and demand fluctuations are subject to uncertainty. To develop the model, two additional objective functions are added to the classical aggregate production planning. Therefore, the proposed multi-objective model includes the minimization of the expected total cost of supply chain, the minimization of the variability of the total cost of supply chain and the minimization of the expected value of the greenhouse gas emission level. Then, the proposed model is solved applying compromise programming method. Finally, a numerical example is solved to describe the proposed model.

Convergence analysis of sliding mode trajectories in multi-objective neural networks learning

The Pareto-optimality concept is used in this paper in order to represent a constrained set of solutions that are able to trade-off the two main objective functions involved in neural networks supervised learning: data-set error and network complexity. The neural network is described as a dynamic system having error and complexity as its state variables and learning is presented as a process of controlling a learning trajectory in the resulting state space. In order to control the trajectories, sliding mode dynamics is imposed to the network. It is shown that arbitrary learning trajectories can be achieved by maintaining the sliding mode gains within their convergence intervals. Formal proofs of convergence conditions are therefore presented. The concept of trajectory learning presented in this paper goes further beyond the selection of a final state in the Pareto set, since it can be reached through different trajectories and states in the trajectory can be assessed individually against an additional objective function.

PASS Approximation: A Framework for Analyzing and Designing Heuristics

We introduce a new framework for designing and analyzing algorithms. Our framework applies best to problems that are inapproximable according to the standard worst-case analysis. We circumvent such negative results by designing guarantees for classes of instances, parameterized according to properties of the optimal solution. Given our parameterized approximation, called PArametrized by the Signature of the Solution (PASS)approximation, we design algorithms with optimal approximation ratios for problems with additive and submodular objective functions such as the capacitated maximum facility location problems. We consider two types of algorithms for these problems. For greedy algorithms, our framework provides a justification for preferring a certain natural greedy rule over some alternative greedy rules that have been used in similar contexts. For LP-based algorithms, we show that the natural LP relaxation for these problems is not optimal in our framework. We design a new LP relaxation and show that this LP relaxation coupled with a new randomized rounding technique is optimal in our framework. In passing, we note that our results strictly improve over previous results of Kleinberg, Papadimitriou, and Raghavan [JACM 2004] concerning the approximation ratio of the greedy algorithm.

Comparison of Efficient Global Optimization and Output Space Mapping on the Biobjective Optimization of a Safety Isolating Transformer

The optimal design of electromagnetic devices needs to address two particular aspects: 1) the use of accurate tools and 2) the limited time budget affected to this task. In order to respond to these issues, two low evaluation budget multiobjective optimization techniques—efficient global optimization (EGO) and output space mapping (OSM)—are investigated in this paper with regard to a biobjective optimization benchmark. The device to be optimally sized is a low-voltage safety isolating transformer, represented through two levels of modeling: 1) coarse (analytical model) and 2) fine (numerical 3-D FEM). The biobjective character of the problem is accounted for by OSM through an epsilon-constraint technique. A transformation technique is set up with EGO by considering the constraints as an additional objective function in order to handle the constraints of the initial optimization problem. The biobjective comparison of the two techniques on the transformer benchmark is discussed.

Scheduling an unbounded batching machine with family jobs and setup times

We consider the problem of scheduling n jobs on an unbounded batching machine that can process any number of jobs belonging to the same family simultaneously in the same batch. All jobs in the same batch complete at the same time. Jobs belonging to different families cannot be processed in the same batch, and setup times are required to switch between batches that process jobs from different families. For a fixed number of families m, we present a generic forward dynamic programming algorithm that solves the problem of minimizing an arbitrary regular cost function in pseudopolynomial time. We also present a polynomial-time backward dynamic programming algorithm with time complexity O (mn(n/m+1)m) for minimizing any additive regular minsum objective function and any incremental regular minmax objective function. The effectiveness of our dynamic programming algorithm is shown by computational experiments based on the scheduling of the heat-treating process in a steel manufacturing plant.

Extremal values of global tolerances in combinatorial optimization with an additive objective function

The currently adopted notion of a tolerance in combinatorial optimization is defined referring to an arbitrarily chosen optimal solution, i.e., locally. In this paper we introduce global tolerances with respect to the set of all optimal solutions, and show that the assumption of nonembededdness of the set of feasible solutions in the provided relations between the extremal values of upper and lower global tolerances can be relaxed. The equality between globally and locally defined tolerances provides a new criterion for the multiplicity (uniqueness) of the set of optimal solutions to the problem under consideration.

