MSC Codes 05-XX COMBINATORICS, 90-XX OPERATIONS RESEARCH, MATHEMATICAL programmingWe present a proof system for establishing the correctness of results produced by optimization algorithms, with a focus on mixed-intege...
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The Sequential Approximate integer programming (SAIP) method successfully solves multiple types of large-scale topology optimization problems by solving a sequence of separable approximate integer programming subprobl...
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The Sequential Approximate integer programming (SAIP) method successfully solves multiple types of large-scale topology optimization problems by solving a sequence of separable approximate integer programming subproblems. However, these subproblems must be with quadratic/linear objective function with linear constraints to achieve an explicit analytical dual optimization problem that can be analytically solved by the Canonical Relaxation Algorithm (CRA). Besides, this SAIP must rely on the decreasing volume fraction strategy to stabilize the computation so that it owns difficulties to confront topology optimization problems without active volume constraints. The success of MMA (Method of Moving Asymptotic) inspires us to introduce the classical sequential conservative approximate programming that can generate a sequence of steadily improving feasible designs and present a Sequential Conservative integer programming (SCIP) method for the development of SAIP. This new method generates a sequence of nonlinear approximate integer programming subproblems containing the reciprocal variables, whose conservation is controlled by moving asymptotes. However, CRA is invalid due to the nonlinearity of subproblems. Instead of using the analytic primal-dual relation, a simple design variable update rule derived based on the KKT conditions is given to efficiently solve the nonlinear subproblems. The augmented Lagrange formulation is introduced for topology optimization problems with multiple constraints. Various requirements of topology optimization problems (compliant mechanisms) are handled, including equality or inequality constraints, and inactive or active volume constraints, which demonstrate the effectiveness of SCIP in dealing with topology optimization problems with non-volume constraint or containing multiple nonlinear constraints. Numerical results show that since the conservative property has been inherited, the convergence of the optimization process can be regulated
We consider robust submodular maximization problems (RSMs), where given a set of m monotone submodular objective functions, the robustness is with respect to the worst-case (scaled) objective function. The model we co...
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Multiobjective integer programs (MOIPs) simultaneously optimize multiple objective functions over a set of linear constraints and integer variables. In this paper, we present continuous, convex hull and Lagrangian rel...
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One cannot make truly fair decisions using integer linear programs unless one controls the selection probabilities of the (possibly many) optimal solutions. For this purpose, we propose a unified framework when binary...
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Rail traffic control has received increasing attention in recent years, due to the destructive disruptions caused by floods, fires and equipment failures, etc. In this paper, we propose a resilience-oriented train res...
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Scheduling the transfer of files in distributed computer systems is an increasing concern. The purpose of this paper is to propose a new time-index integer programming model for the file transfer scheduling problem wi...
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In this paper mass minimization of hysteretically damped structures subjected to static and time-harmonic loading is studied via the Topology Optimization of Binary Structures (TOBS) method. Elements are removed or ad...
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In this paper mass minimization of hysteretically damped structures subjected to static and time-harmonic loading is studied via the Topology Optimization of Binary Structures (TOBS) method. Elements are removed or added to the finite element model of a structure in every iteration based on the solution to an integer linear program (ILP). The ILP is constructed from the sensitivity information of the objective function and the constraints which are in the form of the static and dynamic compliance. The proposed methodology is demonstrated on a 2D clamped-clamped beam and compared with published results for a 2D cantilever beam. The optimization starts from the full design domain and solutions with low mass that fulfill the constraints for a range of different bounds are found. The results also indicate that the mass is much more sensitive to changes in the static compliance constraint than in the dynamic compliance constraint. The effect of mass and upper bound of the constraints on the dynamic compliance at the fundamental resonance frequency is also studied, though no clear conclusions can be drawn. Finally the sensitivity information at the converged topology is studied and it is shown that the algorithm converges because the structural regions that are non-critical for the different constraints do not overlap.
This paper presents an inertial neuro-dynamic system to solve zero-one integer programming. We transform the problem of zero-one integer programming into a relatively easy problem only subject to linear equality const...
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This paper addresses the problem of irregularity in polyomino tiling. An integer programming model for tiling with L-tromino and L-tetromino and a heuristic approach based on the Simulated Annealing are introduced. To...
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