The timing problem in the bi-objective just-in-time single-machine job-shop scheduling problem (JiT-JSP) is the task to schedule N jobs whose order is fixed, with each job incurring a linear earliness penalty for fini...
详细信息
The timing problem in the bi-objective just-in-time single-machine job-shop scheduling problem (JiT-JSP) is the task to schedule N jobs whose order is fixed, with each job incurring a linear earliness penalty for finishing ahead of its due date and a linear tardiness penalty for finishing after its due date. The goal is to minimize the earliness and tardiness simultaneously. We propose an exact greedy algorithm that finds the entire Pareto front in time. This algorithm is asymptotically optimal.
This article presents an exact algorithm for the multi-depot vehicle routing problem (MDVRP) under capacity and route length constraints. The MDVRP is formulated using a vehicle-flow and a set-partitioning formulation...
详细信息
This article presents an exact algorithm for the multi-depot vehicle routing problem (MDVRP) under capacity and route length constraints. The MDVRP is formulated using a vehicle-flow and a set-partitioning formulation, both of which are exploited at different stages of the algorithm. The lower bound computed with the vehicle-flow formulation is used to eliminate non-promising edges, thus reducing the complexity of the pricing sub-problem used to solve the set-partitioning formulation. Several classes of valid inequalities are added to strengthen both formulations, including a new family of valid inequalities used to forbid cycles of an arbitrary length. To validate our approach, we also consider the capacitated vehicle routing problem (CVRP) as a particular case of the MDVRP, and conduct extensive computational experiments on several instances from the literature to show its effectiveness. The computational results show that the proposed algorithm is competitive against state-of-the-art methods for these two classes of vehicle routing problems, and is able to solve to optimality some previously open instances. Moreover, for the instances that cannot be solved by the proposed algorithm, the final lower bounds prove stronger than those obtained by earlier methods. (C) 2014 Elsevier B.V. All rights reserved.
A recent study has developed an integer linear program and an exact algorithm for the automated truck transportation freight problem with lane reservation. However, due to its NP-hard nature, their proposed method bec...
详细信息
A recent study has developed an integer linear program and an exact algorithm for the automated truck transportation freight problem with lane reservation. However, due to its NP-hard nature, their proposed method becomes difficult to solve large-size problems within acceptable time. In this paper, we firstly present an improved integer linear program by adding valid inequalities and identify that its several special cases are classical combinatorial optimization problems. Based on analyzed properties, a new efficient two-phase exact algorithm is developed. Computational results on benchmark and new larger-size instances with up to 700 nodes and 55 tasks show that the new algorithm outperforms very favorably the state-of-the-art one. (C) 2017 Elsevier Ltd. All rights reserved.
We study exact algorithms for the MAX-CUT problem. Introducing a new technique, we present an algorithmic scheme that computes a maximum cut in graphs with bounded maximum degree. Our algorithm runs in time O*(2((l-(2...
详细信息
We study exact algorithms for the MAX-CUT problem. Introducing a new technique, we present an algorithmic scheme that computes a maximum cut in graphs with bounded maximum degree. Our algorithm runs in time O*(2((l-(2/Delta))n)). We also describe a MAX-CUT algorithm for general graphs. Its time complexity is O*(2(mn/(m+n))). Both algorithms use polynomial space. (C) 2006 Elsevier B.V. All rights reserved.
Satellite observation scheduling plays a significant role in improving the efficiency of Earth observation systems. To solve the large-scale multisatellite observation scheduling problem, this article proposes an ense...
详细信息
Satellite observation scheduling plays a significant role in improving the efficiency of Earth observation systems. To solve the large-scale multisatellite observation scheduling problem, this article proposes an ensemble of metaheuristic and exact algorithms based on a divide-and-conquer framework (EHE-DCF), including a task allocation phase and a task scheduling phase. In the task allocation phase, each task is allocated to a proper orbit based on a metaheuristic incorporated with a probabilistic selection and a tabu mechanism derived from ant colony optimization and tabu search, respectively. In the task scheduling phase, we construct a task scheduling model for every single orbit and solve the model by using an exact method (i.e., branch and bound, B&B). The task allocation and task scheduling phases are performed iteratively to obtain a promising solution. To validate the performance of the EHE-DCF, we compare it with B&B, three divide-and-conquer-based metaheuristics, and a state-of-the-art metaheuristic. Experimental results show that the EHE-DCF can obtain higher scheduling profits and complete more tasks compared with existing algorithms. The EHE-DCF is especially efficient for large-scale satellite observation scheduling problems.
In the multidimensional multiple choice knapsack problem (MMKP), items with nonnegative profits are partitioned into groups. Each item consumes a predefined nonnegative amount of a set of resources with given availabi...
