Strong branching is an effective branching technique that can significantly reduce the size of the branch-and-bound tree for solving mixedintegernonlinearprogramming (MINLP) problems. The focus of this paper is to ...
详细信息
Strong branching is an effective branching technique that can significantly reduce the size of the branch-and-bound tree for solving mixedintegernonlinearprogramming (MINLP) problems. The focus of this paper is to demonstrate how to effectively use "discarded" information from strong branching to strengthen relaxations of MINLP problems. Valid inequalities such as branching-based linearizations, various forms of disjunctive inequalities, and mixing-type inequalities are all discussed. The inequalities span a spectrum from those that require almost no extra effort to compute to those that require the solution of an additional linear program. In the end, we perform an extensive computational study to measure the impact of each of our proposed techniques. Computational results reveal that existing algorithms can be significantly improved by leveraging the information generated as a byproduct of strong branching in the form of valid inequalities.
This work considers the global optimization of general non-convex nonlinear and mixed-integer nonlinear programming (MINLP) problems with underlying bilinear substructures. We combine reformulation-linearization techn...
详细信息
This work considers the global optimization of general non-convex nonlinear and mixed-integer nonlinear programming (MINLP) problems with underlying bilinear substructures. We combine reformulation-linearization techniques and advanced convex envelope construction techniques to produce tight subproblem formulations for these underlying structures. When incorporated as linear cutting planes, these relaxation strengthening strategies are highly effective at tightening standard linear programming relaxations generated by factorable programming techniques. Because the size of these augmented linear relaxations increases exponentially with the number of variables, we employ cut filtering and selection strategies to ensure that the tightened subproblems are solved efficiently. We introduce algorithms for bilinear substructure detection, cutting plane identification, cut filtering, and cut selection and embed the proposed implementation in Branch-and-Reduce Optimization Navigator at every node in the branch-and-bound tree. A computational study including problem instances from standard literature test libraries is included to assess the performance of the proposed implementation. Results show that underlying bilinear substructures are identified in 30% of the problems in GLOBALLib and MINLPLib and that the exploitation of these structures significantly reduces computational time, branch-and-bound tree size, and required memory.
Maturing distributed generation (DG) technologies have promoted interest in alternative sources of energy for commercial building applications due to their potential to supply on-site heat and power at a lower cost an...
详细信息
Maturing distributed generation (DG) technologies have promoted interest in alternative sources of energy for commercial building applications due to their potential to supply on-site heat and power at a lower cost and emissions rate compared to centralized generation. Accordingly, we present an optimization model that determines the mix, capacity, and operational schedule of DG technologies that minimize economic and environmental costs subject to the heat and power demands of a building and to the performance characteristics of the technologies. The technologies available to design the system include lead-acid batteries, photovoltaic cells, solid oxide fuel cells, heat exchangers, and a hot water storage tank. Modeling the acquisition and operation of discrete technologies requires integer restrictions, and modeling the variable electric efficiency of the fuel cells and the variable temperature of the tank water introduces nonlinear equality constraints. Thus, our optimization model is a nonconvex, mixed-integer nonlinear programming (MINLP) problem. Given the difficulties associated with solving large, nonconvex MINLPs to global optimality, we present convex underestimation and linearization techniques to bound and solve the problem. The solutions provided by our techniques are close to those provided by existing MINLP solvers for small problem instances. However, our methodology offers the possibility to solve large problem instances that exceed the capacity of existing solvers and that are critical to the real-world application of the model.
This paper aims at selecting different raw materials, using an MINLP (mixed-integer nonlinear programming) model, when considering the usage of more favourable raw materials for methanol production. The best selection...
详细信息
This paper aims at selecting different raw materials, using an MINLP (mixed-integer nonlinear programming) model, when considering the usage of more favourable raw materials for methanol production. The best selection of raw material alternatives was sought for methanol production. Methanol is produced from synthesis gas that is produced from different raw materials - natural gas or biogas. The basic starting point when comparing them is the same mass inlet flow rate for both raw materials. Methanol production was simulated for both natural gas or biogas as the raw material, using an Aspen Plus simulator with a real chemical thermodynamic. Methanol production can be enlarged by simultaneous structuring such as selecting the usage of more favourable raw materials, and parameter optimisation using the MINLP. The selection of raw methanol with optimal parameters has the greatest impact on higher methanol production. Optimal methanol conversion can take place during this operation, by applying optimal parametric data within a reformer unit (temperature = 840 degrees C and pressure = 8 bar), using natural gas. The optimal production of methanol from natural gas was 17 510 kg/h under optimal parameters for 8.4% higher production than under existing parameters. (C) 2014 Elsevier B.V. All rights reserved.
We will analyze mixed-0/1 second-order cone programs where the continuous and binary variables are solely coupled via the conic constraints. We devise a cutting-plane framework based on an implicit Sherali-Adams refor...
详细信息
We will analyze mixed-0/1 second-order cone programs where the continuous and binary variables are solely coupled via the conic constraints. We devise a cutting-plane framework based on an implicit Sherali-Adams reformulation. The resulting cuts are very effective as symmetric solutions are automatically cut off and each equivalence class of 0/1 solutions is visited at most once. Further, we present computational results showing the effectiveness of our method and briefly sketch an application in optimal pooling of securities. (C) 2014 Elsevier B.V. All rights reserved.
