Surrogate Worth Trade-off Method Research Articles

Surrogate worth trade-off method for multi-objective thermal power load dispatch

The multi-objective thermal power dispatch (MTPLD) problem allocates power demand among the committed generating units while minimizing the operating cost and pollutant's emission objectives simultaneously, subject to physical and technological constraints. The success to find MTPLD solution relies on the decision-maker's ability to select compromised solution under uncertain/diverse conditions and the search algorithm's potential to generate non-dominated solutions. Owing to ambiguous choice of objectives, this paper presents a fuzzy surrogate worth trade-off approach to decide the preferred solution among the non-dominated solution set. The uniformity of non-dominated solution set is maintained exploiting a quality measure approach. This paper presents a novel foraging activity paradigm to generate non-dominated solutions. The presented approach comprises of fly and walk behavior of preys. The direction of turn heuristic of prey handles system's equality constraint. The search algorithm balances exploration and exploitation and handles system constraints autonomously. The performance of proposed algorithm is investigated using generalized benchmark functions and multi-fuel, medium and large power system MTPLD problems. The experimental results shows that the proposed approach is robust, depends on least parameters and retains Pareto quality in independent trials while generating non-dominated solutions in a trial run.

Water Management Trade-offs between Agriculture and the Environment: A Multiobjective Approach and Application

AbstractPractical plans for agricultural water use within multiobjective frameworks require feasible solutions that meet the objectives of competing interests and this is the root of common decision problems that plague water resources systems. To find the best solutions among the set of feasible solutions, decision-makers can analyze their worth functions, which is the goal of the surrogate worth trade-off (SWT) method, which enables assessment of the worth functions after solutions that are optimal to separate groups are analyzed. The SWT method uses Lagrange multipliers to determine the set of Pareto optimal solutions and requires the exact equation of each objective function and its derivative or gradient. This is normally impractical in watershed scale problems because each objective function comprises a set of interactive physical and hydrological equations, but the problem can be partially overcome by incorporating a genetic algorithm. This approach was applied to a case study of California’s San J...

A multi-objective stochastic programming model for designing supply chain networks

A multi-objective stochastic programming model is developed for supply chain design under uncertainty using an interactive approach. This is a comprehensive model, which includes both the strategic and tactical levels. The uncertainty regarding demands, supplies, processing and transportation costs is captured by generating discrete scenarios with given probabilities of occurrences. The objective functions involved are the expected total cost (min), the variance of the total costs (min) to get a robust design, and the probability of not meeting a certain budget (min). Then, an interactive multi-objective technique with explicit trade-off information given named surrogate worth trade-off (SWT) method is used to solve the multi-objective model.

Fuzzy Satisfying Multiobjective Thermal Power Dispatch Based on Surrogate Worth Trade-off Method

In multiobjective optimization, trade-off analysis plays an important role in determining the best search direction to reach a most preferred solution. As in many cases, the objectives contradict with each other and cannot be handled by conventional scalar optimization techniques. This article deals with the multiobjective optimization problem relating to real and reactive power scheduling of thermal power generating units. In deciding the most preferred solution, operating cost, emission pollutants are the objectives undertaken to be minimized simultaneously while satisfying the security constraints. The real and reactive power line flows are obtained with the help of generalized Z-bus distribution factors (GZBDF). The non-inferior solutions, along with the trade-off functions between the conflicting objectives, are generated by implementing the ε-constraint method. Exploiting fuzzy set theory to access the indifference band, interaction with the decision maker is obtained via surrogate worth trade-off (SWT) functions of the membership functions of the objectives. The surrogate worth trade-off functions are constructed in the functional space and then transformed into the decision space, so the surrogate worth trade-off functions of objectives relate the decision maker's preferences to non-inferior solutions. The goal/objectives being of fuzzy nature can be quantified by defining their membership functions. The effectiveness of the method is demonstrated on IEEE 11-bus system, which comprises 3-generators.

