Planning Algorithms

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ahmad bassiouny

Planning Algorithms

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A Heuristic is a technique to solve a problem faster than classic methods, or to find an approximate solution when classic methods cannot. This is a kind of a shortcut as we often trade one of optimality, completeness, accuracy, or precision for speed. A Heuristic (or a heuristic function) takes a look at search algorithms. At each branching step, it evaluates the available information and makes a decision on which branch to follow.

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This article describes an effective and simple primal heuristic to greedily encourage a reduction in the number of binary or 0-1 logic variables before an implicit enumerative-type search heuristic is deployed to find integer-feasible solutions to “hard” production scheduling problems. The basis of the technique is to employ well-known smoothing functions used to solve complementarity problems to the local optimization problem of minimizing the weighted sum over all binary variables the product of themselves multiplied by their complement. The basic algorithm of the “smooth-and-dive accelerator” (SDA) is to solve successive linear programming (LP) relaxations with the smoothing functions added to the existing problem’s objective function and to use, if required, a sequence of binary variable fixings known as “diving”. If the smoothing function term is not driven to zero as part of the recursion then a branch-and-bound or branch-and-cut search heuristic is called to close the procedure finding at least integer-feasible primal infeasible solutions. The heuristic’s effectiveness is illustrated by its application to an oil-refinery’s crude-oil blendshop scheduling problem, which has commonality to many other production scheduling problems in the continuous and semi-continuous (CSC) process domains.

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CHAPTER Modeling and Analysis: Heuristic Search Methods and Simulation LEARNING OBJECTIVES • Explain the basic concepts of simulation and heuristics, and when to use them • Understand how search methods are used to solve some decision support models • Know the concepts behind and applications of genetic algorithms • Explain the differences among algorithms, blind search, and heuristics • Understand the concepts and applications of different types of simulation • Explain what is meant by system dynamics, agent-based modeling, Monte Carlo, and discrete event simulation • Describe the key issues of model management I n this chapter, we continue to explore some additional concepts related to the model base, one of the major components of decision support systems (DSS). As pointed out in the last chapter, we present this material with a note of caution: The purpose of this chapter is not necessarily for you to master the topics of modeling and analysis. Rather, the material is geared toward gaining familiarity with the important concepts as they relate to DSS and their use in decision making. We discuss the structure and application of some successful time-proven models and methodologies: search methods, heuristic programming, and simulation. Genetic algorithms mimic the natural process of evolution to help find solutions to complex problems. The concepts and motivating applications of these advanced techniques are described in this chapter, which is organized into the following sections: 10.1 Opening Vignette: System Dynamics Allows Fluor Corporation to Better Plan for Project and Change Management 436 10.2 Problem-Solving Search Methods 437 10.3 Genetic Algorithms and Developing GA Applications 441 10.4 Simulation 446 435 436 Pan IV • Prescriptive Analytics 10.5 Visu al Interactive Simulatio n 453 10.6 System Dynamics Modeling 458 10.7 Agents-Based Mode ling 461 10.1 OPENING VIGNETTE: System Dynamics Allows Fluor Corporation to Better Plan for Project and Change Management INTRODUCTION Fluor is an engineering and construction company with over 36,000 employers spread over several countries worldwide . The company's net income in 2009 amounted to about $680 million based on total revenue o f $22 b illion. As part of its operations, Fluor manages varying sizes of projects that are subject to scope changes, design changes, and schedule changes. PRESENTATION OF PROBLEM Fluor estimated that changes accounted for about 20 to 30 percent of revenue . Most changes were due to secondary impacts like ripple effects, disruptions, and p roductivity loss. Previously, the changes were collated and reported at a later period and the burden of cost allocated to the stakeholder responsible. In certain instances when late su rprises abou t cost and project schedule are attributed to clients, it causes friction between clients and Fluor, w hich eventually affect future business dealings. .

