Effects of different objective functions on optimal decision variables: a study using modified complex method to optimize hamburger cooking

LWT ◽  
2005 ◽  
Vol 38 (2) ◽  
pp. 111-118 ◽  
Author(s):  
Ferruh Erdogdu ◽  
Susana E. Zorrilla ◽  
R. Paul Singh
Author(s):  
Rajdip Paul ◽  
Sujit Dalui

The present study consists of shape optimization of a rectangular plan shaped tall building with horizontal limbs under wind attack, which would minimize the wind pressure on all the faces of the building model simultaneously. For the purpose, the external pressure coefficients on different faces of the building (Cpe) are selected as the objective functions. The position of the limbs and the wind incidence angle are taken as design variables. The design of experiment (DOE) is done using random sampling. The values of the objective functions are obtained by using Computational Fluid Dynamics method of simulated wind flow at each design point. The building model has a constant plan area 22500 mm2. The length and velocity scales are taken as 1:300 and 1:5, respectively. The results are used to construct the surrogate models of the objective functions using Response Surface Approximation method. The optimization study is done using the Multi-Objective Genetic Algorithm. The building shapes corresponding to the Pareto optimal decision variables are shown. The function values corresponding to the decision variables are verified by further introducing a CFD study.


2016 ◽  
Vol 2016 ◽  
pp. 1-28 ◽  
Author(s):  
Wanjin Guo ◽  
Ruifeng Li ◽  
Chuqing Cao ◽  
Xunwei Tong ◽  
Yunfeng Gao

A new methodology using a direct method for obtaining the best found trajectory planning and maximum dynamic load-carrying capacity (DLCC) is presented for a 5-degree of freedom (DOF) hybrid robot manipulator. A nonlinear constrained multiobjective optimization problem is formulated with four objective functions, namely, travel time, total energy involved in the motion, joint jerks, and joint acceleration. The vector of decision variables is defined by the sequence of the time-interval lengths associated with each two consecutive via-points on the desired trajectory of the 5-DOF robot generalized coordinates. Then this vector of decision variables is computed in order to minimize the cost function (which is the weighted sum of these four objective functions) subject to constraints on joint positions, velocities, acceleration, jerks, forces/torques, and payload mass. Two separate approaches are proposed to deal with the trajectory planning problem and the maximum DLCC calculation for the 5-DOF robot manipulator using an evolutionary optimization technique. The adopted evolutionary algorithm is the elitist nondominated sorting genetic algorithm (NSGA-II). A numerical application is performed for obtaining best found solutions of trajectory planning and maximum DLCC calculation for the 5-DOF hybrid robot manipulator.


Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Bo Wang ◽  
Yanjing Li ◽  
Fei Yang ◽  
Xiaohua Xia

A technoeconomic optimization problem for a domestic grid-connected PV-battery hybrid energy system is investigated. It incorporates the appliance time scheduling with appliance-specific power dispatch. The optimization is aimed at minimizing energy cost, maximizing renewable energy penetration, and increasing user satisfaction over a finite horizon. Nonlinear objective functions and constraints, as well as discrete and continuous decision variables, are involved. To solve the proposed mixed-integer nonlinear programming problem at a large scale, a competitive swarm optimizer-based numerical solver is designed and employed. The effectiveness of the proposed approach is verified by simulation results.


2015 ◽  
Vol 23 (1) ◽  
pp. 69-100 ◽  
Author(s):  
Handing Wang ◽  
Licheng Jiao ◽  
Ronghua Shang ◽  
Shan He ◽  
Fang Liu