Dual worth trade-off method and its application for solving multiple criteria decision making problems

To overcome the limitations of the traditional surrogate worth trade-off (SWT) method and solve the multiple criteria decision making problem more efficiently and interactively, a new method labeled dual worth tradeoff (DWT) method is proposed. The DWT method dynamically uses the duality theory related to the multiple criteria decision making problem and analytic hierarchy process technique to obtain the decision maker's solution preference information and finally find the satisfactory compromise solution of the decision maker. Through the interactive process between the analyst and the decision maker, trade-off information is solicited and treated properly, the representative subset of efficient solutions and the satisfactory solution to the problem are found. The implementation procedure for the DWT method is presented. The effectiveness and applicability of the DWT method are shown by a practical case study in the field of production scheduling.

A multi-objective resource allocation problem in PERT networks

We develop a multi-objective model for resource allocation problem in PERT networks with exponentially or Erlang distributed activity durations, where the mean duration of each activity is a non-increasing function and the direct cost of each activity is a non-decreasing function of the amount of resource allocated to it. The decision variables of the model are the allocated resource quantities. The problem is formulated as a multi-objective optimal control problem that involves four conflicting objective functions. The objective functions are the total direct costs of the project (to be minimized), the mean of project completion time (min), the variance of project completion time (min), and the probability that the project completion time does not exceed a certain threshold (max). The surrogate worth trade-off method is used to solve a discrete-time approximation of the original problem.

The surrogate worth trade-off approach for multiobjective thermal power dispatch problem

A multiobjective thermal power dispatch problem is solved that has non-commensurable objectives such as operating cost and minimal emissions. Typically, the objectives will conflict in that there is no feasible solution that minimizes them all simultaneously. In such a case, some form of conflict resolution must be adopted to arrive at a solution. In this study, ϵ-constraint method is used to generate non-inferior solutions along with the trade-off function between the conflicting objectives. To access the indifference band, interaction with the decision maker is obtained via surrogate worth trade-off (SWT) method and utility approach. The SWT functions are constructed in the functional space and then are transformed into the decision space. So, SWT functions relate the decision maker's preferences to non-inferior solutions. The validity and effectiveness of the method have been proved by analysing a six-generator system.

Optimal burn-in for minimizing cost and multiobjectives

In general, a small proportion of components will be weak because of some imperfection in the control of the production process or in the design of the components. This paper discusses an optimal burn-in procedure to minimize total costs based on the assumption that some of the components are weak and deteriorate faster than the strong components. The procedure will define the costs of burn-in errors. In practice, it may be impossible to eliminate all weak components through burn-in due to a nonzero proportion of defectives of the components. Therefore, burn-in errors could occur for some reasons. Probability models and cost models are formulated to find the optimal burn-in time that minimizes the expected total cost. An example is included to show how to use the results. Finally, multiobjective optimal burn-in for series systems is presented using the surrogate worth trade-off method.

Multi-Objective Optimization Of Reliability-based Structural Design

Both reliability-based structural design and multi-objective optimization techniques have received extensive attention. The proposed approach, using multi-objective optimization strategies, aims to deal with reliability-based. structural design optimization problems with multi-pie design goals. Among reliability analysis, a transformation method based on the advanced firsl order second moment (AFOSM) method is used to evaluate the failure probability of single failure mode, and the Cornell’s upper bound is used to estimate system failure probability with multifailure mode. In multi-objective optimization, the promising surrogate worth trade-off method (SWT) is used. Through the numerical solution of two design examples. it is concluded that the multi-objective 0plimization approach, which improvc.~ the decision-making capability of designers or decision makers and it is an effective design tool for engineers in the solution of multi-objective problems with uncertainties.

Multiobjective dynamic optimization of a nonvaporizing nylon 6 batch reactor

AbstractMultiobjective dynamic optimization has been carried out on a nonvaporizing nylon 6 batch reactor. Three objective functions have been identified, viz., minimization of the concentration of unreacted monomer in the product, minimization of the dimer concentration, and minimization of the reaction time, for producing polymer having a specified value, μn, d, of the number average chain length. Two problems have been studied in this paper, each consisting of two objective functions taken from the above set. Pareto solutions have been generated using an algorithm based on Pontryagin's minimum principle and the method of Lagrangian multipliers. The effects of various physical and computational parameters have been studied, and methods have been developed to overcome the numerical difficulties that arise during the solution. The Pareto sets so generated can be coupled with the surrogate worth trade‐off (SWT) method, which facilitates interaction with a decision maker (DM). The optimal temperature histories obtained for the two problems studied are quite different and suggest that one must solve the three‐dimensional problem in which the vector objective function incorporates all three objective functions. Results from the present study could be used as starting guesses to converge rapidly on the solution of the three‐dimensional problem.