A common structure in convex mixed-integernonlinear programs (MINLPs) is separable nonlinear functions. In the presence of such structures, we propose three improvements to the outer approximation algorithms. The fir...
详细信息
A common structure in convex mixed-integernonlinear programs (MINLPs) is separable nonlinear functions. In the presence of such structures, we propose three improvements to the outer approximation algorithms. The first improvement is a simple extended formulation, the second is a refined outer approximation, and the third is a heuristic inner approximation of the feasible region. As a side result, we exhibit a simple example where a classical implementation of the outer approximation would take an exponential number of iterations, whereas it is easily solved with our modifications. These methods have been implemented in the open source solver BONMIN and are available for download from the Computational Infrastructure for Operations Research project website. We test the effectiveness of the approach on three real-world applications and on a larger set of models from an MINLP benchmark library. Finally, we show how the techniques can be extended to perspective formulations of several problems. The proposed tools lead to an important reduction in computing time on most tested instances.
In this work, the energy-optimal motion planning problem for planar robot manipulators with two revolute joints is studied, in which the end-effector of the robot manipulator is constrained to pass through a set of wa...
详细信息
In this work, the energy-optimal motion planning problem for planar robot manipulators with two revolute joints is studied, in which the end-effector of the robot manipulator is constrained to pass through a set of waypoints, whose sequence is not predefined. This multi-goal motion planning problem has been solved as a mixed-integer optimal control problem in which, given the dynamic model of the robot manipulator, the initial and final configurations of the robot, and a set of waypoints inside the workspace of the manipulator, one has to find the control inputs, the sequence of waypoints with the corresponding passage times, and the resulting trajectory of the robot that minimizes the energy consumption during the motion. The presence of the waypoint constraints makes this optimal control problem particularly difficult to solve. The mixed-integer optimal control problem has been converted into a mixed-integer nonlinear programming problem first making the unknown passage times through the waypoints part of the state, then introducing binary variables to enforce the constraint of passing once through each waypoint, and finally applying a fifth-degree Gauss-Lobatto direct collocation method to tackle the dynamic constraints. High-degree interpolation polynomials allow the number of variables of the problem to be reduced for a given numerical precision. The resulting mixed-integer nonlinear programming problem has been solved using a nonlinearprogramming-based branch-and-bound algorithm specifically tailored to the problem. The results of the numerical experiments have shown the effectiveness of the approach.
The nonlinear Discrete Transportation Problem (NDTP) belongs to the class of the optimization problems that are generally difficult to solve. The selection of a suitable optimization method by which a specific NDTP ca...
详细信息
The nonlinear Discrete Transportation Problem (NDTP) belongs to the class of the optimization problems that are generally difficult to solve. The selection of a suitable optimization method by which a specific NDTP can be appropriately solved is frequently a critical issue in obtaining valuable results. The aim of this paper is to present the suitability of five different mixed-integer nonlinear programming (MINLP) methods, specifically for the exact optimum solution of the NDTP. The evaluated MINLP methods include the extended cutting plane method, the branch and reduce method, the augmented penalty/outer-approximation/equality-relaxation method, the branch and cut method, and the simple branch and bound method. The MINLP methods were tested on a set of NDTPs from the literature. The gained solutions were compared and a correlative evaluation of the considered MINLP methods is shown to demonstrate their suitability for solving the NDTPs.
This paper presents a methodology for economic optimization of combined cycle district heating systems. Heat and power requirements vary over 24 h periods due to changing weather conditions and consumer requirements. ...
详细信息
This paper presents a methodology for economic optimization of combined cycle district heating systems. Heat and power requirements vary over 24 h periods due to changing weather conditions and consumer requirements. System thermal performance is highly dependent on ambient temperature and operating load, because individual component performances are nonlinear functions of these parameters. Since electric grid charges are much higher for on-peak than off-peak periods, on-site fuel choices vary in prices, and cheaper fuel availabilities are limited by suppliers, opportunities arise to optimally schedule system operation, and minimize total daily running cost. For such problems a mixed-integer nonlinear programming formulation is proposed. Limited fuel availability constraints make problem solving difficult using classical techniques such as the branch-and-bound method. As an alternative, a genetic algorithm is proposed in which a genetic search is applied only on integer variables and a gradient search is applied on continuous variables. A comparative study using actual system operation data shows optimal scheduling can reduce total daily running cost by 11% and improve system operating efficiency by 6%. (C) 2014 Elsevier Ltd. All rights reserved.
We present an improved Bernstein global optimization algorithm to solve polynomial mixed-integer nonlinear programming (MINLP) problems. The algorithm is of branch-and-bound type, and uses the Bernstein form of the po...
详细信息
We present an improved Bernstein global optimization algorithm to solve polynomial mixed-integer nonlinear programming (MINLP) problems. The algorithm is of branch-and-bound type, and uses the Bernstein form of the polynomials for the global optimization. The new ingredients in the algorithm include a modified subdivision procedure, a vectorized Bernstein cut-off test and a new branching rule for the decision variables. The performance of the improved algorithm is tested and compared with earlier reported Bernstein global optimization algorithm (to solve polynomial MINLPs) and with several state-of-the-art MINLP solvers on a set of 19 test problems. The results of the tests show the superiority of the improved algorithm over the earlier reported Bernstein algorithm and the state-of-the-art solvers in terms of the chosen performance metrics. Similarly, efficacy of the improved algorithm in handling a real-world MINLP problem is brought out via a trim-loss minimization problem from the process industry.
暂无评论