Amir Azaron

Solving a dynamic cell formation problem using metaheuristics

In this paper, solving a cell formation (CF) problem in dynamic condition is going to be discussed by using some traditional metaheuristic methods such as genetic algorithm (GA), simulated annealing (SA) and tabu search (TS). Most of previous researches were done under the static condition. Due to the fact that CF is a NP-hard problem, then solving the model using classical optimization methods needs a long computational time. In this research, a nonlinear integer model of CF is first given and then solved by GA, SA and TS. Then, the results are compared with the optimal solution and the efficiency of the proposed algorithms is discussed.

A hybrid method for solving stochastic job shop scheduling problems

This paper presents a nonlinear mathematical programming model for a stochastic job shop scheduling problem. Due to the complexity of the proposed model, traditional algorithms have low capability in producing a feasible solution. Therefore, a hybrid method is proposed to obtain a near-optimal solution within a reasonable amount of time. This method uses a neural network approach to generate initial feasible solutions and then a simulated annealing algorithm to improve the quality and performance of the initial solutions in order to produce the optimal/near-optimal solution. A number of test problems are randomly generated to verify and validate the proposed hybrid method. The computational results obtained by this method are compared with lower bound solutions reported by the Lingo 6 optimization software. The compared results of these two methods show that the proposed hybrid method is more effective when the problem size increases.

Dynamic shortest path in stochastic dynamic networks: Ship routing problem

In this paper, we apply the stochastic dynamic programming to find the dynamic shortest path from the source node to the sink node in stochastic dynamic networks, in which the arc lengths are independent random variables with exponential distributions. In each node there is an environmental variable, which evolves in accordance with a continuous time Markovprocess. The parameter of the exponential distribution of the transition time of each arc is also a function of the state of the environmental variable of its initiative node. Upon arriving at each node, we can move toward the sink node through the best outgoing arc or wait. At the beginning, it is assumed that upon arriving at each node, we know the state of its environmental variable and also the states of the environmental variables of its adjacent nodes. Then we extend this assumption such that upon arriving at each node, we know the states of the environmental variables of all nodes. In the ship routing problem, which we focus in this paper, the environmental variables of all nodes are known, but it is shown that the complexity of the algorithm becomes exponential in this case. 2002 Elsevier Science B.V. All rights reserved.

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. 2005 Elsevier B.V. All rights reserved.

Improved estimation of electricity demand function by using of artificial neural network, principal component analysis and data envelopment analysis

Due to various seasonal and monthly changes in electricity consumption and difficulties in modeling it with the conventional methods, a novel algorithm is proposed in this paper. This study presents an approach that uses Artificial Neural Network (ANN), Principal Component Analysis (PCA), Data Envelopment Analysis (DEA) and ANOVA methods to estimate and predict electricity demand for seasonal and monthly changes in electricity consumption. Pre-processing and post-processing techniques in the data mining field are used in the present study. We analyze the impact of the data pre-processing and post-processing on the ANN performance and a 680 ANN-MLP is constructed for this purpose. DEA is used to compare the constructed ANN models as well as ANN learning algorithm performance. The average, minimum, maximum and standard deviation of mean absolute percentage error (MAPE) of each constructed ANN are used as the DEA inputs. The DEA helps the user to use an appropriate ANN model as an acceptable forecasting tool. In the other words, various error calculation methods are used to find a robust ANN learning algorithm. Moreover, PCA is used as an input selection method, and a preferred time series model is chosen from the linear (ARIMA) and nonlinear models. After selecting the preferred ARIMA model, the Mcleod-Li test is applied to determine the nonlinearity condition. Once the nonlinearity condition is satisfied, the preferred nonlinear model is selected and compared with the preferred ARIMA model, and the best time series model is selected. Then, a new algorithm is developed for the time series estimation; in each case an ANN or conventional time series model is selected for the estimation and prediction. To show the applicability and superiority of the proposed ANN-PCA-DEA-ANOVA algorithm, the data regarding the Iranian electricity consumption from April 1992 to February 2004 are used. The results show that the proposed algorithm provides an accurate solution for the problem of estimating electricity consumption.

