Computational Methods in Engineering

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Many important problems in Artificial Intelligence can be defined as Constraint Satisfaction Problems (CSP). These types of problems are defined by a limited set of variables, each having a limited domain and a number of Constraints on the values of those variables (these problems are also called Consistent Labeling Problems (CLP), in which “Labeling means assigning a value to a variable.) Solution to these problems is a set of unique values for variables such that all the problem constraints are satisfied. Several search algorithms have been proposed for solving these problems, some of which reduce the need for backtracking by doing some sort of looking to future, and produce more efficient solutions. These are the so-called Forward Checking (FC), Partially Lookahead (PL), and Fully Lookahead (FL) algorithms. They are different in terms of the amount of looking to the future, number of backtracks that are performed, and the quality of the solution that they find. In this paper, we propose a new search algorithm we call Modified Fully Lookahead (MFL) which is Shown to be more efficient than the original Fully Lookahead algorithm

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A special class of the knapsack problem is called the separable nonlinear knapsack problem. This problem has received considerable attention recently because of its numerous applications. Dynamic programming is one of the basic approaches for solving this problem. Unfortunately, the size of state-pace will dramatically increase and cause the dimensionality problem. In this paper, an efficient algorithm is developed to find surrogate multipliers in each stage of dynamic programming in order to transform the original problem to a single constraint problem called surrogate problem. The upper and lower bounds obtained by solving the surrogate problem can eliminate a large number of state variables in dynamic programming and extremely reduce the duality gap according to our computational results.

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Mobile robotic systems, which include a mobile platform with one or more manipulators, mounted at specific locations on the mobile base, are of great interest in a number of applications. In this paper, after thorough kinematic studies on the platform and manipulator motions, a systematic methodology will be presented to obtain the dynamic equations for such systems without violating the base nonholonomic constraints. Combining the kinematic model with the initial dynamic equations and eliminating Lagrange multiplier with natural orthogonal complement technique lead to the comprehensive dynamic model. The variables of this model include the path of a reference point of the base and the position and orientation of the end-effector. The proposed approach will be applied on a car-like platform and a manipulator with 5 degrees-of freedom. The calculations for deriving such a model will be implemented by a program in Maple which can be used for control design and simulation purposes. The validity of the methodology is demonstrated using a second model and comparing the elements of these two models with each other. With trajectory generation for platform and manipulator generalized coordinates separately, set points for control system design will be provided. Motion generation for the platform, which due to the nonholonomic constraint has more sensitivity, will be dealt with by two motion modes. Inverting the model in terms of joint space variables, strict control of the work space variables is accomplished. Introducing state space variables and inverting the system into first order equations, the necessary preliminaries for control system design will be provided. Based on two simulation programs in Matlab, two controllers are designed with model-based algorithm (MBA) and Transposed Jacobian (TJ) control. Simulating different external conditions such as parameter perturbation, disturbances and noise, the robotic system behavior in the vicinity of real conditions will be examined. The results obtained show the merits of the TJ algorithm in controlling highly nonlinear and complex systems with multiple degrees- of freedom (DOF), without requiring a priori knowledge of plant dynamics, and with reduced computational burden which motivates further work on this algorithm

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A novel version of Ant Colony Optimization (ACO) algorithms for solving continuous space problems is presented in this paper. The basic structure and concepts of the originally reported ACO are preserved and adaptation of the algorithm to the case of continuous space is implemented within the general framework. The stigmergic communication is simulated through considering certain direction vectors which are memorized. These vectors are normalized gradient vectors that are calculated using the values of the evaluation function and the corresponding values of object variables. The proposed Gradient-based Continuous Ant Colony Optimization (GCACO) method is applied to several benchmark problems and the results are compared and contrasted with other population-based algorithms such as Evolutionary Strategies (ES), Evolutionary Programming (EP), and Genetic Algorithms (GA). The results obtained from GCACO compare satisfactorily with those of other algorithms and in some cases are superior in terms of accuracy and computational demand.

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Active vehicle suspension system is designed to increase the ride comfort and road holding of vehicles. Due to limitations in the external force produced by actuator, the design problem encounters the constraint on the control input. In this paper, a novel nonlinear controller with the input constraint is designed for the active suspension system. In the proposed method, at first, a constrained multi-objective optimization problem is defined. In this problem, a performance index is defined as a weighted combination of the predicted responses of the nonlinear suspension system and control input. Then, this problem is solved by the modified firefly optimization algorithm to find the constrained optimal control input. To evaluate the performance of the proposed method, the results of the unconstrained and constrained controllers are provided and discussed for various road excitations. The results show a remarkable increase in the ride comfort with the limited force, while other suspension outputs including the suspension travel and tire deflection being in the acceptable ranges. In addition, these controllers are compared with Sliding Mode Control (SMC) and Nonlinear Model Predictive Control (NMPC) in the presence of model uncertainty.

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In this paper, a multi-mode resource constrained project selection and scheduling problem is investigated considering the reinvestment strategy in a flexible time horizon. Among a set of available projects, a number of projects are selected and scheduled regarding the constraints on renewable resources and precedence relations. The benefits of project portfolio selection and scheduling are compared in both fixed and flexible time horizons. For this purpose, upper and lower tolerance limits are considered for the predetermined time horizon. If the schedule exceeds the time horizon, a penalty cost will be charged. The objective is to determine the optimal time horizon. A mixed-integer linear programming model is proposed for this problem, and solved by GAMS software/CPLEX solver and also a combination of a proposed heuristic algorithm, Genetic Algorithm, and a local search method. Numerical results show that the proposed approach has an acceptable performance in terms of the quality of the solution and the running time. Also, dealing with the problem in a flexible time horizon is more profitable compared to a fixed time horizon.