Application of planning-graph with weight in logistics vehicles dispatching system

2015 ◽  
pp. 147-150 ◽  
Keyword(s):  
Planning Graph

Fast Planning Through Planning Graph Analysis.

1995 ◽  
Author(s):  
Avrim L. Blum ◽  
Merrick L. Furst
Keyword(s):  
Graph Analysis ◽  
Planning Graph

FIP: A Fast Planning-Graph-Based Iterative Planner

2008 ◽  
Author(s):  
Jicheng Fu ◽  
Farokh Bastani ◽  
Vincent Ng ◽  
I-Ling Yen ◽  
Yansheng Zhang
Keyword(s):  
Planning Graph

Designing a Product Package Platform

2010 ◽  
Author(s):  
Margaret Devendorf ◽  
Kemper Lewis
Keyword(s):  
Design Theory ◽  
Product Family ◽  
Optimal Arrangement ◽  
Family Identity ◽  
Product Packaging ◽  
Product Families ◽  
Product Identity ◽  
Cereal Boxes ◽  
Planning Graph ◽  
Paper Product

An essential part of designing a successful product family is establishing a recognizable, familiar, product family identity. It is very often the case that consumers first identify products based on their physical embodiment. The Apple iPod, DeWalt power tools, and KitchenAid appliances are all examples of product families that have successfully branded themselves based on physical principles. While physical branding is often the first trait apparent to designers, there are some products that cannot be differentiated based on physical appearance. This is especially common for consumable products. For example, it is impossible to differentiate between diet Coke, Classic Coke, and Pepsi when each is poured into separate glasses. When differentiation is difficult to achieve from a product’s physical characteristics, the product’s package becomes a vital part of establishing branding and communicating membership to a product family while maintaining individual product identity. In this paper, product packaging is investigated with a focus on the graphic packaging components that identify product families. These components include: color, shape, typography, and imagery. Through the application of tools used in facilities layout planning, graph theory, social network theory, and display design theory an approach to determine an optimal arrangement of graphic components is achieved. This approach is validated using a web based survey that tracks user-package interactions across a range of commonly used cereal boxes.

scholarly journals Friends or Foes? On Planning as Satisfiability and Abstract CNF Encodings

2009 ◽  
Vol 36 ◽  
pp. 415-469 ◽  
Author(s):  
C. Domshlak ◽  
J. Hoffmann ◽  
A. Sabharwal
Keyword(s):  
Point Of View ◽  
Theoretical Point ◽  
Optimal Plan ◽  
Interesting Phenomenon ◽  
State Spaces ◽  
Planning Task ◽  
Resolution Refutation ◽  
International Planning ◽  
Almost All ◽  
Planning Graph

Planning as satisfiability, as implemented in, for instance, the SATPLAN tool, is a highly competitive method for finding parallel step-optimal plans. A bottleneck in this approach is to *prove the absence* of plans of a certain length. Specifically, if the optimal plan has N steps, then it is typically very costly to prove that there is no plan of length N-1. We pursue the idea of leading this proof within solution length preserving abstractions (over-approximations) of the original planning task. This is promising because the abstraction may have a much smaller state space; related methods are highly successful in model checking. In particular, we design a novel abstraction technique based on which one can, in several widely used planning benchmarks, construct abstractions that have exponentially smaller state spaces while preserving the length of an optimal plan. Surprisingly, the idea turns out to appear quite hopeless in the context of planning as satisfiability. Evaluating our idea empirically, we run experiments on almost all benchmarks of the international planning competitions up to IPC 2004, and find that even hand-made abstractions do not tend to improve the performance of SATPLAN. Exploring these findings from a theoretical point of view, we identify an interesting phenomenon that may cause this behavior. We compare various planning-graph based CNF encodings F of the original planning task with the CNF encodings F_abs of the abstracted planning task. We prove that, in many cases, the shortest resolution refutation for F_abs can never be shorter than that for F. This suggests a fundamental weakness of the approach, and motivates further investigation of the interplay between declarative transition-systems, over-approximating abstractions, and SAT encodings.

scholarly journals A Hybrid LP-RPG Heuristic for Modelling Numeric Resource Flows in Planning

2013 ◽  
Vol 46 ◽  
pp. 343-412 ◽  
Author(s):  
A. Coles ◽  
A. Coles ◽  
M. Fox ◽  
D. Long
Keyword(s):  
Resource Use ◽  
Raw Materials ◽  
Integer Program ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Additional Information ◽  
Planning Graph ◽  
Planning Problems ◽  
Interval Valued ◽  
Numeric Reasoning

Although the use of metric fluents is fundamental to many practical planning problems, the study of heuristics to support fully automated planners working with these fluents remains relatively unexplored. The most widely used heuristic is the relaxation of metric fluents into interval-valued variables --- an idea first proposed a decade ago. Other heuristics depend on domain encodings that supply additional information about fluents, such as capacity constraints or other resource-related annotations. A particular challenge to these approaches is in handling interactions between metric fluents that represent exchange, such as the transformation of quantities of raw materials into quantities of processed goods, or trading of money for materials. The usual relaxation of metric fluents is often very poor in these situations, since it does not recognise that resources, once spent, are no longer available to be spent again. We present a heuristic for numeric planning problems building on the propositional relaxed planning graph, but using a mathematical program for numeric reasoning. We define a class of producer--consumer planning problems and demonstrate how the numeric constraints in these can be modelled in a mixed integer program (MIP). This MIP is then combined with a metric Relaxed Planning Graph (RPG) heuristic to produce an integrated hybrid heuristic. The MIP tracks resource use more accurately than the usual relaxation, but relaxes the ordering of actions, while the RPG captures the causal propositional aspects of the problem. We discuss how these two components interact to produce a single unified heuristic and go on to explore how further numeric features of planning problems can be integrated into the MIP. We show that encoding a limited subset of the propositional problem to augment the MIP can yield more accurate guidance, partly by exploiting structure such as propositional landmarks and propositional resources. Our results show that the use of this heuristic enhances scalability on problems where numeric resource interaction is key in finding a solution.

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