A fuzzy multiobjective programming algorithm in decision support systems

Multicriteria analysis is one of the analytical functions in the problem processing system of decision support systems (DSS). In this paper, an interactive and iterative fuzzy programming method for solving a quasi-optimization problem in complex decisions under constraints involving a multiple objective function is proposed. Comparing with an adapted gradient search method, a surrogate worth tradeoff method, and a Zionts—Wallenius method, an approximate preference structure is emphasized in the proposed method.

Fuzzy multicriteria programming in economic systems analysis

s I 1 ! Fuzzy Multicriteria Programming in Economic Systems Analysis L. D. Xu Information Systems, University of Wisconsin, La Crosse, Wisconsin 54601 In this paper, four main aspects of both the inquiring and operational systems of economic systems analysis are explored: (1) A new philosophical paradigm as the foundation of general methodology in place of Kantian-Newtonian inquiring systems is proposed. (2) A new problem formulation space--a multidimensional, synergetic, and autopoietic model--is proposed. (3) The new philosophical paradigm is characterized as a Singerian inquiring system, and Marglin's multiobjective analysis is replaced by Singerian multiobjective analysis. (4) Fuzzy set theory and fuzzy Markov theory are introduced for multiobjective analysis. An interactive and iterative fuzzy programming method is proposed for solving a quasi-optimization problem under constraints involving a multiple objective function. Comparing this with the adapted gradient search method, surrogate worth trade-off method, and the Zionts-Wallenius method, the approximate preference structure is emphasized. The paper discusses how to specify a set of nondominated solutions and approach a nondominated extreme point from the perspective of the decision maker. One difference between the surrogate worth trade-off method and the proposed method is that the former indicates the marginal rates of substitution with the limitation of pair trade-off, while the latter shows an approximate preference structure for generating a new ideal point. The trade-off of pairs is substituted by multidimensional evaluations without assuming that certain conditions remain unchanged. Application of Possibility Theory to Learning in Knowledge-Based Systems with an Imperfect Teacher Maria Zemankova Computer Science Department, University of Tennessee, 107 Ayres Hall, Knoxville, Tennessee 37996-1301 The goal of the learning process is to build a knowledge base consisting of a set of concepts defined over an object set described by its attributes. The object set is be grouped into equivalence classes using similarity relations defined on attribute domains. The learning algorithm is based on finding a possibility function value for each equivalence class or the degree to which this class satisfies the concept being learned. This function is translated into an optimized description of the concept that can be easily read by users. During the learning process the teacher provides positive and negative examples, and the system computes the possibility function values for the boundary region that can be corrected by the teacher if necessary. The teacher may be imperfect' ' --he or she does not have to know the concepts exactly--and the system will

An application to the grafting operations of vascular prostheses by multi-goal programming.

In the grafting operation of vascular prostheses, decision variables are tensile force (F) during pre-clotting and required time (t) for pre-clotting. An optimization problem is constructed which contains three objective functions; maximize the porosity (Q1) (to maintain initial porosity over a long period of time), minimize the porosity (Q2) after pre-clotting (to reduce bleeding from the vascular prosheses during grafting), and minimize the required time (t) for pre-clotting (to reduce required time for grafting). The following regression equations are formulated using experimental data: Q1=2850+8.7F and Q2=αexp(-0.038t) where α is 38 or 311 according to the sample blood A or B drawn from two dogs. The tensile force (F) is assumed to have no relation with porosity (Q2), thus enabling two-criterion decision making to be applied. The approaches of the three solution methods; ε-constraint approach, goal programming and surrogate worth trade-off method, have also been applied. Consequently, the most effective approach is goal programming. The same solution is obtained for different blood samples A and B.