Strategic capacitor placement in distribution systems by minimisation of harmonics amplification because of resonance

The capacitor placement problem (CPP) has been widely studied throughout the years. However, traditional methodologies either do not consider non-linear loads in the formulations or are highly dependent on the spectrum of the harmonic currents. Therefore the traditional methodologies have become unsuitable for distribution system planning studies. The proposed approach formulates the CPP as a multi-objective optimisation model while including economic and technical aspects in the minimisation process. An additional objective function introduces a quadratic minimisation of the voltage harmonic distortions produced by the harmonic currents drawn by non-linear loads according to the IEEE Std. 519-1992 limits. A new constraint based on a resonance index (RI) is also introduced as a form to extend the capacitors- lifetime. Furthermore, an aging model of capacitor dielectric insulation under a non-sinusoidal waveform scenario is used to estimate the expected real lifetime of capacitors. The proposed methodology was exhaustively tested on a 69-bus system and the results show that the methodology is adequate for planning capacitors and eliminates the need to focus in great detail on harmonic system data.

Multimodal Optimization Using a Bi-Objective Evolutionary Algorithm

In a multimodal optimization task, the main purpose is to find multiple optimal solutions (global and local), so that the user can have better knowledge about different optimal solutions in the search space and as and when needed, the current solution may be switched to another suitable optimum solution. To this end, evolutionary optimization algorithms (EA) stand as viable methodologies mainly due to their ability to find and capture multiple solutions within a population in a single simulation run. With the preselection method suggested in 1970, there has been a steady suggestion of new algorithms. Most of these methodologies employed a niching scheme in an existing single-objective evolutionary algorithm framework so that similar solutions in a population are deemphasized in order to focus and maintain multiple distant yet near-optimal solutions. In this paper, we use a completely different strategy in which the single-objective multimodal optimization problem is converted into a suitable bi-objective optimization problem so that all optimal solutions become members of the resulting weak Pareto-optimal set. With the modified definitions of domination and different formulations of an artificially created additional objective function, we present successful results on problems with as large as 500 optima. Most past multimodal EA studies considered problems having only a few variables. In this paper, we have solved up to 16-variable test problems having as many as 48 optimal solutions and for the first time suggested multimodal constrained test problems which are scalable in terms of number of optima, constraints, and variables. The concept of using bi-objective optimization for solving single-objective multimodal optimization problems seems novel and interesting, and more importantly opens up further avenues for research and application.

A Multiobjective Stochastic Production‐Distribution Planning Problem in an Uncertain Environment Considering Risk and Workers Productivity

A multi‐objective two stage stochastic programming model is proposed to deal with a multi‐period multi‐product multi‐site production‐distribution planning problem for a midterm planning horizon. The presented model involves majority of supply chain cost parameters such as transportation cost, inventory holding cost, shortage cost, production cost. Moreover some respects as lead time, outsourcing, employment, dismissal, workers productivity and training are considered. Due to the uncertain nature of the supply chain, it is assumed that cost parameters and demand fluctuations are random variables and follow from a pre‐defined probability distribution. To develop a robust stochastic model, an additional objective functions is added to the traditional production‐distribution‐planning problem. So, our multi‐objective model includes (i) the minimization of the expected total cost of supply chain, (ii) the minimization of the variance of the total cost of supply chain and (iii) the maximization of the workers productivity through training courses that could be held during the planning horizon. Then, the proposed model is solved applying a hybrid algorithm that is a combination of Monte Carlo sampling method, modified ε‐constraint method and L‐shaped method. Finally, a numerical example is solved to demonstrate the validity of the model as well as the efficiency of the hybrid algorithm.

Algorithm Development for Measurement and Prediction the Traffic in Broad Band Integrated Service Networks

Problem statement: In this study an effort had been made to develop an algorithm for traffic prediction and measurement for a wide use networks such as B-ISDN. Such algorithm should base on valuable parameters during the various stages of data elements transmission. The offered algorithm was expected to enforce the main sources of congestion problem in network. With this technique the admission decision is made according to the prediction of a few quality of service parameters expected for the new connections. Approach: This research aimed to find out the suitable method for improving the performance and the quality of service during the real time work in wide used networks now days. The improvement of quality of services in B-ISDN can be achieved by a significant estimation of the network state and discovering the most critical situation during the work time. The most repeated problems in such networks are loses of connection, delay time and saturation of communication lines. These problems are known and some solution could be sufficient to deal with, but not for a long time. Results: The proposed solution was based on the need of traffic prediction method in real time to determine the state of network and decide how to deal with. Such method should base on finding the most significant parameters in network during the real time work and use them as prediction variable to predict the situation or the state of network in the future time and then take the appropriate action. Suffering from permanent problems finding the most significant parameters, which can be estimated at the real time to help for solving a raw problems which encountered during the work in networks such as saturation, bottleneck, disconnecting and time delay. Conclusion: The results which achieved by this research was based on the developed algorithm which can be used to predict the traffic in B-ISDN, optimizing the bandwidth and making the bandwidth available to the behaving sources under congestion situation and also when there is no congestion. Meet the QoS demands of the network traffic during congestion situation and also when there is no congestion. Reject/drop all the packets. First guideline for future study in this direction is investigation additional objective functions, such as bandwidth limitation for archive more general results.

