Multiple sourcing under supplier failure risk and quantity discount: A genetic algorithm approach

Cell formation problem mainly addresses how machines should be grouped and parts be processed in cells. In dynamic environments, product mix and demand are changed in each period of the planning horizon. Incorporating such assumption in the model increases flexibility of the system to meet customers' requirements. In this model, to ensure the reliability of the system in presence of unreliable machines, alternative routing process as well as buffer storage are considered to reduce detrimental effects of machine failure. This problem is presented by a nonlinear mixed integer programming model attempting to minimize the overall cost of the system. To solve the model in large scale for practical purposes, a genetic algorithm approach is adopted as the model belongs to NP-hard class of problems. Sensitivity analysis is used to show the validity of the proposed model. Besides, numerical examples are used both, for small-sized and large- sized instances to show the efficiency of the method in finding near optimal solution.

Constant increase in urban road traffic is forcing traffic authorities to confront unavoidable congestion problems these days. This creates new challenges for city planners to generate traffic routes with better designs and improve the existing roads. In order to analyze and improve traffic routes, there is a need to understand movement patterns of major vehicular traffic inside the city. Origin Destination(OD) estimation is one such method for understanding the movement patterns. The objective is to find an optimal OD matrix for city traffic, which is a subtle process for classic algorithms. The solution to this problem is Genetic Algorithm (GA) approach which is a search heuristics to find optimal solution from a set of random solutions. A Genetic Algorithm approach has been developed to find an optimal OD matrix, showing the actual travel patterns of significant number of vehicles inside the city. Once the best OD matrix is obtained, it yields a big opportunity for traffic planners to analyze and improve traffic scenario. Genetic Algorithm can play a major role in solving complex problems. In this paper, one such problem of estimating OD matrix of a city is discussed and implemented. In conjunction to genetic algorithm, Mean Absolute Percentage Error(MAPE) has been used as a fitness criteria for finding the optimal OD matrix.

This study deals with estimation of the total and industrial sector electricity consumption based on genetic algorithm (GA) approach, and then proposes two scenarios to project future consumptions. Total electricity consumption is estimated based on gross national product (GNP), population, import and export figures of Turkey. Industrial sector electricity is calculated based on the GNP, import and export figures. Three forms of the genetic algorithm electricity demand (GAED) models for the total and two forms for the industrial electricity consumption are developed. The best-fit GAED model in terms of total minimum relative average errors between observed and estimated values is selected for future demand estimation. ‘High- and low-growth scenarios’ are proposed for predicting the future electricity consumption. Results showed that the GAED estimates the electricity demand in comparison with the other electricity demand projections. The GAED model plans electricity demand of Turkey until 2020. Copyright © 2005 John Wiley & Sons, Ltd.

The application of genetic algorithms in behavioural ecology, illustrated with a model of anti-predator vigilance

A bi-level optimization model is proposed for locating billboards on road network links in cities. Since billboard locations are largely driven by the flow on the underlying network, factors that impact traffic considerations of users are accounted for, including link congestion and road link pricing. Safety aspects associated with billboard distraction to users of the network are also incorporated within the proposed Mixed Integer Non-Linear Programming (MINLP) model. The model is multi-objective in nature, and it is solved through adopting the augmented ε -constraint method to obtain a sample of non-dominated points on the Pareto front. Due to the non-convexity induced by the bi-level structure of the model, a model reformulation scheme based on the use of equilibrium conditions is presented. A linearization scheme is also adopted that involves the introduction of mixed integer variables.

Global optimization of multiscenario mixed integer nonlinear programming models arising in the synthesis of integrated water networks under uncertainty

Design of two-dimensional FIR digital filters for sampling structure conversion by genetic algorithm approach

Clinching is a convenient and efficient cold forming process that can join two sheets without any additional part. This study establishes an intelligent system for optimizing the clinched joint. Firstly, a mathematical model which introduces the ductile damage constraint to prevent cracking during clinching process is proposed. Meanwhile, an optimization methodology and its corresponding computer program are developed by integrated finite element model (FEM) and genetic algorithm (GA) approach. Secondly, Al6061-T4 alloy sheets with a thickness of 1.4mm are used to verify this optimization system. The optimization program automatically acquires the largest axial strength which is approximately equal to 872N. Finally, sensitivity analysis is implemented, in which the influence of geometrical parameters of clinching tools on final joint strength is analyzed. The sensitivity analysis indicates the main parameters to influence joint strength, which is essential from an industrial point of view.

Design and optimization of rudder bulb based on CFD and genetic algorithm

Last-mile delivery is an important part of a logistics activity in the city. Usually, delivery workers are required to manually unload goods at customer locations. These manual tasks induce physiological fatigue in the workers and increase delivery time. This paper discusses a genetic algorithm (GA) approach to the open vehicle routing problem with split delivery (SDOVRP), where manual unloading is addressed. The workers are pre-assigned to vehicle and split delivery is allowed. Its objective is to minimize the total cost of total fixed cost of vehicles and delivery workers and total transportation cost. For safety, the total physical workload imposed on each worker must not exceed the daily limit. Since an optimization approach cannot find the optimal solution within reasonable computation time especially when solving large size problem. A GA with heuristic for pre-determine split delivery is developed to solve the problem. The computational experiment results show that the GA approach is efficient and can obtain near-optimal SDOVRP solutions.