Multi-objective time–cost trade-off in dynamic PERT networks using an interactive approach

Abstract We develop a multi-objective model for the time–cost trade-off problem in a dynamic PERT network using an interactive approach. The activity durations are exponentially distributed random variables and the new projects are generated according to a renewal process and share the same facilities. Thus, these projects cannot be analyzed independently. This dynamic PERT network is represented as a network of queues, where the service times represent the durations of the corresponding activities and the arrival stream to each node follows a renewal process. At the first stage, we transform the dynamic PERT network into a proper stochastic network and then compute the project completion time distribution by constructing a continuous-time Markov chain. At the second stage, the time–cost trade-off problem is formulated as a multi-objective optimal control problem that involves four conflicting objective functions. Then, the STEM method is used to solve a discrete-time approximation of the original problem. Finally, the proposed methodology is extended to the generalized Erlang activity durations.

Multi-objective reliability optimization for dissimilar-unit cold-standby systems using a genetic algorithm

A genetic algorithm approach is used to solve a multi-objective discrete reliability optimization problem in a k dissimilar-unit non-repairable cold-standby redundant system. Each unit is composed of a number of independent components with generalized Erlang distributions arranged in a series-parallel configuration. There are multiple component choices with different distribution parameters available for being replaced with each component of the system. The objective of the reliability optimization problem is to select the best components, from the set of available components, to be placed in the standby system in order to minimize the initial purchase cost of the system, maximize the system MTTF (mean time to failure), minimize the system VTTF (variance of time to failure) and also maximize the system reliability at the mission time. Finally, we apply a genetic algorithm with double strings using continuous relaxation based on reference solution updating (GADSCRRSU) to solve this multi-objective problem, using goal attainment formulation. The results are also compared against the results of a discrete-time approximation technique to show the efficiency of the proposed GA approach.

A multi-objective lead time control problem in multi-stage assembly systems using genetic algorithms

In this paper, we develop a multi-objective model to optimally control the lead time of a multi-stage assembly system, using genetic algorithms. The multi-stage assembly system is modelled as an open queueing network. It is assumed that the product order arrives according to a Poisson process. In each service station, there is either one or infinite number of servers (machines) with exponentially distributed processing time, in which the service rate (capacity) is controllable. The optimal service control is decided at the beginning of the time horizon. The transport times between the service stations are independent random variables with generalized Erlang distributions. The problem is formulated as a multi-objective optimal control problem that involves four conflicting objective functions. The objective functions are the total operating costs of the system per period (to be minimized), the average lead time (min), the variance of the lead time (min) and the probability that the manufacturing lead time does not exceed a certain threshold (max). Finally, we apply a genetic algorithm with double strings using continuous relaxation based on reference solution updating (GADSCRRSU) to solve this multi-objective problem, using goal attainment formulation. The results are also compared against the results of a discrete-time approximation technique to show the efficiency of the proposed genetic algorithm approach.

Reliability evaluation of multi-component cold-standby redundant systems

A new methodology for the reliability evaluation of an l-dissimilar-unit non-repairable cold-standby redundant system is introduced in this paper. Each unit is composed of a number of independent components with generalized Erlang distributions of lifetimes, arranged in any general configuration. We also extend the proposed model to the general types of non-constant hazard functions. To evaluate the system reliability, we construct a directed stochastic network with exponentially distributed arc lengths, in which each path of this network corresponds with a particular minimal cut of the reliability graph of system. Then, we present an analytical method to solve the resulting system of differential equations and to obtain the reliability function of the standby system. The time complexity of the proposed algorithm is O(2^n), which is much less than the standard state-space method with the complexity of O(3^n^^^2). Finally, we generalize the proposed methodology, in which the failure mechanisms of the components are different.

Modelling complex assemblies as a queueing network for lead time control

In this paper we develop an open queueing network for optimal design of multi-stage assemblies, in which each service station represents a manufacturing or assembly operation. The arrival processes of the individual parts of the product are independent Poisson processes with equal rates. In each service station, there is a server with exponential distribution of processing time, in which the service rate is controllable. The transport times between the service stations are independent random variables with exponential distributions. By applying the longest path analysis in queueing networks, we obtain the distribution function of time spend by a product in the system or the manufacturing lead time. Then, we develop a multi-objective optimal control problem, in which the average lead time, the variance of the lead time and the total operating costs of the system per period are minimized. Finally, we use the goal attainment method to obtain the optimal service rates or the control vector of the problem. 2005 Elsevier B.V. All rights reserved.