Surrogate Worth Trade-off Research Articles

Multi-Objective Dynamic Economic and Emission Generation Scheduling of Coordinated Power System Considering Renewable Energy Sources and Pumped Storage Hydro Plants via Fuzzy Surrogate-Assisted Coronavirus Herd Immunity Optimization

Globally, the power generation from renewable energy sources (RES) has received considerable attention to reduce pollutant emissions and the total operating costs of power generation. In this context, this study aims to extend the multi-objective dynamic economic and emission dispatch (MODEED) problem by incorporating RES and pumped storage hydro plants. The complex constrained MODEED problem is solved by a fuzzy surrogate-assisted coronavirus herd immunity optimization (FSACHIO) algorithm in which a self-adaptive speed factor and Lévy flight mechanism are utilized to ensure populace diversity, prevent premature convergence and achieve an ideal stability among the exploration and exploitation of the algorithm. Surrogate worth tradeoff methodology is used to discover a solution that provides the optimal balance between the objectives such as operating expenses and emission pollutants. The performance of FSACHIO algorithm is validated on a small-scale and a large-scale test systems, involving 10-unit, and 40-unit test systems, and compared with that of the coronavirus herd immunity optimization, red fox optimizer, Remora optimization algorithm, and other erstwhile approaches. Besides, a fuzzy constraint handling method based on a dominance relationship is integrated to fulfill the restrictions of the MODEED problem. The simulation results reveal that: (i) the operating costs and emissions are reduced by 173785.54 $/day and 2992.1848 lb/day in the small-scale test system and by 6383.9903 $/day and 216631.4877 lb/day in the large-scale test system, respectively for the MODEED problem with the presence of RES and pumped storage hydro plants; (ii) the suggested approach may offer a well-distributed Pareto-optimal frontier and superior tradeoffs among the operating expenses and pollution objectives in comparison to the other approaches.

A Demand-Side Inoperability Input–Output Model for Strategic Risk Management: Insight from the COVID-19 Outbreak in Shanghai, China

This paper proposes the dynamic inoperability input–output model (DIIM) to analyze the economic impact of COVID-19 in Shanghai in the first quarter of 2022. Based on the input–output model, the DIIM model introduces the sector elasticity coefficient, assesses the economic loss of the system and the influence of disturbances on other sectors through sectoral dependence, and simulates the inoperability and economic loss changes through time series. A multi-evaluation examination of the results reveals that the degree of inoperability of sub-sectors is inconsistent with the ranking of economic losses and that it is hard to quantify the impact of each sector directly. Different from the traditional DIIM model that only considers the negative part of the disaster, the innovation of this paper is that the negative value of the inoperability degree is used to measure the indirect positive growth of sectors under the impact of the Shanghai pandemic shock. At the same time, policymakers need to consider multi-objective optimization when making risk management decisions. This study uses surrogate worth trade-off to construct a multi-objective risk management framework to expand the DIIM model to enable policymakers to quantify the trade-off between economic benefit and investment costs when making risk management decisions.

Multi-objective generation scheduling of integrated energy system using fuzzy based surrogate worth trade-off approach

The aim of this research work is to resolve the economic, emission and multi-objective scheduling problem (MOSP) of the integrated energy system (IES). The integrated energy system incorporates pumped storage hydrothermal system (PSHTS) with wind, solar and battery units. The pumped storage unit can work in generating or pumping mode and its operation is controlled by binary decision variables, hence, the integrated energy system consist mixed mode decision variables. In order to search optimum generation schedule, a modified crisscross PSO (MCPSO) and improved binary PSO technique has been undertaken. The crisscross search in the CPSO technique exhibits horizontal and vertical crossover operators to explore the search space in every dimension and mitigate the stagnancy problem. In MCPSO technique, the search has been enhanced in way of pattern search in every search direction. In this work, the surrogate worth trade-off (SWT) function perform as an interface between the decision maker and Pareto-front to select the best-compromised solution of the MOSP and reduces the computational efforts. The performance of the MCPSO-SWT has been verified on four different test systems. The test results achieved from the economic, emission and MOSP have been compared with results obtain from the well-established techniques and found satisfactory.

