We obtain some new common fixed point theorems satisfying a weak contractive condition in the framework of partially ordered metric spaces. The main result generalizes and extends some known results given by some authors in the literature.
IntroductionAs part of an industrial manufacturing system, installing an assembly line is a costly decision and requires a considerable time for execution and therefore it is important to be well designed and properly balanced to guarantee maximum efficiency in operation.An important assembly design problem is the assembly line balancing (ALB) problem. This decisional problem is a classic Operations Research (OR) optimization problem that aims to determine the allocation of the tasks to an ordered sequence of workstations such that every task is assigned at just one station, the precedence relations are not violated and certain objectives are fulfilled.Since the bin-packing problem, which is an ALB problem without precedence constraints [5], is NP-hard, even the simple case of the ALB problem is NP-hard by nature. Indeed, m tasks and r preference constraints generate m!/2r feasible solutions of the problem [2], as there are m!/2r possible task sequences. As one can observe, the problem size grows very rapidly with the number of tasks and/or workstations.Because of the high computational complexity, conventional optimization methods do not seem appropriate for this simple or multi-objective practical optimization problem.Due to the complexity of the ALB problem and its practical importance for industrial applications, many approaches based on metaheuristics such as Tabu Search, Simulated Annealing, Evolutionary Algorithms, Agent -based approaches (Ant Colony Optimization and Particle Swarm Optimization) or hybrid Artificial Intelligence methods have been applied recently in attempts to solve this manufacturing optimization problem. A survey study of soft computing applications in ALB problems is presented in [15]. Other comprehensive reviews of assembly systems and different balancing problems are presented in [2].This study proposes a model and a solution approach to a multi-objective ALB problem considering three evaluation criteria. This multi-objective problem is solved by a discrete PSO algorithm whose efficiency is enhanced due to the development of a fuzzy controller for tuning inertia weight. Assembly Line Balancing (ALB) Problems: Basic Concepts and TypologiesAssembly lines are production lines consisting of several consecutive workstations (i=1,...,m) located along a conveyor belt that transports the production units through the line with a constant transportation speed. Abstract: The Assembly Line Balancing problem is an industrial optimization problem of considerable importance in lean systems. It has been extensively studied in literature through classical optimization methods. However, conventional computing paradigms have not proved practical utility for complex problems. Metaheuristic solutions such as "Tabu Search", "Simulated Annealing", "Genetic Algorithms", "Evolutionary Programming", "Ant Colony", "Particle Swarm Optimization" were a preoccupation mainly for the last two decades. This paper presents a model of a multi-objective Assembly Line Balancing problem and a solution approach based on ...
This paper aims to develop a new Genetic Algorithm based approach to solve the Combined Environmental Economic Power Dispatch Problem. The essential features of our proposed algorithm include a diploid based complex-encoding with meiosis specific attributes and new mutation operators that performs global search during the initial generations and local search in the later generations. Using the parallel searching mechanism and the new defined mutation operators, the local searching ability of the algorithm is improved, as well as the algorithm's efficiency.Results of comparative tests on a sample power system are presented, showing the better computation efficiency and convergence property of the proposed methodology.
Abstract. This paper presents an improved Genetic Algorithm to solve the Transportation Network Design Problem (CTNDP) with interactions among different links. The CTNDP is formulated in an optimal design as a bi-level programming model. A key factor in the present approach is the combination of diploid based complex-encoding with meiosis specific features. The novel mutation operator proposed is another improvement that leads to a better robustness and convergence stability.The computational results obtained by comparing the performance of the proposed algorithm and other Genetic Algorithms for a test network demonstrates its better local searching ability, as well as its high efficiency.Finally, suggestions for further research and extensions are given.Key words: Genetic Algorithm, bi-level programming, Network Design Problem, complex-encoding. The Transportation Network Design Problem -general descriptionThe Transportation Network Design Problem (TNDP) involves optimal decisions in determining a set of design parameters for improving an existing transportation network in response to an increasing level of traffic demand. The general increase in flow level results in traffic congestion, delays, higher fuel and maintenance costs, air pollution and accidents. The improvements of a transportation network, such as expansion of the capacities of the existing congested links, addition or deletion of links, traffic signal control adjustment, are made in accordance with a system optimum while considering the travel and route choice behavior of network users. The system optimum usually represents the minimization of the total travel time and construction costs.The network user's decisions correspond to a set of nonlinear relations that are formulated as an independent mathematical programming problem.In fact, a transportation network improvement involves the interaction of two parties with own objectives: the network planner represented by the transportation system authority and the network users that use the provided services. The traffic authority tries to optimize some overall objectives in the network, while the network users try to minimize their travel times/costs or perceived travel times/costs.The decision variables of the network planner affect the route choice behavior of network users which is based on two equilibrium principles:-the deterministic user equilibrium (DUE) condition [1] wherein network users choose the route with the shortest travel time/ the lower travel cost and equilibrium is reached where no user can unilaterally change routes to improve his/her own travel time or cost; assumptions of DUE can be somewhat unrealistic because of the variations in network conditions, variations in demand and no perfect information available for network users; -the stochastic user equilibrium (SUE) condition [2] where no user can unilaterally change routes to improve his/her own perceived travel time or cost; SUE may reflect travelers' behavior more realistically than DUE. One can consider that DUE is a special...
The goal of a Virtual Organization is to find the most appropriate partners in terms of expertise, cost wise, quick response, and environment. In this study we propose a model and a solution approach to a partner selection problem considering three main evaluation criteria: cost, time and risk. This multiobjective problem is solved by an improved GA that includes meiosis specific characteristics and step-size adaptation for the mutation operator. The algorithm performs strong exploration initially and exploitation in later generations. It has high global search ability and a fast convergence rate and also avoids premature convergence. On the basis of the numerical investigations, the incorporation of the proposed enhancements has been successfully proved.
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