A stochastic discounted multi-objective solid transportation problem for breakable items using Analytical Hierarchy Process

In this paper, a multi-objective solid transportation problem (MOSTP) for a breakable item is considered with two different criteria: cost and time for transportation. Here breaking for the item depends on two modes- (i) type of conveyance and (ii) transported amount. The item breaks at constant rate for the modes of conveyance and randomly for the transported amount. The requirement of the destination is crisp, but due to presence of breakability, the fulfillment of demand at destination is stochastic, which is solved by the chance-constraint method. In this paper, a nested discount (IQD within AUD) is presented on the transportation cost. The considered model is formulated to minimize the total transportation cost and time to transport all units of the item with respect to the transported amounts of the item from origins to destinations. Thus the problem reduces to a multi-objective problem. A set of pareto optimal solutions are obtained by multi-objective genetic algorithm (MOGA). The best solution out of this set is presented using Analytical Hierarchy Process (AHP). The MOSTP has also been formulated with entropy function defined by Shannons measure of entropy. The entropy function is used as an additional objective function which acts as a measure of dispersion. To illustrate the model, numerical example has been presented. The effect of entropy on transported amount is illustrated. A sensitivity analysis on the total cost due to the changes in breakability rate is presented.

An analytical approach to the problem of inverse optimization with additive objective functions: an application to human prehension

We consider the problem of what is being optimized in human actions with respect to various aspects of human movements and different motor tasks. From the mathematical point of view this problem consists of finding an unknown objective function given the values at which it reaches its minimum. This problem is called the inverse optimization problem. Until now the main approach to this problems has been the cut-and-try method, which consists of introducing an objective function and checking how it reflects the experimental data. Using this approach, different objective functions have been proposed for the same motor action. In the current paper we focus on inverse optimization problems with additive objective functions and linear constraints. Such problems are typical in human movement science. The problem of muscle (or finger) force sharing is an example. For such problems we obtain sufficient conditions for uniqueness and propose a method for determining the objective functions. To illustrate our method we analyze the problem of force sharing among the fingers in a grasping task. We estimate the objective function from the experimental data and show that it can predict the force-sharing pattern for a vast range of external forces and torques applied to the grasped object. The resulting objective function is quadratic with essentially non-zero linear terms.

Towards a simple dynamic process conceptualization in rainfall–runoff models using multi‐criteria calibration and tracers in temperate, upland catchments

AbstractEmpirically based understanding of streamflow generation dynamics in a montane headwater catchment formed the basis for the development of simple, low‐parameterized, rainfall–runoff models. This study was based in the Girnock catchment in the Cairngorm Mountains of Scotland, where runoff generation is dominated by overland flow from peaty soils in valley bottom areas that are characterized by dynamic expansion and contraction of saturation zones. A stepwise procedure was used to select the level of model complexity that could be supported by field data. This facilitated the assessment of the way the dynamic process representation improved model performance. Model performance was evaluated using a multi‐criteria calibration procedure which applied a time series of hydrochemical tracers as an additional objective function. Flow simulations comparing a static against the dynamic saturation area model (SAM) substantially improved several evaluation criteria. Multi‐criteria evaluation using ensembles of performance measures provided a much more comprehensive assessment of the model performance than single efficiency statistics, which alone, could be misleading. Simulation of conservative source area tracers (Gran alkalinity) as part of the calibration procedure showed that a simple two‐storage model is the minimum complexity needed to capture the dominant processes governing catchment response. Additionally, calibration was improved by the integration of tracers into the flow model, which constrained model uncertainty and improved the hydrodynamics of simulations in a way that plausibly captured the contribution of different source areas to streamflow. This approach contributes to the quest for low‐parameter models that can achieve process‐based simulation of hydrological response. Copyright © 2009 John Wiley & Sons, Ltd.

Reliability Optimization of Entropy Based Series-Parallel System Using Global Criterion Method

In this paper, we have considered a series-parallel system to find out optimum system reliability with an additional entropy objective function. Maximum system reliability of series-parallel system is depending on proper allocation of redundancy component in different stage. The goal of entropy based reliability redundancy allocation problem is to find optimal number of redundancy component in each stage such a manner that maximize the system reliability subject to available total system cost. Global criterion method is used to analyze entropy based reliability optimization problem with different weight function of objective functions. Numerical examples have been provided to illustrate the model.