In this paper, the problem of maximizing the median of a convex combination of vectors having important applications in finance is considered. The objective function is a highly nonlinear, nondifferentiable function w...
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In this paper, the problem of maximizing the median of a convex combination of vectors having important applications in finance is considered. The objective function is a highly nonlinear, nondifferentiable function with many local minima and the problem was shown to be APX hard. We present two hybrid Large Neighborhood Search algorithms that are based on mixed-integer programs and include a time limit for their running times. We have tested the algorithms on three testbeds and showed their superiority compared to other state-of-the-art heuristics for the considered problem. Furthermore, we achieved a significant reduction in running time for large instances compared to solving it exactly while retaining high quality of the solutions returned. (C) 2012 Elsevier Ltd. All rights reserved.
An optimization study of reverse-osmosis networks (RON) for wastewater treatment has been carried Out by describing the system as a nonconvex mixed-integer nonlinear problem (MINLP). A mixed-integer linear problem (MI...
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An optimization study of reverse-osmosis networks (RON) for wastewater treatment has been carried Out by describing the system as a nonconvex mixed-integer nonlinear problem (MINLP). A mixed-integer linear problem (MILP) is derived from the original nonlinear problem by the convex relaxation of the nonconvex terms in the MINLP to provide bounds for the global optimum. The MILP model is solved iteratively to Supply different initial guesses for the nonconvex MINLP model. It is found that such a procedure is effective in finding local optimum solutions in reasonable time and overcoming possible convergence difficulties associated with MINLP local search methods. Examples of water desalination and wastewater treatment from the pulp and paper industry are considered as case Studies to illustrate the proposed solution Strategy. (C) 2007 Elsevier B.V All rights reserved.
The generalized vertex packing problem seeks to identify a largest subset of nodes from an undirected graph, such that the subgraph induced by this subset of nodes contains no more than some threshold number of edges....
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The generalized vertex packing problem seeks to identify a largest subset of nodes from an undirected graph, such that the subgraph induced by this subset of nodes contains no more than some threshold number of edges. This paper derives a class of valid inequalities based on certain special subgraphs called webs, which are general structures that subsume cliques, matchings, odd holes, and odd anti-holes. We also provide a set of conditions for this class of valid inequalities to be facet-inducing for the web subgraph polytope. Finally, we prescribe a web subgraph identification procedure. and test the computational benefits obtained by solving generalized vertex packing instances with formulations augmented by these web-based valid inequalities. (C) 2004 Elsevier B.V. All rights reserved.
In this paper, we present a novel formulation of the inverse kinematics (IK) problem with generic constraints as a mixed-integer convex optimization program. The proposed approach can solve the IK problem globally wit...
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In this paper, we present a novel formulation of the inverse kinematics (IK) problem with generic constraints as a mixed-integer convex optimization program. The proposed approach can solve the IK problem globally with generic task space constraints: a major improvement over existing approaches, which either solve the problem in only a local neighborhood of the user initial guess through nonlinear non-convex optimization, or address only a limited set of kinematics constraints. Specifically, we propose a mixed-integer convex relaxation of non-convex SO(3) rotation constraints, and apply this relaxation on the IK problem. Our formulation can detect if an instance of the IK problem is globally infeasible, or produce an approximate solution when it is feasible. We show results on a seven-joint arm grasping objects in a cluttered environment, an 18-degree-of-freedom quadruped standing on stepping stones, and a parallel Stewart platform. Moreover, we show that our approach can find a collision free path for a gripper in a cluttered environment, or certify such a path does not exist. We also compare our approach against the analytical approach for a six-joint manipulator. The open-source code is available at .
In this paper, we explore alternative solutions to the Capacitated Fixed Charge Facility Location problem (CFCFL) that usually arises in Supply Chain Network Design problems. More specifically, we aim to investigate i...
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In this paper, we explore alternative solutions to the Capacitated Fixed Charge Facility Location problem (CFCFL) that usually arises in Supply Chain Network Design problems. More specifically, we aim to investigate in which cases these solutions can be considered as good as the optimal one from the point of view of decision-making in real-world problems. A method, as well as four enhancement variations, based on a mixed-integer programming (MIP) model is proposed, which allows K-best alternative solutions to be obtained. The method and its variations were applied to two benchmark instance sets available in the literature and the computational times were evaluated. The results have shown that the gap between the optimal solutions and the 20-best alternative ones were, on average, less than 1%;more surprisingly, 63.8% of all these alternative solutions had a gap smaller than 0.5%. This suggests that our approach may be used to identify whether near-optimal alternative solutions can yield to a better overall solution from the point of view of the decision-maker, by allowing other qualitative attributes to be considered. We were also able to rate the robustness of some selected facilities since many candidates have appeared in all 20 best solutions. In addition, the results may also suggest a way to measure the difficulty of benchmark instances for combinatorial problems and thus enhance the comparison of different heuristics proposed to solve them;not to mention that the uncertainty in input data of such strategic problems may reduce the relevance of the effort to find the best solution in the contexts in which several high-quality solutions arise. (C) 2017 Elsevier Ltd. All rights reserved.
