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## A Developmental Solution to (Dynamic) Capacitated Arc Routing Problems using Genetic Programming

Citations: | 1 - 1 self |

### Citations

3732 |
Genetic programming: on the programming of computers by means of natural selection.
- Koza
- 1992
(Show Context)
Citation Context ...ways. 1) We utilize an indirect representation. The genotypes in our approach are heuristic functions, encoded as trees of mathematical functions in the style well-known from Genetic Programming (GP) =-=[23]-=-. In a developmental genotypephenotype mapping (GPM), the genotypes drive a greedy construction process. This process starts with an empty schedule and iteratively adds the edge which is rated with th... |

570 |
Algorithm 97 (Shortest Path).
- Floyd
- 1962
(Show Context)
Citation Context ...that the list of edges route(ei,ej) describing least-cost path between the end node of any edge ei and the starting node of any edge ej is known, as it can easily be calculated with Floyd’s Algorithm =-=[15]-=-. The total cost of any edge list r with a vehicle starting at the end of the first edge then is defined as pathCost in Equation 1. Additionally, we introduce a special edge, the depot loop e = −−−−→ ... |

158 | Grammatical Evolution: Evolving Programs for an Arbitrary Language.
- Ryan, Collins, et al.
- 1998
(Show Context)
Citation Context ...e phenotypes. The GPM may be an arbitrarily complex decoder, but it only uses the information given in the genotypes as input. One example for such mappings in the area of GP is Grammatical Evolution =-=[29, 32]-=-, where the genotypes are integer strings and the candidate solutions are sentences of a language defined by a given grammar. Here, the GPM starts with the starting symbol of that static grammar as cu... |

149 |
Grammatical Evolution: Evolutionary Automatic Programming in an Arbitrary Language.
- O’Neill, Ryan
- 2003
(Show Context)
Citation Context ...e phenotypes. The GPM may be an arbitrarily complex decoder, but it only uses the information given in the genotypes as input. One example for such mappings in the area of GP is Grammatical Evolution =-=[29, 32]-=-, where the genotypes are integer strings and the candidate solutions are sentences of a language defined by a given grammar. Here, the GPM starts with the starting symbol of that static grammar as cu... |

47 |
Capacitated arc routing problems;
- Golden, Wong
- 1981
(Show Context)
Citation Context ...first discuss existing research on CARP followed by research regarding ontogenic representations, and finally concern works on hyper-heuristics. 3.1 CARP CARPs belong to the class of NP-hard problems =-=[16, 34]-=- which means that algorithms for exact solutions are only feasible for problem instances of small scale or with otherwise special properties. This gives rise to a wide set of heuristic and metaheurist... |

47 |
Atabu search heuristic for the capacitated arc routing problem;
- Hertz, Laporte, et al.
- 2000
(Show Context)
Citation Context ...y feasible for problem instances of small scale or with otherwise special properties. This gives rise to a wide set of heuristic and metaheuristic methods in the area. The Tabu Search approach carpet =-=[20]-=- represents a candidate solution as set of routes, each of which being a list of vertices annotated with a Boolean variable indicating whether the edge between two vertices should be served or not. A ... |

42 |
Arc Routing: Theory, Solutions and Applications
- Dror, editor
- 2000
(Show Context)
Citation Context ...12/07. 1. INTRODUCTION Arc Routing Problems (ARPs) are logistic planning problems where the goal is to find optimal routes for vehicles that need to visit certain streets which require some treatment =-=[10]-=-. Classical examples for ARPs are road gritting and salting [18, 19] and the Chinese Postman Problem [13, 17]. In Capacitated Arc Routing Problems (CARPs), the vehicles are initially located at a sing... |

41 |
The ways to grow designs: A comparison of embryogenies for an evolutionary design problem
- Bentley, Kumar
- 1999
(Show Context)
Citation Context ...dependent from it. Especially the latter case is interesting, as such representations are suitable to solve large-scale problems. At least two classes of indirect representations may be distinguished =-=[2, 9]-=-: generative and ontogenic approaches. In the generative method, the GPM is a one-shot functional mapping from the genotypes to the phenotypes. The GPM may be an arbitrarily complex decoder, but it on... |