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.

Multi-objective thermal power load dispatch using chaotic differential evolutionary algorithm and Powell’s method

In this work, a chaotic differential evolutionary and Powell’s pattern search (CDEPS) algorithm is proposed to solve multi-objective thermal power load dispatch (MTPLD) problem. The chaotic differential evolutionary method is responsible for the diversification, and Powell’s pattern search is dedicated to exploitation. Further, the performance of two CDEPS variants based on Gauss map and Tent map is investigated. The proposed MTPLD solution procedure either identifies a solution close to Pareto front or diversifies the existing Pareto frontier and finally selects a suitable compromising solution among the available options. In order to select the best compromising solution, a combination of surrogate worth trade-off approach and fuzzy theory is proposed as choice of objectives is ambiguous. The uniformity of Pareto front is evaluated by exploiting a quality measure approach. The performance analysis is done using generalized benchmark test functions and complex MTPLD problems. The ability of CDEPS to diversify Pareto front is verified by uniformity analysis of Pareto front. The one-sample Wilcoxon’s test and two-sample Mann Whitney’s test are used to analyze the experimental results. The exhaustive analysis shows that the Tent map-based CDEPS has better ability to generate quality generation schedule with uniform Pareto front quality and faster convergence rate.

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.

RISK-BASED MULTIATTRIBUTE DECISION-MAKING IN PROPERTY AND WATERSHED MANAGEMENT

. Determining best management systems for properties and evaluating their sustainability at the watershed scale are useful and important aspects of integrated watershed management. Multiattribute decision-making (MADM) is very useful for modeling the selection of best management systems for properties in a watershed. This paper reviews four MADM approaches including utility theory, surrogate worth tradeoff, free iterative search and stochastic dominance with respect to a function (SDWF). Emphasis is on determining how the first three methods could be used to determine the best (most preferred) combinations of attributes and associated management systems for a property. An application of the expected utility method with risk neutral preferences is presented in which farmer's preferences for five attributes are used to rank five farming systems for an agricultural watershed in Missouri. A framework is presented for assessing the sustainability of the best management systems for all properties in a watershed and the cost-effectiveness of policies for enhancing sustainable resource management at the watershed scale.

Interactive fuzzy decision making for multiobjective load dispatch

The multiobjective load dispatch (MLD) problem is a multiple non-commensurable objective problem that minimises both cost and emission together subject to power balance and generators’ capacity constraints. In this paper, the MLD problem is converted into a single objective function using the weighting method. Weights are simulated to generate a non-inferior solution along with trade-off functions between the conflicting objectives. Exploiting fuzzy decision-making theory to access the indifference band, interaction with the decision maker (DM) is obtained via surrogate worth trade-off (SWT) functions of the objectives. The SWT functions are constructed in the functional space and then transformed into the decision space, so the SWT functions of objectives relate the DM's preferences to non-inferior solutions through optimal weight patterns. The optimal solution is obtained by considering real and reactive power losses. Fast decoupled load flow analysis is performed to find the losses. The validity of the proposed method is demonstrated on the 11-bus, 17-lines IEEE system, comprising of three generators.

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.

Fuzzy satisfying interactive multiobjective thermal power dispatch: SWT approach

In multiobjective optimization, trade-off analysis plays an important role in determining most preferred solution. This paper presents an explicit interactive trade-off analysis based on the surrogate worth trade-off function to determine the best compromised solution. In the multiobjective framework thermal power dispatch problem is undertaken in which four objectives viz. cost, NOx emission, SOx emission and COx emission are minimized simultaneously. The interactive process is implemented using a weighting method by regulating the relative weights of objectives in systematic manner. Hence the weighting method facilitates to simulate the trade-off relation between the conflicting objectives in non-inferior domain. Exploiting fuzzy decision making theory to access the indifference band, interaction with the decision maker is obtained via surrogate worth trade-off (SWT) 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 through optimal weight patterns. The optimal solution of thermal power dispatch problem is obtained by considering real and reactive power losses. Decoupled load flow analysis is performed to find the transmission losses. The validity of the proposed method is demonstrated on 11-bus, 17-lines IEEE system, comprising of three 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.

