Geometric Programming Subject to System of Fuzzy Relation Inequalities

In this paper, an optimization model with geometric objective function is presented. Geometric programming is widely used; many objective functions in optimization problems can be analyzed by geometric programming. We often encounter these in resource allocation and structure optimization and technology management, etc. On the other hand, fuzzy relation equalities and inequalities are also used in many areas. We here present a geometric programming model with a monomial objective function subject to the fuzzy relation inequality constraints with maxproduct composition. Simplification operations have been given to accelerate the resolution of the problem by removing the components having no effect on the solution process. Also, an algorithm and two practical examples are presented to abbreviate and illustrate the steps of the problem resolution

A Public Bicycle Sharing System Considering Renting and Middle Stations

Recently, public bicycle sharing system (PBSS) has become one of the most favorite urban transportation systems that can help governments to decrease environmental problems such as pollution and traffic. This paper studies a sharing system that includes two types of stations. The first category contains stations that users can rent or return back bicycles and each bicycle can be rented by any new user who arrives to the stations. The second group is the stations which are near shopping centers, historical and other places that users and tourists can stop and visit them. These stations are used only for parking the rented bicycles for a period of time and after that, the users must ride their bicycles and turn them back to their destination stations. After discussing the network of the model under the closed Jackson network, the Mean Value Analysis (MVA) method will be used to calculate the mean queue of each station and analyzing the proposed model

Approximate solution for quadratic Riccati differential equation

The quadratic Riccati differential equations are a class of nonlinear differential equations of much importance, and play a significant role in many fields of applied science. This paper introduces an efficient method for solving the quadratic Riccati differential equation and the Riccati differential-difference equation. In this technique, the Bezier curves method is considered as an algorithm to find the approximate solution of the nonlinear Riccati equation. Some examples in different cases are given to demonstrate simplicity and efficiency of the proposed method

Modification of some scalarization approaches for multiobjective optimization

In this paper, we propose revisions of two existing scalarization approaches, namely the feasible-value constraint and the weighted constraint. These methods do not easily provide results on proper efficient solutions of a general multiobjective optimization problem. By proposing some novel modifications for these methods, we derive some interesting results concerning proper efficient solutions. These scalarization approaches need no convexity assumption of the objective functions. We also demonstrate the efficiency of the proposed method using numerical experiments. In particular, a rocket injector design problem involving four objective functions illustrates the performance of the proposed method

MINIMIZING A LINEAR OBJECTIVE FUNCTION SUBJECT TO FUZZY RELATION EQUATIONS CONSTRAINTS WITH MAX-HAMACHER PRODUCT COMPOSITION

In this paper, an optimization model with a linear objective function subject to a system of fuzzy relation equations, using max-Hamacher product composition operator, is presented. Since its nonempty feasible solution set is in general a nonconvex set, conventional linear programming methods are not suitable to solve such a problem, so an efficient solution procedure for such problems is necessary. In this paper, the feasible solution set of this problem is studied at first. Then, one efficient algorithm (i.e. tabular method algorithm) is proposed in order to solve the problem. Some procedures are also presented to reduce the original problem. Then, the reduced problem is decomposed (if possible) into several sub-problems with smaller dimensions, so solving them becomes very easier by the algorithm. By combining the algorithm and these procedures, another more efficient algorithm is suggested in order to obtain the optimal solution of the original problem. Some numerical examples are also given to illustrate the algorithms.Fuzzy relation equation, max-Hamacher product composition, linear objective function minimization problem

A Hybrid Modified Ant Colony for Solving the Capacitated Open Vehicle Routing Problem

The vehicle routing problem (VRP) involves routing a fleet of vehicles for serving to a number of customers, with the objective of minimizing the total distance traveled by all the vehicles. In this Problem, the vehicles are required to return to the depot after completing service. The open vehicle routing problem (OVRP) is different from most variants of vehicle routing problems from the literature in that the vehicle does not return to the depot after serving the last customer. The constraints considered in this problem are the following: all the vehicles have the same capacity the traveling time of each vehicle should not exceed a given threshold, which is defined by the drivers_ legal traveling time the total demand of all the customers on a route must not exceed the capacity of the vehicle each customer is visited just once by one of the vehicles, and its requirements must be completely fulfilled. The ant colony system (ACS) is one of the most famous metaheuristic algorithms that differs from the other ant colony optimization (ACO) instances due to its transition rule and updating pheromone. Aimed at the disadvantages existed in the current ACS algorithms for solving the OVRP, two effective modificitions including heuristic information and transition rule are proposed in this paper. Furthermore, this algorithm is mixed with lin-kernigan local search for improving solutions of the ants and exploites more strong solutions. Computational results on sixteen standard benchmark problem instances show that the proposed algorithm is comparable in terms of solution quality to the best performing published heuristics

A hybrid modified meta-heuristic algorithm for solving the traveling salesman problem

Abstract The traveling salesman problem (TSP) is one of the most important combinational optimization problems that has nowadays received much attention because of its practical applications in industrial and service problems. In this paper, a hybrid twophase meta-heuristic algorithm called MACSGA used forsolving the TSPis presented. At the first stage, the TSP is solved by themodified ant colony system (MACS) in each iteration, and at the second stage, the modified genetic algorithm (GA) and 2-opt local searchare used for improving the solutions of the ants for that iteration. This process avoids the premature convergence and makes better solutions. Computational results on several standard instances of TSP show the efficiency of theproposedalgorithm comparedwith the GA, ant colony optimization and other meta-heuristic algorithms

A Cross-Efficiency Approach for Evaluating Decision Making Units in Presence of Undesirable Outputs

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