40 | Competitive memetic algorithms for arc routing problems;
- Lacomme, Prins, et al.
- 2004
(Show Context)
Citation Context ...dicating whether the edge between two vertices should be served or not. A first Memetic Algorithm (MA) for CARPs, based on a hybridization of a Genetic Algorithm with a local search, is introduced in =-=[24]-=-. Here, the solutions are represented as the sequences in which edges are served and in which intermediate edges, needed for routing purposes only, are omitted. Different from our definition, the solu... |

33 | A simple modification in cma-es achieving linear time and space complexity,”
- Ros, Hansen
- 2008
(Show Context)
Citation Context ...) In [9], the function driving the development in the ontogenic synthesis of beam data structures is represented as a multi-layer perceptron (MLP) whose weight vector is evolved with a CMA-ES variant =-=[30]-=-. This is also possible in our scenario and we will run corresponding experiments in the near future in order to find out whether GP or MLPs are more efficient in this scenario. We will also test whet... |

32 |
A deterministic tabu search algorithm for the capacitated arc routing problem,”
- Brandão, Eglese
- 2008
(Show Context)
Citation Context ...n is only one sequence of tasks which is later divided into separate tours using a heuristic [35]. A deterministic Tabu Search method which can outperform both the carpet and this MA is introduced in =-=[3]-=-. This algorithm is further improved by introducing a global repair operator which can amend low-cost infeasible solutions [27]. This rts algorithm is still amongst the best approaches for CARPs. An E... |

24 |
comparison of heuristics for the capacitated chinese postman problem; Dissertation,
- DeArmon
- 1981
(Show Context)
Citation Context ...ristic value assigned to the edge e in the previous round of edge selection. 5. EXPERIMENTS 5.1 Benchmark Datasets We tested our algorithm on five sets of CARP benchmark instances, namely the gdb set =-=[6]-=-, the val set [1], the egl set [11, 12, 26], the br-egl set [3], and the kshs set [22]. These benchmark data sets differ widely in terms of scale, i.e., in the number of vertices, the original number ... |

22 |
An interactive algorithm for vehicle routing for winter-gritting,”
- Li, Eglese
- 1996
(Show Context)
Citation Context ...e in the previous round of edge selection. 5. EXPERIMENTS 5.1 Benchmark Datasets We tested our algorithm on five sets of CARP benchmark instances, namely the gdb set [6], the val set [1], the egl set =-=[11, 12, 26]-=-, the br-egl set [3], and the kshs set [22]. These benchmark data sets differ widely in terms of scale, i.e., in the number of vertices, the original number of edges nd+nu, and the number of tasks nR ... |

21 | A genetic programming hyper-heuristic approach for evolving 2-D strip packing heuristics
- Burke, Hyde, et al.
- 2010
(Show Context)
Citation Context ...oach searches the perfect heuristic for a fixed scenario. Therefore, we only use one single test case, which also is the training case, at a time. Hyper-heuristics need to use multiple training cases =-=[5]-=- in order to avoid overfitting to a specific case and test their heuristics on test cases not used during the evolution [21]. Overfitting is acceptable in our approach as it may lead to good approxima... |

17 | X.: A Global Repair Operator for Capacitated Arc Routing Problem
- Mei, Tang, et al.
- 2009
(Show Context)
Citation Context ...ted in their capacity, i.e., the amount of product that they can transport. Traversing any road takes a certain time (cost) and the goal is to find tours of minimum cost that satisfy all requirements =-=[27, 28, 34, 37]-=-. CARPs are usually tackled with an optimization algorithm that produces a solution for one specific, static problem instance. Currently, the algorithms obtaining the best results are Memetic Algorith... |