Nonlinear Reservoir Analysis with Risk-Benefit Objectives

ABSTRACT The surrogate worth trade-off method has been extended to a quadratic programming optimization model and risk has been incorporated into the vector of objective functions which explicitly shows the decision maker the trade-offs between net benefits and increased reliability of the system or the trade-offs between competing reliabilities such as flood control and water supply. The approach is called the Nonlinear Risk-Benefit (NRB) Algorithm. The NRB Algorithm is applied to the Broken Bow Reservoir to illustrate the increased information made available by this approach.

A comparative evaluation of interactive solution methods for multiple objective decision models

This paper describes a laboratory experiment which compares the performance from the user's point of view of four different solution methods for multiple objective decision models with continuous variables. These are the method of Zionts and Wallenius, the surrogate worth tradeoff method, the method of Steuer and Choo and a simplistic ‘naive’ solution method. The users exhibited different preferences among the different solution methods with the method of Steuer and Choo favoured overall. The results highlight a need for solution methods to accommodate the decision making characteristics of the user.

Interactive computer graphics-based multiobjective decision-making for regional groundwater management

This paper presents a comprehensive set of procedures by which decision-makers can select a single strategy from a set of alternative strategies. Application of these procedures in developing a regional conjunctive water management strategy for an important rice producing area in Arkansas, U.S.A., is described. The importance of interactive decision-making and efficient presentation of information through interactive graphics and computations is also demonstrated. The optimization model considers two different objectives: minimization of the total cost of water use (including opportunity cost due to the loss in agricultural production caused by non-availability of water); and maximization of total withdrawal (pumping) from the aquifer. Application of the surrogate worth tradeoff method together with interactive computer graphics display of relevant information is presented as part of the procedures for selecting a regional sustained groundwater withdrawal strategy.

Integration of the surrogate worth trade-off method and the analytic hierarchy process

The field of multiple-criteria decision making (MCDM) has developed into one of the fastest growing fields in the last ten years. This paper outlines the MCDM process and then presents two of the more well-known methods: the analytic hierarchy process and the surrogate worth trade-off method. These methods will be presented in terms of the types of problems for which they are best suited along with advantages and disadvantages possessed by each. Finally, an integrated approach will be proposed which attempts to capture the advantages of both methods in order to develop one robust solution strategy.

Expansion Planning of Hydrothermal Power Systems, Optimizing the Multiple Uses of the Water from Hydroelectric Power Plant Reservoirs, via Conversational Multi-Objective Algorithms

Often the development of hydroelectricity has an overwhelming role in the utilization planning of regional water resources. For such situation, it is proposed in this paper to approach the power system expansion problem on a two objective basis. The first one is the cost minimization of the power supply, while the second one is the maximization of the overall net benefit accruing from the multi-purpose regional water usage. The nature of the problem is such that conversational multi-objective methods are particularly attractive for its solution. The joint optimization of the two objectives is carried out with the help of two powerfull alternative conversational techniques: the Surrogate Worth Trade-off Method and the Interactive Sequential Goal Programming Method. Applications to the generation system of a Brazilian power supply utility indicate the former method as the best for this class of problems. The expansion plans are provided by a “global” (it performs the expansion and operation steps simultaneously) generation planning model using linear programming.

Integrated risk and uncertainty assessment in water resources within a multiobjective framework

Abstract The process of risk-and-uncertainty assessment in water resources is examined within a multiobjective framework. In this context, appropriate methodologies — the surrogate worth trade-off (SWT) method, the multiobjective statistical method (MSM), the partitioned multiobjective risk method (PMRM), the risk dispersion index method (RDIM), and the uncertainty sensitivity index method (USIM) — are very briefly discussed. A need for an approach that integrates the assessment of risk and uncertainty within a multiobjective framework, accounting for random variables with both known and unknown probability distributions is suggested. This paper is dedicated to the memory of Ven Te Chow, a distinguished educator, prominent researcher, renowned scholar and dedicated public servant, who dominantly influenced the field of hydrology and water resources.

An Interactive Method for Multiobjective Decision Making

The interactive multiabjective decision making technique presented in this paper is based on the surrogate worth trade-off (SWT) method, but it only requires the decision maker (DM) to declare whether he is willing to proceed with the trade-off, which makes it easier for him to answer questions raised by the analyst. The bisection procedure suggested by this technique helps one to approach his preferred solution ultimately. This method is used for tackling a water resource planning problem in China.