scholarly journals Cable tree wiring - benchmarking solvers on a real-world scheduling problem with a variety of precedence constraints

Constraints ◽  
2021 ◽  
Author(s):  
Jana Koehler ◽  
Josef Bürgler ◽  
Urs Fontana ◽  
Etienne Fux ◽  
Florian Herzog ◽  
...  
Keyword(s):  
State Of The Art ◽  
Precedence Constraints ◽  
Traveling Salesman ◽  
Mixed Integer ◽  
Automated Manufacturing ◽  
Scheduling Problem ◽  
Tasks Scheduling ◽  
Optimization Modulo Theories ◽  
Coupled Tasks ◽  
Np Hardness

AbstractCable trees are used in industrial products to transmit energy and information between different product parts. To this date, they are mostly assembled by humans and only few automated manufacturing solutions exist using complex robotic machines. For these machines, the wiring plan has to be translated into a wiring sequence of cable plugging operations to be followed by the machine. In this paper, we study and formalize the problem of deriving the optimal wiring sequence for a given layout of a cable tree. We summarize our investigations to model this cable tree wiring problem (CTW). as a traveling salesman problem with atomic, soft atomic, and disjunctive precedence constraints as well as tour-dependent edge costs such that it can be solved by state-of-the-art constraint programming (CP), Optimization Modulo Theories (OMT), and mixed-integer programming (MIP). solvers. It is further shown, how the CTW problem can be viewed as a soft version of the coupled tasks scheduling problem. We discuss various modeling variants for the problem, prove its NP-hardness, and empirically compare CP, OMT, and MIP solvers on a benchmark set of 278 instances. The complete benchmark set with all models and instance data is available on github and was included in the MiniZinc challenge 2020.

scholarly journals Exact Methods for the Traveling Salesman Problem with Drone

2021 ◽  
Vol 55 (2) ◽  
pp. 315-335
Author(s):  
Roberto Roberti ◽  
Mario Ruthmair
Keyword(s):  
Dynamic Programming ◽  
Traveling Salesman Problem ◽  
State Of The Art ◽  
The State ◽  
Set Partitioning ◽  
Traveling Salesman ◽  
Mixed Integer ◽  
Branch And Price ◽  
Last Mile ◽  
The Traveling Salesman Problem

Efficiently handling last-mile deliveries becomes more and more important nowadays. Using drones to support classical vehicles allows improving delivery schedules as long as efficient solution methods to plan last-mile deliveries with drones are available. We study exact solution approaches for some variants of the traveling salesman problem with drone (TSP-D) in which a truck and a drone are teamed up to serve a set of customers. This combination of truck and drone can exploit the benefits of both vehicle types: the truck has a large capacity but usually low travel speed in urban areas; the drone is faster and not restricted to street networks, but its range and carrying capacity are limited. We propose a compact mixed-integer linear program (MILP) for several TSP-D variants that is based on timely synchronizing truck and drone flows; such an MILP is easy to implement but nevertheless leads to competitive results compared with the state-of-the-art MILPs. Furthermore, we introduce dynamic programming recursions to model several TSP-D variants. We show how these dynamic programming recursions can be exploited in an exact branch-and-price approach based on a set partitioning formulation using ng-route relaxation and a three-level hierarchical branching. The proposed branch-and-price can solve instances with up to 39 customers to optimality outperforming the state-of-the-art by more than doubling the manageable instance size. Finally, we analyze different scenarios and show that even a single drone can significantly reduce a route’s completion time when the drone is sufficiently fast.

scholarly journals Some complexity and approximation results for coupled-tasks scheduling problem according to topology

2016 ◽  
Vol 50 (4-5) ◽  
pp. 781-795 ◽  
Author(s):  
Benoit Darties ◽  
Rodolphe Giroudeau ◽  
Jean-Claude König ◽  
Gilles Simonin
Keyword(s):  
Scheduling Problem ◽  
Tasks Scheduling ◽  
Coupled Tasks

scholarly journals Branch-and-Cut-and-Price algorithms for the preemptive RCPSP

2018 ◽  
Vol 52 (2) ◽  
pp. 513-528
Author(s):  
Pierre Fouilhoux ◽  
A.Ridha Mahjoub ◽  
Alain Quilliot ◽  
Hélène Toussaint
Keyword(s):  
Valid Inequalities ◽  
Precedence Constraints ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Scheduling Problem ◽  
Computational Results ◽  
Resource Constrained ◽  
Integer Variables ◽  
Integer Formulations

In this article, we address the preemptive Resource-Constrained Precedence Scheduling Problem. We propose two mixed integer formulations containing an exponential number of variables and inequalities. An antichain is a set of pairwise incomparable elements with respect to the precedence constraints. In the first formulation, the integer variables are associated with the antichains. For the second, the integer variables are limited to a particular subset of antichains. We propose two Branch-and-Cut-and-Price algorithms for each of these formulations. We introduce some valid inequalities in order to reinforce the second formulation. Finally, we give some computational results on instances of the PSPLIB and compare the formulations.