详细信息
In the multidimensional multiple choice knapsack problem (MMKP), items with nonnegative profits are partitioned into groups. Each item consumes a predefined nonnegative amount of a set of resources with given availability. The problem looks for a subset of items consisting of exactly one item for each group that maximizes the overall profit without violating the resource constraints. The MMKP is among the most complex problems in the knapsack family. In the literature, although a plethora of heuristic approaches have been proposed, very few exact methods can be found, and all of them work only on limited size instances. In this paper, we propose a new exact approach for the problem. The method exactly solves subproblems of increasing size by means of a recursive variable-fixing process until an optimality condition is satisfied. The algorithm has several properties. Memory requirement remains almost constant during computation, and the method is general enough to be easily adapted to other knapsack problems. Finally, it can be converted at no cost into a heuristic approach. We close to optimality 10 open benchmark instances and improve the best-known values for many of the remaining ones. Interesting enough, our algorithm is able to find, within three minutes, better solutions than the ones found by Gurobi in one hour.
A binary constraint satisfaction problem (BCSP) consists in determining an assignment of values to variables that is compatible with a set of constraints. The problem is called binary because the constraints involve o...
详细信息
A binary constraint satisfaction problem (BCSP) consists in determining an assignment of values to variables that is compatible with a set of constraints. The problem is called binary because the constraints involve only pairs of variables. The BCSP is a cornerstone problem in Constraint Programming (CP), appearing in a very wide range of real-world applications. In this work, we develop a new exact algorithm which effectively solves the BCSP by reformulating it as a k-clique problem on the underlying microstructure graph representation. Our new algorithm exploits the cutting-edge branching scheme of the stateof-the-art maximum clique algorithms combined with two filtering phases in which the domains of the variables are reduced. Our filtering phases are based on colouring techniques and on heuristically solving an associated boolean satisfiability (SAT) problem. In addition, the algorithm initialization phase performs a reordering of the microstructure graph vertices that produces an often easier reformulation to solve. We carry out an extensive computational campaign on a benchmark of almost 20 0 0 instances, encompassing numerous real and synthetic problems from the literature. The performance of the new algorithm is compared against four SAT-based solvers and three general purpose CP solvers. Our tests reveal that the new algorithm significantly outperforms all the others in several classes of BCSP instances. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://***/licenses/by-nc-nd/4.0/ )
In this paper, we study the multi-period inspector scheduling problem (MPISP). This problem aims to determine a set of routes for a team of inspectors performing inspection jobs in different locations across multiple ...
详细信息
In this paper, we study the multi-period inspector scheduling problem (MPISP). This problem aims to determine a set of routes for a team of inspectors performing inspection jobs in different locations across multiple days, with the objective of maximizing the total workloads that the inspectors undertake. Since an inspector can only perform inspections or travel during working periods and rest at other times, a route for an inspector is divided into several segments. This characteristic, on the one hand, differentiates the MPISP from many routing problems in the literature;on the other hand, however, makes the routing decisions more complicated and challenging. To solve the MPISP, we first formulate it into a set-packing model and then propose an exact branchand-price algorithm. In particular, we design a tailored label-setting algorithm for the pricing subproblem, which is a variant of the elementary shortest path problem with resource constraints. Moreover, we implement some acceleration techniques, such as bidirectional search, label pruning, decremental search space relaxation, and heuristic column generator. Extensive computational experiments were conducted on a set of benchmark instances, and the results have demonstrated the effectiveness of the proposed algorithm.
Given a graph, the maximum clique problem (MCP) asks for determining a complete subgraph with the largest possible number of vertices. We propose a new exact algorithm, called CliSAT , to solve the MCP to proven optim...
详细信息
Given a graph, the maximum clique problem (MCP) asks for determining a complete subgraph with the largest possible number of vertices. We propose a new exact algorithm, called CliSAT , to solve the MCP to proven optimality. This problem is of fundamental importance in graph theory and combinatorial optimization due to its practical relevance for a wide range of applications. The newly developed ex-act approach is a combinatorial branch-and-bound algorithm that exploits the state-of-the-art branching scheme enhanced by two new bounding techniques with the goal of reducing the branching tree. The first one is based on graph colouring procedures and partial maximum satisfiability problems arising in the branching scheme. The second one is a filtering phase based on constraint programming and domain propagation techniques. CliSAT is designed for structured MCP instances which are computationally difficult to solve since they are dense and contain many interconnected large cliques. Extensive experi-ments on hard benchmark instances, as well as new hard instances arising from different applications, show that CliSAT outperforms the state-of-the-art MCP algorithms, in some cases by several orders of magnitude.(c) 2022 Elsevier B.V. All rights reserved.
We propose an exact algorithm to determine the satisfiability of oblivious read-twice branching programs. Our algorithm runs in 2(1-Omega(1/log c))n time for instances with n variables and cn nodes.
We propose an exact algorithm to determine the satisfiability of oblivious read-twice branching programs. Our algorithm runs in 2(1-Omega(1/log c))n time for instances with n variables and cn nodes.
暂无评论