TABLE OF CONTENTS

 page

A C K N O W L E D G M E N T S ......... .................................................................................... iii

LIST O F FIG U R E S .... .............................. ....................... ........ .. ............... vi

ABSTRACT .............. .......................................... ix

CHAPTER

1 IN TR OD U CTION .................. ............................ ............. .............. .

 Multiple Robot Positioning and Communication ..................................................... 1
 O p tim iz atio n ........................................................... ........ ...... 2

2 M O D ELIN G TH E PR O B LEM .......................................................................... ........ 5

 A M ap of Points ............... ............................................ ... .................... 5
 Polygon Triangulation A pproach.................................... ........................... ........ 6
 G rid B ased A p p ro ach ............................................................................. .. ....... 6
 Initial Line-of-Sight M ethod ........................................................................ 7
 Initial Shadow Area Calculation....................................... ..................................... 10
 Line-of-Sight and Shadow Area Method Revisited ................................................. 12
 Line Segm ent Intersection M ethod.................................................................... 13
 Line-of-Sight Determination...................... ...... ........................... 14
 Shadow A rea C alculation.................................................. ......................... 15
 Prelim inary results ......... ................ .... .......... .... .......... 15

3 AN OVERVIEW OF OPTIMIZATION TECHNIQUES............... ...............17

 B ackgrou n d ..................................................... 17
 G olden Section M ethod ................................................... ................................. 18
 G radient Techniques ...................................................... ..... .............. 21
 Steepest Descent ......................................... 21
 M onte Carlo Integer Program ming................................................... ................. 23

4 GEN ETIC ALG OR ITM S ........................................... .................. ............... 25

 Traditional Methods versus Genetic Algorithms..................................................... 25
 Sim ple G enetic A lgorithm .......................................................... ... .............. 27