section{Planning and Scheduling} label{sec:planingscheduling}
Automated planning is concerned with making a plan for solving a problem. When working with these kind of problems, the difficulty primarily lies in defining the problem in a precise yet relatively simple way.
There are different approaches on how to do this, based on what kind of problem needs to be solved. Often their representation will include definitions of states, actions and functions which map states to a new state. The state describes the current world situation. When an action occurs the situation is affected and transits into other states. States, actions and functions are described as mathematical setscite{AutomatedPlanning}:
% is a scheduling system - Jalil
egin{itemize}
item $Sigma = (S, A, gamma)$ item $S: states$ item $A: actions$ item $gamma$: state transition function $(gamma: S imes A ightarrow S)$ end{itemize} A planning problem is often defined as:
egin{equation}
P = (Sigma, s_0, g) end{equation} Where $s_0$ describes the initial state and $g$ describes the desired goal state. The idea is to find a transition from $s_0$ to $g$ through different actions. If all the states have to be explicitly defined, it will quickly grow to an extreme amount of definitions of states. To solve this problem, new states are defined dynamically through the actions applied to the states.
subsection{Set-Theoretic Representation}label{subsec:settheoretic}
The set-theoretic representation is one of the ways to represent a planning problem. Given a finite set $L$ of propositions, we can describe the environment as following:
egin{equation}
L = {p_1, ..., p_n} end{equation} An example of a proposition could be a function named f...
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...ith $gamma^-1(s, a)$. It is the same principle as finding the the successors of a state, but instead it goes the opposite direction and finds the states leading to a state.
%egin{itemize}
% item $gamma^{-1}(g, a) (g - effects^+(a)) cup precond(a)$
% item $gamma(s, a) in s_g $ iff $ gamma^{-1}(g, a) subseteq s$
% item $Gamma^{-1}(g) = {Gamma^{-1}(g, a) mid a in A $ is relevant for $ g}$
% item Supersets reachable of g: $hat{Gamma}^{-1}(g) = Gamma^{-1}(g) cup Gamma^{-2}(g) cup….$
%end{itemize}
%egin{itemize}
% item[] P has solution iff $S_g cap hat{Gamma} eq emptyset$
% item[] P has solution iff s0 is a superset of some element in $hat{Gamma}^{-1}(g)$
% item[] P and P' have the same statement then both P and P' have the same set of reachable states $hat{Gamma}(s0)$ and the same set of solutions.
%end{itemize}
This is called the rate determining step. The rate determining step must be equal to the experimental determined step because the rate of reaction will be controlled. For the majority of the experiment, a catalyst (Im) will be utilized to help speed up the reaction. A catalyst will generate an alternative path when driving the reaction forward by lowering the energy of activation, resulting in a faster reaction and isn’t consumed during the reaction but can be included in the law due to it being a reactant in the determining step. Because the catalyst stabilizes in the high energy transition state structure, it doesn’t affect the free energy reaction.
Anthony R. Cassandra, “A survey of POMDP applications,” in AAAI Fall Symposium on Planning with Partially Observable Markov Decision Processes, 1998
A Cellular Automata can be viewed as an autonomous Finite State Machine[FSM] consisting of a number of cells.
up of three parts. First, a state is a structure with parts that work together
... choose to change a part of that chain. Introducing an indetermined event, by which the determined course will shift, creating another determined course that includes the indetermined act.
allow for each subsequent step to take place. And after each step it becomes increasingly
Termination condition is the condition that ends the evolutionary computation cycles. Termination condition can be the maximum number of cycles allowed, ore in case we know the optimal solution the value of that solution.
ADM offers Commanders and planning staff a tool for the conceptual component of an integrated planning process. The goal is to provide the commander with a cognitive tool that he can use to understand the logic of the system. Design is non-linear in thought and application. Its methodology clari¬fies guidance in the consideration of operational environment, and the current system is understood within existing limitations. The design team pro¬duces an environmental frame, an initial problem statement, and an initial theory of action. As the teams’ understanding increases and the nature of the problem begins to take form, the team explores in greater detail aspects of the environment that appear relevant to the problem. Here choices are made about boundaries and areas for possible inter¬vention. From this deeper understanding, the des...
Forward chaining breaks things down into a way that one can understand and manage what he or she is trying to achieve from the beginning to end, “ In forward chaining the behaviors identified in the task analysis are taught in the naturally occurring order,” (Cooper, Heron, & Heward, 2007). So what the behaviorist could do is identify the target behavior which is hitting the serve with enough speed or accuracy, after this has been analyzed it can be broken down into steps for Brendan to do first. After Brendan has mastered the first step the behaviorist can add a second step to the first doing the first and second steps together until mastered and so on. In order for Brendan to start a new step he must master each step before moving to the next step then all combined together. The backward chaining is like the forward chaining but teaches from end to the beginning. The behaviorist could use this if it would be easier for Brendan to learn with the last step first and the first step last so hitting the ball first then the first normal steps last until all is mastered in steps, “When a backward chaining procedure is used all the behaviors identified in the task analysis are initially completed by the trainer, except for the
In their 1973 article they declared that the ways for solving problems by linear method for problem solving are over and this is the effect of the change in the modern society and increasing social complexities which makes it difficult to define the problems and also that the dependency is based on political reasoning. [ 1] According to the complexities involved in the problem, and methodologies used for solving the problems, planning problems can be categorized into three categories, Tame problems, Wicked problems and Super wicked problems.... ... middle of paper ... ...
“Planning: is specifying the goals to be achieved and deciding in advance the appropriate actions needed to achieve those goals” (Bateman & Snell, 2004, p. 16).
The reason that the states seek survival is because if the states are not exist, they can’t seek any other interests. Waltz introduces that bipolar systems provide a be...
unified because reasoning and problem solving may involve several areas simultaneously. A robot circuitrepair syste m, for instance, needs to reason about circuits in terms of electrical connectivity and physical layout, and about time both for circuit timing analysis and estimating labor costs. The sentences describing time therefore must be capable of being combined w ith those describing spatial layout, and must work equally well for nanoseconds and minutes, and for angstroms and meters. After we present the general ontology, we will apply it to write sentences describing the domain of grocery shopping. A brief reverie on the subject of shopping brings to mind a vast array of topics in need of representation: locations, movement, physical objects, shapes, sizes, grasping, releasing, colors, categories of objects, anchovies, amounts of stuff, nutrition, cooking, nonstick frying pans, taste, time, money, direct debit cards, arithmetic, economics, and so on. The domain is more than adequate to exercise our ontology, and leaves plenty of scope for the reader to do some creative knowledge representation of his or her own. 228 Chapter 8. Building a Knowledge Base Our discussion of the
... the problem, called heuristics. This results in increase in efficiency of the search process in that fewer states are expanded with an informed search than with a blind one. Some nodes or paths are clearly favoured while others are omitted and not elaborated on. Time is not wasted by choosing redundant or irrelevant paths. This means the better the heuristics the better and faster the search will be performed. The fewer the steps needed to obtain the solution path, the better the solution path will be.
Search and Planning: It is an important area when it comes to games like chess and checkers. Various search algorithms are used to search for an appropriate move. Planning algorithms have to be designed in a way to minimize play time and also reduce the use of future resources.