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How to Analyze the Results of Linear Programs—Part 1: Preliminaries HARVEY J. GREENBERG Mathematics Department University of Colorado at Denver PO Box 173364 Denver. Colorado 80217-3364 In a four part series, I describe ways to analyze the results of linear programs beyond what is commonly described in text- books. My intent is to capture the thought process in analysis with two objectives. First, I want to provide a guide to those getting started in applications of linear programming by sug- gesting useful ways of looking at the results. Second, I want to help create an artificially intelligent environment for the analysis of results by presenting a protocol that a knowledge engi- neer can use. The former has been in the folklore for decades; the latter is part of a project to develop an intelligent mathematical programming system. This first part of the series contains basic terms and concepts used in the other three parts: price interpretation, infeasibility diagnosis, and forcing substructures. A great deal of research and develop-ment activity in large-scale linear programming (LP) has been devoted to solving problems faster. A medium-size problem by today's standards contains about 5,000 equations and 20,000 variables. Even microcomputer versions can handle thousands of equations and variables, and supercomputers have been used for problems with millions of variables! How can we understand the results? At one level, in the interests of model management, we must verify that the solution obtained makes sense with respect to the Cupyrighr S) 1993, The Inslilute of Management Sciencos OO91-21U2/93/23O4/OO56S0I.25 This paptr was refereed. PROCRAMMENG—LINEAR INTERFACES 23: 4 July-August 1993 (pp. 56-67) LINEAR PROGRAMS problem represented by tho linear program. Once we think we have a good run, we must delve into the meaning of a solution. Questions of sensitivity play a direct role, such as What if . . .? and Why . . .? For example, we may ask the following. What if the demand for a commodity increases? What if capacity is expanded? What if some resource is made available? Why did this plant not operate? Why is total production so low? Why is the price of some commodity so large? Why does a certain flow pattern occur? Is it preferred to others because of the economic trade-off, or are the flows forced by the constraints? Textbook wisdom does not go far enough in answering these questions in practical terms (see Gal [1979] for an excel- lent mathematical treatment). Also, once an answer is obtained in some mathematical way, how can we present the answer to problem owners who might not know linear programming? We must be able to look at different views of linear programs and their pieces, for example, using graphic techniques to present information about flows. Before we can venture into this world of analysis, we must understand how linear programs are constructed. In this overview, I describe and illustra ...

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Since 1991, tries were made to enhance the stochastic local search techniques (SLS). Some researchers turned their focus on studying the structure of the propositional satisfiability problems (SAT) to better understand their complexity in order to come up with better algorithms. Other researchers focused in investigating new ways to develop heuristics that alter the search space based on some information gathered prior to or during the search process. Thus, many heuristics, enhancements and developments were introduced to improve SLS techniques performance during the last three decades. As a result a group of heuristics were introduced namely Dynamic Local Search (DLS) that could outperform the systematic search techniques. Interestingly, a common characteristic of DLS heuristics is that they all depend on the use of weights during searching for satisfiable formulas. In our study we experimentally investigated the weights behaviors and movements during searching for satisfiability using DLS techniques, for simplicity, DDFW DLS heuristic is chosen. As a results of our studies we discovered that while solving hard SAT problems such as blocks world and graph coloring problems, weights stagnation occur in many areas within the search space. We conclude that weights stagnation occurrence is highly related to the level of the problem density, complexity and connectivity.

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Since 1991, tries were made to enhance the stochast ic local search techniques (SLS). Some researchers turned their focus on studying the stru cture of the propositional satisfiability problems (SAT) to better understand their complexit y in order to come up with better algorithms. Other researchers focused in investigat ing new ways to develop heuristics that alter the search space based on some information gathered prior to or during the search process. Thus, many heuristics, enhancements and development s were introduced to improve SLS techniques performance during the last three decade s. As a result a group of heuristics were introduced namely Dynamic Local Search (DLS) that c ould outperform the systematic search techniques. Interestingly, a common characteristic of DLS heuristics is that they all depend on the use of weights during searching for satisfiable formulas. In our study we experimentally investigated the wei ghts behaviors and movements during searching for satisfiability using DLS techniques, for simplicity, DDFW DLS heuristic is chosen. As a results of our studies we discovered that whil e solving hard SAT problems such as blocks world and graph coloring problems, weights stagnati on occur in many areas within the search space. We conclude that weights stagnation occurren ce is highly related to the level of the problem density, complexity and connectivity.

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