scholarly journals Solving the nuclear dismantling project scheduling problem by combining mixed-integer and constraint programming techniques and metaheuristics

2021 ◽  
Author(s):  
Felix Hübner ◽  
Patrick Gerhards ◽  
Christian Stürck ◽  
Rebekka Volk
Keyword(s):  
Constraint Programming ◽  
Project Scheduling ◽  
Computational Study ◽  
Real Life ◽  
Mixed Integer ◽  
Extensive Literature ◽  
Scheduling Problem ◽  
Multiple Modes ◽  
Project Scheduling Problem ◽  
Optimisation Techniques

AbstractScheduling of megaprojects is very challenging because of typical characteristics, such as expected long project durations, many activities with multiple modes, scarce resources, and investment decisions. Furthermore, each megaproject has additional specific characteristics to be considered. Since the number of nuclear dismantling projects is expected to increase considerably worldwide in the coming decades, we use this type of megaproject as an application case in this paper. Therefore, we consider the specific characteristics of constrained renewable and non-renewable resources, multiple modes, precedence relations with and without no-wait condition, and a cost minimisation objective. To reliably plan at minimum costs considering all relevant characteristics, scheduling methods can be applied. But the extensive literature review conducted did not reveal a scheduling method considering the special characteristics of nuclear dismantling projects. Consequently, we introduce a novel scheduling problem referred to as the nuclear dismantling project scheduling problem. Furthermore, we developed and implemented an effective metaheuristic to obtain feasible schedules for projects with about 300 activities. We tested our approach with real-life data of three different nuclear dismantling projects in Germany. On average, it took less than a second to find an initial feasible solution for our samples. This solution could be further improved using metaheuristic procedures and exact optimisation techniques such as mixed-integer programming and constraint programming. The computational study shows that utilising exact optimisation techniques is beneficial compared to standard metaheuristics. The main result is the development of an initial solution finding procedure and an adaptive large neighbourhood search with iterative destroy and recreate operations that is competitive with state-of-the-art methods of related problems. The described problem and findings can be transferred to other megaprojects.

scholarly journals Optimal Reactive Power Scheduling Using Cuckoo Search Algorithm

2017 ◽  
Vol 7 (5) ◽  
pp. 2349 ◽  
Author(s):  
Surender Reddy Salkuti
Keyword(s):  
Power System ◽  
Reactive Power ◽  
Search Algorithm ◽  
Cuckoo Search ◽  
Cuckoo Search Algorithm ◽  
Optimization Techniques ◽  
Mixed Integer ◽  
Integer Programming Problem ◽  
Scheduling Problem ◽  
Power Scheduling

<p>This paper solves an optimal reactive power scheduling problem in the deregulated power system using the evolutionary based Cuckoo Search Algorithm (CSA). Reactive power scheduling is a very important problem in the power system operation, which is a nonlinear and mixed integer programming problem. It optimizes a specific objective function while satisfying all the equality and inequality constraints. In this paper, CSA is used to determine the optimal settings of control variables such as generator voltages, transformer tap positions and the amount of reactive compensation required to optimize the certain objective functions. The CSA algorithm has been developed from the inspiration that the obligate brood parasitism of some Cuckoo species lay their eggs in nests of other host birds which are of other species. The performance of CSA for solving the proposed optimal reactive power scheduling problem is examined on standard Ward Hale 6 bus, IEEE 30 bus, 57 bus, 118 bus and 300 bus test systems. The simulation results show that the proposed approach is more suitable, effective and efficient compared to other optimization techniques presented in the literature.</p>

scholarly journals Bi-objective unrelated parallel machines scheduling problem with worker allocation and sequence dependent setup times considering machine eligibility and precedence constraints

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Reza Alizadeh Foroutan ◽  
Javad Rezaeian ◽  
Milad Shafipour
Keyword(s):  
Precedence Constraints ◽  
Setup Times ◽  
Scheduling Problem ◽  
Multi Objective ◽  
Worker Allocation ◽  
Sequence Dependent ◽  
Machine Eligibility ◽  
Sequence Dependent Setup ◽  
Dependent Setup Times ◽  
Sequence Dependent Setup Times

<p style='text-indent:20px;'>In today's competitive world, scheduling problems are one of the most important and vital issues. In this study, a bi-objective unrelated parallel machine scheduling problem with worker allocation, sequence dependent setup times, precedence constraints, and machine eligibility is presented. The objective functions are to minimize the costs of tardiness and hiring workers. In order to formulate the proposed problem, a mixed-integer quadratic programming model is presented. A strategy called repair is also proposed to implement the precedence constraints. Because the problem is NP-hard, two metaheuristic algorithms, a multi-objective tabu search (MOTS) and a multi-objective simulated annealing (MOSA), are presented to tackle the problem. Furthermore, a hybrid metaheuristic algorithm is also developed. Finally, computational experiments are carried out to evaluate different test problems, and analysis of variance is done to compare the performance of the proposed algorithms. The results show that MOTS is doing better in terms of objective values and mean ideal distance (MID) metric, while the proposed hybrid algorithm outperforms in most cases, considering other employed comparison metrics.</p>

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