15 |
A tabu search based heuristic for arc routing with a capacity constraint and time deadline.
- Eglese, Li
- 1996
(Show Context)
Citation Context ...e in the previous round of edge selection. 5. EXPERIMENTS 5.1 Benchmark Datasets We tested our algorithm on five sets of CARP benchmark instances, namely the gdb set [6], the val set [1], the egl set =-=[11, 12, 26]-=-, the br-egl set [3], and the kshs set [22]. These benchmark data sets differ widely in terms of scale, i.e., in the number of vertices, the original number of edges nd+nu, and the number of tasks nR ... |

15 |
Graphic programming using odd or even points,
- Guan
- 1960
(Show Context)
Citation Context ...nd optimal routes for vehicles that need to visit certain streets which require some treatment [10]. Classical examples for ARPs are road gritting and salting [18, 19] and the Chinese Postman Problem =-=[13, 17]-=-. In Capacitated Arc Routing Problems (CARPs), the vehicles are initially located at a single depot and have to deliver some product (such as salt or mail) to the roads. This product is available at t... |

14 | Decomposition-Based Memetic Algorithm for Multi-Objective Capacitated Arc Routing Problem;
- Mei, Tang, et al.
- 2011
(Show Context)
Citation Context ...ted in their capacity, i.e., the amount of product that they can transport. Traversing any road takes a certain time (cost) and the goal is to find tours of minimum cost that satisfy all requirements =-=[27, 28, 34, 37]-=-. CARPs are usually tackled with an optimization algorithm that produces a solution for one specific, static problem instance. Currently, the algorithms obtaining the best results are Memetic Algorith... |

13 |
Building processes optimization : Toward an artificial ontogeny based approach, Universit Paris-Sud
- Devert
- 2009
(Show Context)
Citation Context ...lowing genes. Ontogenic (or developmental) mappings additionally involve feedback from simulations or the process of computing the objective values when building the phenotypes in an iterative manner =-=[7, 9]-=-. Our work is a developmental, ontogenic approach which iteratively adds edges to a solution based on an environment’s state. A good example for such a constellation is the experiment described in [14... |

11 | Dynamic scheduling with genetic programming.
- Jakobovic, Budin
- 2005
(Show Context)
Citation Context ...aining case, at a time. Hyper-heuristics need to use multiple training cases [5] in order to avoid overfitting to a specific case and test their heuristics on test cases not used during the evolution =-=[21]-=-. Overfitting is acceptable in our approach as it may lead to good approximations of the global optimum. Yet, we will show in the experiments in Section 5 that the heuristics discovered with our GP me... |

10 |
The Capacitated Arc Routing Problem
- Benavent, Campos, et al.
- 1992
(Show Context)
Citation Context ...t loop has an unscaled demand of −L. 2. load. The remaining amount of the product inside the vehicle divided by the vehicle’s capacity L. 3. cost(e). The cost of servicing edge e ∈ E, normalized into =-=[0, 1]-=-. These costs contain at least the traversal cost C(e). If load ≥ demand(e), then routing costs from the current location of the vehicle to the starting node head(e) of e are added. Otherwise, routing... |

10 |
X.: Robust route optimization for gritting/salting trucks: a CERCIA experience
- Handa, Chapman, et al.
- 2006
(Show Context)
Citation Context ...planning problems where the goal is to find optimal routes for vehicles that need to visit certain streets which require some treatment [10]. Classical examples for ARPs are road gritting and salting =-=[18, 19]-=- and the Chinese Postman Problem [13, 17]. In Capacitated Arc Routing Problems (CARPs), the vehicles are initially located at a single depot and have to deliver some product (such as salt or mail) to ... |