There can be a complicated mapping relation between decision variables and objective functions in multi-objective optimization problems (MOPs). It is uncommon that decision variables influence objective functions equally. Decision variables act differently in different objective functions. Hence, often, the mapping relation is unbalanced, which causes some redundancy during the search in a decision space. In response to this scenario, we propose a novel memetic (multi-objective) optimization strategy based on dimension reduction in decision space (DRMOS). DRMOS firstly analyzes the mapping relation between decision variables and objective functions. Then, it reduces the dimension of the search space by dividing the decision space into several subspaces according to the obtained relation. Finally, it improves the population by the memetic local search strategies in these decision subspaces separately. Further, DRMOS has good portability to other multi-objective evolutionary algorithms (MOEAs); that is, it is easily compatible with existing MOEAs. In order to evaluate its performance, we embed DRMOS in several state of the art MOEAs to facilitate our experiments. The results show that DRMOS has the advantage in terms of convergence speed, diversity maintenance, and portability when solving MOPs with an unbalanced mapping relation between decision variables and objective functions.


2011 ◽  
Vol 48-49 ◽  
pp. 232-235
Author(s):  
Sheng Li Chen

By constructing the exponential delay cost function, we formulate the consumer decision model based on the threshold strategies in dual-mechanism, and prove that there exists a unique symmetric Nash equilibrium in which the high-valuation consumers use a threshold policy to choose between the two selling channels. On the basis of the consumer’s threshold strategies, taking the auction length, the auctioned quantity in each period, and the posted price as the decision variables, we develop the seller’ optimal decision model in dual-mechanism, and show the optimal auction design principle and strategy by numerical analysis.


2013 ◽  
Vol 397-400 ◽  
pp. 2595-2600
Author(s):  
Zhi Bing Lin

In this paper, we consider a newsvendor model while its demand randomness is changeable. We analyze how the demand randomness affects the decision variables and objective functions in two difference situations: (1) the retail price is fixed;(2) the retail price is changeable. In first situation, we characterize the optimal order quantity, expected profit and variance of profit based on the benchmark model. In second situation, we show that the expected profit is joint concave function with respect to order quantity and retail price, also give the first order conditions. Finally, we use number analysis to show the effects of demand randomness on optimal retail price and order quantity


2016 ◽  
Vol 41 (4) ◽  
Author(s):  
Rana Azmi Dandis ◽  
Mohammed Al-Haj Ebrahem

Assessing the reliability of a product is very important to improve the product’s quality and to get the trust of customers. Degradation experiments are usually used to assess the reliability of highly reliable products,which are not expected to fail under the traditional life tests. Several decision variables, such as the sample size, the inspection frequency, and the termination time, have a direct influence on the experimental cost and the estimation precision of lifetime information. This paper deals with the optimal design of a degradation experiment where the degradation rate follows a log-logistic distribution. Under the constraint that the total experimental cost does not exceed a predetermined budget, the optimal decision variables are obtained by minimizing the mean squared error of the estimated 100pth percentile of thelifetime distribution of the product. A simulation study and a real example of drug potency data are provided to illustrate the proposed method.


Transport ◽  
2020 ◽  
Vol 35 (3) ◽  
pp. 283-299
Author(s):  
Ronghan Yao ◽  
Wensong Zhang ◽  
Meng Long

Left-turn bays are often installed on the road segment between paired intersections. Such left-turn bays may reduce the approach capacities and impact on one another. Four optimization models are put forward for uncoordinated paired intersections with left-turn bays. The phase effective green times and the left-turn bay lengths are the decision variables, maximizing the intersection capacities, minimizing the intersection delays and both of them are respectively regarded as different objective functions, and minimizing the total delay for paired intersections is viewed as another objective function. The total capacity-to-delay ratio is defined to evaluate the operations of paired intersections as a whole. Using the field data, the sensitivities of the optimized outcomes to the weighting factors of the objective functions are analysed. To clarify the influences of different scenarios on traffic stream operations, seven scenarios are tested using VISSIM. The interval estimation and hypothesis testing are used to analyse the simulated data. Three concrete models are recommended to apply in practice with the procedure of model application being provided. The achievements can be applied to optimally assign the temporal-spacial resources for paired intersections when left-turn bays need to be installed and coordinated signals do not need to be considered.