Station -based Bike -sharing systems have been implemented in multiple major cities, offering a low-cost and environmentally friendly transportation alternative. As a remedy to unbalanced stations, operators typically...
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Station -based Bike -sharing systems have been implemented in multiple major cities, offering a low-cost and environmentally friendly transportation alternative. As a remedy to unbalanced stations, operators typically rebalance bikes by trucks. The resulting dynamic planning has received significant attention from the Operations Research community. Due to its modeling flexibility, mixed -integerprogramming remains a popular choice. However, the complex planning problem requires significant simplifications to obtain a computationally tractable model. As a result, existing models have used a large variety of modeling assumptions and techniques regarding decision variables and constraints. Unfortunately, the impact of such assumptions on the solutions' performance in practice remains generally unexplored. In this paper, we first systematically survey the literature on rebalancing problems and their modeling assumptions. We then propose a general mixed -integerprogramming model for multi -period rebalancing problems that can be easily adapted to different assumptions, including trip modeling, time discretization, trip distribution, and event sequences. We develop an instance generator to synthesize realistic station networks and customer trips, as well as a realistic fine-grained simulator to evaluate the operational performance rebalancing strategies. Finally, extensive numerical experiments are carried out, both on the synthetic and real world data, to analyze the effectiveness of various modeling assumptions and techniques. Based on our results, we identify the assumptions that empirically provide the most effective rebalancing strategies in practice. Specifically, a set of specific trip distribution constraints and event sequences ignored in the previous literature seem to provide particularly good results.
We consider the robust version of items selection problem, in which the goal is to choose representatives from a family of sets, preserving constraints on the allowed items' combinations. We prove NP-hardness of t...
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We consider the robust version of items selection problem, in which the goal is to choose representatives from a family of sets, preserving constraints on the allowed items' combinations. We prove NP-hardness of the deterministic version, and establish polynomially solvable special cases. Next, we consider the robust version in which we aim at minimizing the maximum regret of the solution under interval parameter uncertainty. We show that this problem is hard for the second level of polynomial-time hierarchy. We develop exact solution algorithms for the robust problem, based on cut generation and mixed-integer programming, and present the results of computational experiments.
In this paper, we consider mixedinteger linear programming (MIP) formulations for piecewise linear functions (PLFs) that are evaluated when an indicator variable is turned on. We describe modifications to standard MI...
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In this paper, we consider mixedinteger linear programming (MIP) formulations for piecewise linear functions (PLFs) that are evaluated when an indicator variable is turned on. We describe modifications to standard MIP formulations for PLFs with desirable theoretical properties and superior computational performance in this context. (C) 2013 Elsevier B.V. All rights reserved.
Despite the value of energy optimization in desalination processes, modeling dynamic operations for monthly billing periods has remained a computational challenge. This work proposes a framework for energy flexibility...
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Despite the value of energy optimization in desalination processes, modeling dynamic operations for monthly billing periods has remained a computational challenge. This work proposes a framework for energy flexibility optimization, which includes new modeling features for independent operation of parallel skids, start-up delays associated with chemical stabilization, the consideration of industrial energy tariff structures, and inclusion of hourly electrical carbon intensities. This is done using a modular and computationally efficient formulation that guarantees a globally optimal solution with standard optimization solvers. The approach is demonstrated in two distinct case studies: a seawater desalination plant in Santa Barbara, CA, and an indirect potable reuse facility in San Jose, CA. Trends predicted from the model are validated against operational facility measurements from a demand response shutdown event. Preliminary results show that optimizing energy flexibility can result in 18.51% monthly cost savings over energy efficiency-optimized operation. The value extracted from a facility-wide shutdown during peak electricity price hours is hampered by start-up delays in post-treatment chemical stabilization. In cases in which a facility does not have much excess capacity, using a flow equalization tank or operating over a wide recovery range may be cost-effective.
Anew scenario based stochastic and possibilistic mixedintegerprogramming model for a multi-objective closed-loop supply chain network design problem by considering financial and collection risks is proposed. Uncerta...
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Anew scenario based stochastic and possibilistic mixedintegerprogramming model for a multi-objective closed-loop supply chain network design problem by considering financial and collection risks is proposed. Uncertainties in the form of randomness and fuzziness are handled together for a better reflection of the problem. Different risk measures such as "variability index", "downside risk" and "conditional value at risk" are integrated within the proposed model. Particularly, for the downside risk measure, target/threshold values are considered as fuzzy and described by their own possibility distribution. The proposed hybrid model is applied to an illustrative example inspired by the lead/acid industry in Turkey. Computational results of applying the different risk measures suggest that using downside risk model with fuzzy targets is found to be an appropriate choice for the stated closed-loop supply chain network design problem in terms of "computational efficiency", "handling uncertainty" and "solution quality" (C) 2014 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
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