This study deals with the school timetabling problem for the case of Greek high schools. At first, the problem is modelled as a mixed integer programming problem for ten instances referring to Greek high schools. Then...
详细信息
This study deals with the school timetabling problem for the case of Greek high schools. At first, the problem is modelled as a mixed integer programming problem for ten instances referring to Greek high schools. Then, the problem is coded using the MathProg programming language. Two different linear programming solvers are employed, Gurobi and CPLEX, to solve the problem for the instances at hand. Two methodologies are proposed. The first one deals with the problem utilising a model that includes all hard and soft constraints, called "monolithic" model, while the second one is based on a decomposition of the problem to six sub-problems. It should be stated that Gurobi and CPLEX did not produced satisfactory results when the monolithic model was the case. Computational results demonstrate the effectiveness of the second proposed methodology, as optimal solutions or new lower bounds were found. In addition, the results produced by mixed integer programming are compared with the best so far published results, obtained by two Nature Inspired algorithms namely Particle Swarm Optimization and Cat Swarm Optimization.
mixed integer programming has become a very powerful tool for modeling and solving real-world planning and scheduling problems, with the breadth of applications appearing to be almost unlimited. A critical component i...
详细信息
mixed integer programming has become a very powerful tool for modeling and solving real-world planning and scheduling problems, with the breadth of applications appearing to be almost unlimited. A critical component in the solution of these mixedinteger programs is a set of routines commonly referred to as presolve. Presolve can be viewed as a collection of preprocessing techniques that reduce the size of and, more importantly, improve the "strength" of the given model formulation, that is, the degree to which the constraints of the formulation accurately describe the underlying polyhedron of integer-feasible solutions. As our computational results will show, presolve is a key factor in the speed with which we can solve mixedinteger programs and is often the difference between a model being intractable and solvable, in some cases easily solvable. In this paper we describe the presolve functionality in the Gurobi commercial mixed integer programming code. This includes an overview, or taxonomy of the different methods that are employed, as well as more-detailed descriptions of several of the techniques, with some of them appearing, to our knowledge, for the first time in the literature.
Planning for management actions that address threats to biodiversity is important for securing its long term persistence. However, systematic conservation planning (SCP) has traditionally overlooked this aspect and ju...
详细信息
Planning for management actions that address threats to biodiversity is important for securing its long term persistence. However, systematic conservation planning (SCP) has traditionally overlooked this aspect and just focused on identifying priority areas without any recommendation on actions needed. This paper develops a mixedinteger mathematical programming (MIP) approach for the multi-action management planning problem (MAMP), where the goal is to find an optimal combination of management actions that abate threats, in an efficient way while accounting for connectivity. An extended version of the MAMP model (MAMP-E) is also proposed that adds an expression for minimizing fragmentation between different actions. To evaluate the efficiency of the two models, they were applied to a case study corresponding to a large area of the Mitchell River in Northern Australia, where 45 species of freshwater fish are exposed to the presence of four threats. The evaluation compares our exact MIP approach with the conservation planning software Marxan and the heuristic approach developed in Cattarino et al. (2015). The results obtained show that our MIP models have three advantages over their heuristic counterparts: shorter execution times, higher solutions quality, and a solution quality guarantee. Hence, the proposed MIP methodology provides a more effective framework for addressing the multi-action conservation problem.
The bilevel programming problem is a static version of the Stackelberg's leader follower game in which Stackelberg strategy is used by the higher level decision maker called the leader given the rational reaction ...
详细信息
The bilevel programming problem is a static version of the Stackelberg's leader follower game in which Stackelberg strategy is used by the higher level decision maker called the leader given the rational reaction of the lower decision maker called the follower. The bilevel programming problem (BLPP) is a two-level hierarchical optimisation problem and is non-convex. This paper deals with finding links between the bilevel linear fractional/linear programming problem (BF/LP), the generalised linear fractional complementarity problem (GFCP) and mixedinteger linear fractional programming problem (MIFP). The (BF/LP) is reformulated as a (GFCP) which in turn is reformulated as an (MIFP). The method is supported with the help of a numerical example.
This article presents a two-stage algorithm for piecewise affine (PWA) regression. In the first stage, a moving horizon strategy is employed to simultaneously estimate the model parameters and to classify the training...
详细信息
This article presents a two-stage algorithm for piecewise affine (PWA) regression. In the first stage, a moving horizon strategy is employed to simultaneously estimate the model parameters and to classify the training data by solving a small-size mixed-integer quadratic programming problem. In the second stage, linear multicategory separation methods are used to partition the regressor space. The framework of PWA regression is adapted to the identification of PWA AutoRegressive with eXogenous input (PWARX) models as well as linear parameter-varying (LPV) models. The performance of the proposed algorithm is demonstrated on an academic example and on two benchmark experimental case studies. The first experimental example concerns modeling the placement process in a pick-and-place machine, while the second one consists in the identification of an LPV model describing the input-output relationship of an electronic bandpass filter with time-varying resonant frequency.