2019 ◽  
Vol 13 (4) ◽  
pp. 787-803
Author(s):  
Maurizio Faccio ◽  
Mojtaba Nedaei ◽  
Francesco Pilati

Purpose The current study aims to propose a new analytical approach by considering energy consumption (EC), maximum tardiness and completion time as the primary objective functions to assess the performance of parallel, non-bottleneck and multitasking machines operating in dynamic job shops. Design/methodology/approach An analytical and iterative method is presented to optimize a novel dynamic job shop under technical constraints. The machine’s performance is analyzed by considering the setup energy. An optimization model from initial processing until scheduling and planning is proposed, and data sets consisting of design parameters are fed into the model. Findings Significant variations of EC and tardiness are observed. The minimum EC was calculated to be 141.5 hp.s when the defined decision variables were constantly increasing. Analysis of the optimum completion time has shown that among all studied methods, first come first served (FCFS), earliest due date (EDD) and shortest processing time (SPT) have resulted in the least completion time with a value of 20 s. Originality/value Considerable amount of energy can be dissipated when parallel, non-bottleneck and multitasking machines operate in lower-power modes. Additionally, in a dynamic job shop, adjusting the trend and arrangement of decision variables plays a crucial role in enhancing the system’s reliability. Such issues have never caught the attention of scientists for addressing the aforementioned problems. Therefore, with these underlying goals, this paper presents a new approach for evaluating and optimizing the system’s performance, considering different objective functions and technical constraints.


2021 ◽  
Author(s):  
Israel Mayo-Molina ◽  
Juliana Y. Leung

Abstract The Steam Alternating Solvent (SAS) process has been proposed and studied in recent years as a new auspicious alternative to the conventional thermal (steam-based) bitumen recovery process. The SAS process incorporates steam and solvent (e.g. propane) cycles injected alternatively using the same configuration as the Steam-Assisted Gravity-Drainage (SAGD) process. The SAS process offers many advantages, including lower capital and operational cost, as well as a reduction in water usage and lower Greenhouse Gas (GHG) Emissions. On the other hand, one of the main challenges of this relatively new process is the influence of uncertain reservoir heterogeneity distribution, such as shale barriers, on production behaviour. Many complex physical mechanisms, including heat transfer, fluid flows, and mass transfer, must be coupled. A proper design and selection of the operational parameters must consider several conflicting objectives. This work aims to develop a hybrid multi-objective optimization (MOO) framework for determining a set of Pareto-optimal SAS operational parameters under a variety of heterogeneity scenarios. First, a 2-D homogeneous reservoir model is constructed based on typical Cold lake reservoir properties in Alberta, Canada. The homogeneous model is used to establish a base scenario. Second, different shale barrier configurations with varying proportions, lengths, and locations are incorporated. Third, a detailed sensitivity analysis is performed to determine the most impactful parameters or decision variables. Based on the results of the sensitivity analysis, several objective functions are formulated (e.g., minimizing energy and solvent usage). Fourth, Response Surface Methodology (RSM) is applied to generate a set of proxy models to approximate the non-linear relationship between the decision variables and the objective functions and to reduce the overall computational time. Finally, three Multi-Objective Evolutionary Algorithms (MOEAs) are applied to search and compare the optimal sets of decision parameters. The study showed that the SAS process is sensitive to the shale barrier distribution, and that impact is strongly dependent on the location and length of a specific shale barrier. When a shale barrier is located near the injector well, pressure and temperature may build up in the near-well area, preventing additional steam and solvent be injected and, consequently, reducing the oil production. Operational constraints, such as bottom-hole pressure, steam trap criterion, and bottom-hole gas rate in the producer, are among various critical decision variables examined in this study. A key conclusion is that the optimal operating strategy should depend on the underlying heterogeneity. Although this notion has been alluded to in other previous steam- or solvent-based studies, this paper is the first to utilize a MOO framework for systematically determining a specific optimal strategy for each heterogeneity scenario. With the advancement of continuous downhole fibre-optic monitoring, the outcomes can potentially be integrated into other real-time reservoir characterization and optimization work-flows.


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