10 |
An exact algorithm for the capacitated arc routing problem using parallel branch and bound method.
- Kiuchi, Shinano, et al.
- 1995
(Show Context)
Citation Context ...IMENTS 5.1 Benchmark Datasets We tested our algorithm on five sets of CARP benchmark instances, namely the gdb set [6], the val set [1], the egl set [11, 12, 26], the br-egl set [3], and the kshs set =-=[22]-=-. These benchmark data sets differ widely in terms of scale, i.e., in the number of vertices, the original number of edges nd+nu, and the number of tasks nR = |{e : e ∈ E ∧R(e) > 0}|, as well as the n... |

9 | Robust solution of salting route optimisation using evolutionary algorithms
- Handa, Lin, et al.
- 2006
(Show Context)
Citation Context ...planning problems where the goal is to find optimal routes for vehicles that need to visit certain streets which require some treatment [10]. Classical examples for ARPs are road gritting and salting =-=[18, 19]-=- and the Chinese Postman Problem [13, 17]. In Capacitated Arc Routing Problems (CARPs), the vehicles are initially located at a single depot and have to deliver some product (such as salt or mail) to ... |

6 | Robustness and the Halting Problem for Multicellular Artificial Ontogeny
- Devert, Bredèche, et al.
- 2011
(Show Context)
Citation Context ...iment can also be considered as proof for the noise robustness of our method. Such behavior has been found in many works on ontogenic mappings such as [14] and likely explanations for it are given in =-=[8]-=-. 6. CONCLUSIONS AND FUTUREWORK With the results in this paper, we have demonstrated that a developmental approach to the Capacitated Arc Routing Problem is feasible for both static and dynamic cases.... |

6 | A Study on Scalable Representations for Evolutionary Optimization of Ground Structures
- Devert, Weise, et al.
(Show Context)
Citation Context ...dependent from it. Especially the latter case is interesting, as such representations are suitable to solve large-scale problems. At least two classes of indirect representations may be distinguished =-=[2, 9]-=-: generative and ontogenic approaches. In the generative method, the GPM is a one-shot functional mapping from the genotypes to the phenotypes. The GPM may be an arbitrarily complex decoder, but it on... |

6 |
Routing winter gritting vehicles. Discrete applied mathematics
- Eglese
- 1994
(Show Context)
Citation Context ...e in the previous round of edge selection. 5. EXPERIMENTS 5.1 Benchmark Datasets We tested our algorithm on five sets of CARP benchmark instances, namely the gdb set [6], the val set [1], the egl set =-=[11, 12, 26]-=-, the br-egl set [3], and the kshs set [22]. These benchmark data sets differ widely in terms of scale, i.e., in the number of vertices, the original number of edges nd+nu, and the number of tasks nR ... |

5 |
First competitive ant colony scheme for the CARP
- Lacomme, Prins, et al.
(Show Context)
Citation Context ...s are not treated as black boxes: knowledge about their structure is, e.g., used in search operations such as 2-opt [24]. Different from that, the Ant Colony Optimization algorithm (ACO) described in =-=[25]-=- combines local and global information in the search. In ACO, (simulated) pheromones correspond to local information that simulated ants use to choose the next step on their path. Based on the overall... |

4 | Dynamical blueprints: exploiting levels of system-environment interaction
- Estévez, Lipson
- 2007
(Show Context)
Citation Context ... 9]. Our work is a developmental, ontogenic approach which iteratively adds edges to a solution based on an environment’s state. A good example for such a constellation is the experiment described in =-=[14]-=-: The evolution of shapes serving the purpose of heat shields. One shape is made of cells in a grid, one cell is either filled or empty. The decision regarding a cells filling is made by a cellular au... |

2 |
A Survey of Hyper-Heuristics. Computer Science
- Burke, Hyde, et al.
- 2009
(Show Context)
Citation Context ...hereas the genotypes in [9] are multi-layer perceptrons representing the modification function, encoded as real vectors containing, e.g., only 12 neural weights. 3.3 Hyper-Heuristics Hyper-heuristics =-=[4, 31]-=- are methods with a search space of heuristics. This is also the search space of our method. However, there is a semantic difference: hyper-heuristics build heuristics in order to solve a general clas... |