This paper concerns an optimization problem over the efficient set of a multiobjective linear programming problem. We propose and solve an equivalent mixed integer programming (MIP) problem to compute an optimal solut...
详细信息
This paper concerns an optimization problem over the efficient set of a multiobjective linear programming problem. We propose and solve an equivalent mixed integer programming (MIP) problem to compute an optimal solution to the original problem. Compared with the previous MIP approach by Sun, the proposed approach relaxes a strong assumption and reduces the numbers of constraints and binary variables of the MIP problem. By conducting numerical experiments, we find that the proposed approach is more accurate and faster than the previous MIP approach. The proposed MIP problem can be efficiently solved with current state-of-the-art MIP solvers when the objective function is convex or linear.
This work presents a new methodology for planning and tracking a time-optimal trajectory for class 8 vehicles on roads in which traffic lights exist. This approach takes the non-convex nature of the problem and simpli...
详细信息
This work presents a new methodology for planning and tracking a time-optimal trajectory for class 8 vehicles on roads in which traffic lights exist. This approach takes the non-convex nature of the problem and simplifies it by introducing a set of integer decision variables. Due to the planned trajectory taking place over distances greater than a kilometer, an inner loop controller is developed to refine the high-level trajectory and guarantee that the ego vehicle does not cross into intersections during a red light phase. In order to account for model differences between the inner loop and outer loop systems an event triggered replan methodology is introduced. This event triggered replan allows for the high-level plan to adjust the trajectory to the current states of the ego vehicle without creating an unnecessary computational burden. This full system is then evaluated on three test scenarios in which the ego vehicle must navigate through two intersections with varying red light phases. The tests successfully demonstrate the feasibility of this method for generating safe, time-optimal trajectories for class 8 vehicles. Copyright (c) 2024 The Authors.
The double row layout problem(DRLP)is to assign facilities on two rows in parallel so that the total cost of material handling among facilities is *** it is vital to save cost and enhance productivity,the DRLP plays a...
详细信息
The double row layout problem(DRLP)is to assign facilities on two rows in parallel so that the total cost of material handling among facilities is *** it is vital to save cost and enhance productivity,the DRLP plays an important role in many application ***,it is very hard to handle the DRLP because of its complex *** this paper,we consider a new simplified model for the DRLP(SM-DRLP)and provide a mixed integer programming(MIP)formulation for *** continuous decision variables of the DRLP are divided into two parts:start points of double rows and adjustable clearances between adjacent *** former one is considered in the new simplified model for the DRLP with the purpose of maintaining solution quality,while the latter one is not taken into account with the purpose of reducing computational *** evaluate its performance,our SM-DRLP is compared with the model of a general DRLP and the model of another simplified *** experimental results show the efficiency of our proposed model.
Despite their great success in recent years, neural networks have been found to be vulnerable to adversarial attacks. These attacks are often based on slight perturbations of given inputs that cause them to be misclas...
详细信息
Despite their great success in recent years, neural networks have been found to be vulnerable to adversarial attacks. These attacks are often based on slight perturbations of given inputs that cause them to be misclassified. Several methods have been proposed to formally prove robustness of a given network against such attacks. However, these methods typically give rise to high computational demands, which severely limit their scalability. Recent state-of-the-art approaches state the verification task as a minimisation problem, which is formulated and solved as a mixed-integer linear programming (MIP) problem. We extend this approach by leveraging automated algorithm configuration techniques and, more specifically, construct a portfolio of MIP solver configurations optimised for the neural network verification task. We test this approach on two recent, state-of-the-art MIP-based verification engines, MIPVerify and Venus, and achieve substantial improvements in CPU time by average factors of up to 4.7 and 10.3, respectively.
Construction site layout planning, the arrangement of temporary facilities and equipment on site, is a fundamental part of construction preparation. In construction, the operation of tower cranes has a great impact on...
详细信息
Construction site layout planning, the arrangement of temporary facilities and equipment on site, is a fundamental part of construction preparation. In construction, the operation of tower cranes has a great impact on construction process execution and preparation costs. Therefore, tower cranes should be chosen and placed such that they enable smooth construction processes at minimal cost. Since the majority of loads on site are transported either from or to a storage area, the transport routes taken between tower cranes and storage areas have a high impact. This paper presents a mathematical model that computes cost-optimal positions for both tower cranes and storage areas. The model consists of two linked mixedinteger programs, allowing for the detailed quality assessment of the obtained solutions. Time dependency is considered by subdividing the construction process into several construction phases. Conditions on site and construction elements can be retrieved from a building information model. Particular advantages of our approach include the close approximation of complex shapes via convex hulls. Available positions on site are represented by a fine grid and calculated during runtime, which allows for freer placement instead of restricting to a fixed number of possible locations given as input. Using mixed integer programming offers tremendous modeling possibilities and a rigorous quality guarantee for the obtained solutions. In contrast to existing heuristic approaches, the returned solutions are provably optimal up to the chosen optimality gap. A case study is provided to demonstrate the practical applicability of the proposed model.
暂无评论