Reza Hassanzadeh

A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths

Abstract We are concerned with the design of a model and an algorithm for computing the shortest path in a network having various types of fuzzy arc lengths. First, a new technique is devised for the addition of various fuzzy numbers in a path using α -cuts by proposing a least squares model to obtain membership functions for the considered additions. Due to the complexity of the addition of various fuzzy numbers for larger problems, a genetic algorithm is presented for finding the shortest path in the network. For this, we apply a recently proposed distance function for comparison of fuzzy numbers. Examples are worked out to illustrate the applicability of the proposed approach.

A genetic algorithm for optimization problems with fuzzy relation constraints using max-product composition

We consider nonlinear optimization problems constrained by a system of fuzzy relation equations. The solution set of the fuzzy relation equations being nonconvex, in general, conventional nonlinear programming methods are not practical. Here, we propose a genetic algorithm with max-product composition to obtain a near optimal solution for convex or nonconvex solution set. Test problems are constructed to evaluate the performance of the proposed algorithm showing alternative solutions obtained by our proposed model.

A bi-objective stochastic programming model for optimising automated material handling systems with reliability considerations

The optimisation of material handling systems (MHSs) can lead to substantial cost reductions in manufacturing systems. Choosing adequate and relevant performance measures is critical in accurately evaluating MHSs. The majority of performance measures used in MHSs are time-based. However, moving materials within a manufacturing system utilise time and cost. In this study, we consider both time and cost measures in an optimisation model used to evaluate an MHS with automated guided vehicles. We take into account the reliability of the MHSs because of the need for steadiness and stability in the automated manufacturing systems. Reliability is included in the model as a cost function. Furthermore, we consider bi-objective stochastic programming to optimise the time and cost objectives because of the uncertainties inherent in the optimisation parameters in real-world problems. We use perceptron neural networks to transform the bi-objective optimisation model into a single objective model. We use numerical experiments to demonstrate the applicability of the proposed model and exhibit the efficacy of the procedures and algorithms.

A modified ant colony system for finding the expected shortest path in networks with variable arc lengths and probabilistic nodes

Abstract The problem of finding the expected shortest path in stochastic networks, where the presence of each node is probabilistic and the arc lengths are random variables, have numerous applications, especially in communication networks. The problem being NP-hard we use an ant colony system (ACS) to propose a metaheuristic algorithm for finding the expected shortest path. A new local heuristic is formulated for the proposed algorithm to consider the probabilistic nodes. The arc lengths are randomly generated based on the arc length distribution functions. Examples are worked out to illustrate the applicability of the proposed approach.

A genetic optimization algorithm and perceptron learning rules for a bi-criteria parallel machine scheduling

This work considers scheduling problems minding the setup and removal times of jobs rather than processing times. For some production systems, setup times and removal times are so important to be considered independent of processing times. In general, jobs are performed according to the automatic machine processing in production systems, and the processing times are considered to be constant regardless of the process sequence. As the human factor can influence the setup and removal times, when the setup process is repetitive the setup times decreases. This fact is considered as learning effect in scheduling literature. In this study, a bi-criteria m-identical parallel machines scheduling problem with learning effects of setup and removal times is considered. The learning effect is proposed using a perceptron neural network algorithm. The objective function of the problem is minimization of the weighted sum of total earliness and tardiness. A mathematical programming model is developed for the problem, which is NP-hard. Results of computational tests show that the LINGO 9 software is effective in solving problems with up to 25 jobs and five machines. Therefore, for larger sized problems, a genetic algorithm for optimization is developed.

A Novel Approach for Finding a Shortest Path in a Mixed Fuzzy Network

We present a novel approach for computing a shortest path in a mixed fuzzy network, network having various fuzzy arc lengths. First, we develop a new technique for the addition of various fuzzy numbers in a path using -cuts. Then, we present a dynamic programming method for finding a shortest path in the network. For this, we apply a recently proposed distance function for comparison of fuzzy numbers. Four examples are worked out to illustrate the applicability of the proposed approach as compared to two other methods in the literature as well as demonstrate the novel feature offered by our algorithm to find a fuzzy shortest path in mixed fuzzy networks with various settings for the fuzzy arc lengths.

Lot streaming in a two-stage assembly hybrid flow shop scheduling problem with a work shift constraint

We address the two-stage assembly scheduling problem where there are m machines at the first stage and n assembly machines at the second stage under lot sizing environment. Lot streaming (lot sizing) means breaking a lot into some sublots, where each sublot is transferred to the next machine for continuing operations. This problem can be considered as a production system model consisting of production stage and assembly stage. If different production operations are done in parallel machines independently, then the manufactured parts transferred to the next stage are assembled with purchased parts at n machines according to the operation process chart to produce the final products. Here, work-in-process inventories, work shifts, and sequence-dependent setup times are also considered as three important presumptions in order to make the problem more realistic. The objective is to minimize the sum of weighted completion times of products in each shift in order to furnish better machine utilization for the next shifts. In recent years, much effort has been made to develop good heuristics and search techniques. We propose a genetic algorithm and simulated annealing to compute the best sequence and scheduling for a two-stage assembly hybrid flow shop problem. Our numerical results demonstrate the effectiveness of the presented model and the proposed solution approach.

Applying fuzzy stochastic programming for multi-product multi-time period production planning

This paper presents an integration of fuzzily imprecise and probabilistically uncertain data in multi-time period production planning problem. We consider fluctuation of demands and resources by a fuzzy stochastic approach due to incomplete and/or unavailable information. A mathematical programming model that incorporates these aspects of uncertainty with grading products based on different qualities is developed to maximize total profit, considering total costs includes cost of production, outsourcing, labor, and holding, with subject to constraints associated with customer satisfaction, demand, and holding inventory. We also extend a new approach of defuzzifying and derandomizing methods by measuring the superiority and inferiority of the fuzzy stochastic variables when the model has fuzzy stochastic parameters both in the constraints and in the objective function. To illustrate the behavior of the proposed model and verify the performance of the developed fuzzy stochastic-based approach, we introduce a number of numerical examples to explain the use of the foregoing approach. Consequently, the results obtained are reported and discussed.

Reserve Capacity of Mixed Urban Road Networks, Network Configuration and Signal Settings

The authors formulate the transportation mixed network design problem (MNDP) as a mixed-integer bi-level mathematical problem, based on the concept of reserve capacity. The upper level goal is to maximize the reserve capacity by signal settings at intersections, determine street direction and increase street capacities via addition of lanes. The lower level problem is a deterministic user equilibrium traffic assignment problem to minimize the user travel time. The model being non-convex, meta-heuristic methods are used to solve the problem. A hybridization of genetic algorithm with simulated annealing and a bee algorithm are proposed. Numerical examples are illustrated to verify the effectiveness of the proposed model and the algorithms. KEywoRd Bee Algorithm, Bi-Level Programming, Hybrid Genetic Algorithm, Mixed Road Network Design Problem, Reserve Capacity

Genetic Algorithm for Solving Fuzzy Shortest Path Problem in a Network with mixed fuzzy arc lengths

We are concerned with the design of a model and an algorithm for computing a shortest path in a network having various types of fuzzy arc lengths. First, we develop a new technique for the addition of various fuzzy numbers in a path using α ‐cuts by proposing a linear least squares model to obtain membership functions for the considered additions. Then, using a recently proposed distance function for comparison of fuzzy numbers. we propose a new approach to solve the fuzzy APSPP using of genetic algorithm. Examples are worked out to illustrate the applicability of the proposed model.