Multiple attribute decision analysis for ecosystem management

Implementation of an ecosystem approach to natural resource management requires evaluation of a broad array of ecological services in a multidimensional, community-based watershed approach that empowers people to make informed management decisions. Conventional economic approaches that assign values to ecological services (contingent valuation) or that evaluate the efficiency of preserving and restoring those services (cost–benefit analysis) are quite limited for this purpose. In addition to the methodological difficulties encountered in applying contingent valuation and cost–benefit analysis, several problems occur when nonmarket values of ecological services are estimated independently of ecosystem planning and management. Multiple attribute decision-making (MADM) is an alternative conceptual framework for evaluating and selecting land and water resource management systems (LWRMS). Advantages of MADM are that it facilitates community-based collaborative decision-making, avoids some of the ethical, theoretical and practical shortcomings of conventional economic approaches, does not require assigning monetary values to ecological services, allows consideration of multiple attributes and is not culturally biased. The MADM model described in this paper explains how a property manager selects the most preferred LWRMS for a property based on their multiple stochastic attributes. Application of the model requires determination of the technically feasible LWRMS for a property and specification of the socially acceptable ranges of attributes. This information is combined with economic/biophysical simulations to derive the efficient combination of attributes and LWRMS for a property. The property manager then selects the most preferred combination of attributes from the efficient combinations of attributes for a property using utility maximization, surrogate worth tradeoff, free iterative search, analytical hierarchy process, Aspiration–Reservation Based Decision Support System or stochastic dominance. A watershed alliance can evaluate the sustainability of the most preferred LWRMS for properties in a watershed based on a weak or strong sustainability criterion. If the alliance determines that the most preferred LWRMS are not sustainable, then an index of attributes is used to evaluate the cost effectiveness of alternative public policies for stimulating the adoption of more sustainable LWRMS.

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.

Surrogate worth trade-off technique for multi-objective optimal power flows

Multi-objective programming techniques have been applied in a number of ways to minimise more than one objective simultaneously. Recently, some research work has been reported on multiobjective power flow studies. In this paper, surrogate worth trade-off technique (SWT) is attempted to achieve the best compromise between cost of generation and system transmission losses and the results have been compared with the existing method. It is found that the SWT technique gives encouraging results.

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 study on multi-criteria structural optimum design using qualitative and fuzzy reasoning

In an ordinary optimum design process, designers are often required to express a design problem as a mathematical model with a single objective. However, a number of objectives are usually found in structural designs, and it may then be tedious and difficult for designers to choose just one objective among them. In such cases, it will be natural and reasonable to formulate a multi-objective optimization problem. Recently, many studies have been made on interactive multi-criteria optimum design problems. In conventional methods, designers have been forced to make important and difficult decisions concerning the “trade-off ratio”, “marginal rates of substitution”, “surrogate worth trade-off” and so on, which may give much information in the optimization. To reduce the load of the designer in both the decision-making process and formulation, we have done a series of studies on qualitative optimization which based on qualitative and fuzzy reasoning. In this paper, we review these studies, clarify the definition of the concept of qualitative optimization and then examine the efficiency of the algorithm. From numerical examples of the optimum designs of a parabolic antenna, it is shown that the proposed method is applicable and effective for optimizations of complex structural systems by qualitative understanding, and can well support decision-making by the designers. In the layout optimization problems of a parabolic antenna, we show an extension of the method to the primary stage of the design process, that is, the conceptual or fundamental design, which has seemed difficult to handle in the conventional optimization method.