In this paper, an effective genetic algorithm (GA) approach is proposed for tuning the parameters of membership functions based on input-output pairs. By minimizing a quadratic measure of the error in the least-squares sense, the real-valued chromosomes of a population are evolved to get the best coefficients. Comparison to the well-known back-propagation algorithm for fuzzy logic system shows that both are powerful training algorithms, but much better performance is obtained with the proposed technique. Several numerical design examples are presented to demonstrate the efficiency and effectiveness of this proposed approach.

To solve the problem of long logistics delivery time in supply chain, a Mixed Integer Non-linear Program (MINLP) model is built by using Mixed Integer nonlinear programming theory. Firstly, the General algebraic modeling system (GAMS) is used to build the model to fully integrate each parameter of logistics transportation, the total distribution time of the supply chain network, the coverage radius of the logistics base, the number of users, the total capacity of the logistics base, the mode of railway and road transportation, the nonlinear programming model is built and solved by DICOPT solver in GAMS. The cost of logistics can be decreased, transportation time can be reduced, and the logistics system's operating efficiency can be increased in the long term with the help of this algorithm. The proper operation of the logistics system is critical in encouraging the supply chain circulation of various industries and has a direct impact on the society's economic development. The optimal logistics distribution plan with 5 logistics bases covered users of 18 and railway capacity of 2. With the same railway capacity and the same total budget, the larger the number of covered users, the greater the total distribution time increases, but the larger the total budget, the growth of the total distribution time slows down significantly. Experiments show that MINLP model can solve the problem of logistics-based layout optimization in nonlinear logistics management.

Optimising crop planning in conjunction with intra-seasonal water allocation necessitates the use of daily water budget calculations to determine the timing and amount of irrigation events, which complicates the solution of the problem to global optimality. The main objective of this research was to compare the intra-seasonal water allocation of a mixed integer nonlinear programming (MINLP) model with that of differential evolution (DE), to allocate a limited amount of water while considering irrigable area and the irrigation schedule that will maximise the total gross margin. Results show that both solution procedures adhere to economic theory of water allocation under limited water supply. The conclusion is that the MINLP model most likely achieved very near global optimality as the solutions of the two models were very close to each other. DE holds promise to solve more complex models involving risk and multiple crops.

Sonophotocatalytic treatment of AB113 dye and real textile wastewater using ZnO/persulfate: Modeling by response surface methodology and artificial neural network

A new, R-graph based, superstructure and corresponding MINLP model for designing conventional distillation columns are presented. A GDP representation (GR) of the superstructure is first constructed, then it is transformed to MINLP representation to which, in turn, additional trivial improvements are added. The new model has been tested on binary mixture examples, and the obtained results are compared to the results of an MINLP model which developed according to the GDP model of Yeomans and Grossmann. 9 The new model yields shorter computation time and provides better local optima. Additionally, the new model has been used for optimizing a complex multicomponent separation system consisting of several distillation columns. In order to handle such a complex system with a huge number of nonlinear equations, the outer approximation algorithm is modified to provide good initial values for the NLP subproblems. Distillation is one of the most widespread processes applied for separating multicomponent liquid mixtures. It is used for working up large volume or stream, and it requires high investment and operation outlays. The significance of the design of economically optimal distillation processes is of no question. Enormous interest has also been addressed to the area of designing optimal heat integrated distillation columns and distillation sequences. Minimizing the cost of a distillation process implies finding the optimal configuration of each individual column, as well. In the present article we consider staged column models only. The number of stages, and the stage numbers of the feed and side-stream points, are discrete decision variables. The total cost of a column may be modeled as the sum of the fix (capital) cost, depending on the number of stages and on the column diameter, and the variable (operation) cost related to the utility consumption. The objective of the design procedure is to find the optimal configuration of the column, which has the minimum total (annualized) cost. In order to model these processes, discrete decisions are required for calculating the number of stages. Optimizing single columns is a well-known procedure; all the basic textbooks outline how to do it in an easy manner. 1 After approximately determining the minimum and the estimated optimal number of theoretical stages, optimizing over the continuous variables is performed at varied values of the discrete variables. This is a 2-dimension discrete array of continuous optimization tasks in the case of a single-feed, two-product column, because there are merely two column sections in this case. This task becomes much more difficult if several feeds and side-products are to be taken into account. The real problem, however, is synthesizing a distillation sequence, or a system of advanced distillation columns, or a complex flowsheet containing distillation units when the number of distillation columns and their connections are not known in advance. In order to solve the complex synthesis problem outlined above, a proper superstructure for a single column, together with a proper generalized disjunctive programming (GDP) model or a proper mixed-integer nonlinear programming (MINLP) model, is a minimum requirement. Once such a model works well for a single column, the problem of more complex flowsheets may also be addressed. Mixed-integer nonlinear programming (MINLP) and generalized disjunctive programming (GDP) are the two exact methodologies commonly applied for solving process engineering problems with discrete decisions. The former includes algebraic equations describing the process, and binary variables related to discrete decisions. The latter method uses logic variables and expressions to represent the problem. 2 Both formulations have been successfully applied to rigorous models of distillation columns. Both methods apply a fixed maximum number of stages, and the actually used stages are selected from this set. Mathematical formulations that represent rigorous models of distillation column configurations fall into two categories: (i) one task-one equipment (OTOE) representations and (ii) variable task-equipment (VTE) representations. 3