Title: Optima
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00090046/00063
 Material Information
Title: Optima
Series Title: Optima
Physical Description: Serial
Language: English
Creator: Mathematical Programming Society, University of Florida
Publisher: Mathematical Programming Society, University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: January 2000
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Bibliographic ID: UF00090046
Volume ID: VID00063
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.


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Mathematical Programming Society NeiV'ttewrL



Collections of

SET Cards


We invite OPTIMA readers t

to the problems to Robert Bo

lin.edu). The most attractive

presented in a forthcoming is


o submit solutions 'Set'less Collections of SET Cards

isch (bobb@cs.ober-
Robert A. Bosch
solutions will be August 29, 1999


TS is a card game played with a special 81-card
deck. Each SET card has four attributes (num-
SSETber, color, shading, and shape), and on each card,
each attribute assumes one of three possible values. More precisely, a SET
card displays a drawing of one, two, or three symbols. The symbols are all
red, green, or purple; filled-in, outlined, or striped; oval-shaped, squiggle-
shaped, or diamond-shaped. The SET deck contains 34=81 cards, one for
each possible combination of attribute values.
The basic object in SET is the 'Set,' a collection of three cards that
has, with respect to every attribute, either all or none of its cards in agree-
ment. At the beginning of the game, the deck is shuffled and twelve cards
are laid out on the table, face up. The first player to spot a 'Set' removes
S it, placing it in his or her pile. Then three more cards are placed on the
table, and play continues. Note that the cards displayed in Figure 1 form
a 'Set': all of them agree with respect to color, and none of them agree
with respect to number, shading, or shape.

r -

Purple plwqpf purple
Figure 1. Three set cards that form a 'Set'

The rulebook states "If all players agree that there is no 'Set' in the
twelve cards showing, three more cards (making a total of fifteen) are laid
face up. These cards are not replaced when the next 'Set' is picked up,
reducing the number to twelve again." The implication is that every col-
lection of fifteen cards contains at least one 'Set.' This is not true. In fact,
it is easy to find collections of fifteen cards that are 'Set'less (i.e. contain
no 'Sets').
In December 1996, Rajmohan Rajagopolan-then an undergraduate
student at Oberlin College, and now a graduate student at Cornell
University-realized that integer programming could be used to find a
largest 'Set'less collection of SET cards. Rajagopolan treated each SET
card as a point in S where S is the set {0,1,2}. There are many ways that
this can be done; one possible 'encoding' is given in Figure 2. Note that
the cards corresponding to three distinct points x, y, z e S form a 'Set' if
and only if (x + y, + z) mod 3 0 for i 1,2,3,4.

1 SET is a registered trademark of Set Enterprises Inc.


c number one 0 c color red 0
two 1 green 1
three 2 purple 2

c3 shading filled-in 0 c4 shape oval 0
outlined 1 squiggle 1
striped 2 diamond 2

Figure 2. Mapping a card to a point c


In September 1997, one of my colleagues, Oliver Schirokauer, reported
to me that he and Carl Cotner had written a clever program that used
enumeration to prove that a 'Set'less collection of SET cards can contain
no more than 20 cards. After learning from Schirokauer that I could have
fixed six (carefully chosen) variables at their upper bounds of one, I gave
CPLEX another try. This time, CPLEX was successful, solving
Rajagopolan's integer program in approximately 1,500 seconds and almost
275,000 branch-and-bound nodes.

Rajagopolan's integer program for finding a largest 'Set'less collection is
quite simple:

max Z vx
s.t. vx + vy + v < 2 Vx, z e S4: x, y, z are distinct, and
(x, +y, + z) mod 3-0 for= 1,2,3,4.
v e 0,1} Vxe S4.

There are 81 binary variables, one for each SET card (each x e S'). The
variable v. is assigned the value 1 if and only if the card corresponding to
x is placed in the 'Set'less collection. There are (8)/3 =1,080 constraints,
one for each 'Set.' They ensure that no more than two of the three cards
that form a 'Set' are placed in the collection.
In June 1997, I attempted to solve Rajagopolan's integer program using
branch and bound (version 4.0.9 of CPLEX's Mixed Integer Optimizer).
After fixing four variables at their upper bounds of one, I started the opti-
mization process. Within a few seconds, CPLEX had discovered a feasible
solution with objective value 20. At this point, the upper bound on the
optimal value of the objective function was 35.0, and the branch-and-
bound tree consisted of 1,382 nodes, of which 878 were unexplored.
Approximately 0.4 MB of memory were being used to store the branch-
and-bound tree.
An hour later, branch and bound was still going. The best solution it
had found so far was the one with objective value 20. The upper bound
on the optimal value of the objective function was now 25.5. The branch-
and-bound tree had over 350,000 nodes, and over 200,000 of these nodes
were unexplored. Slightly more that 100 MB of memory were tied up in
the storage of the branch-and-bound tree! At this point, I terminated the


Interested readers may enjoy trying to solve the following problems:
1. Find valid inequalities for Rajagopolan's integer program. Note:
When one additional inequality was added, CPLEX was able to solve
the resulting integer program in approximately 800 seconds, with
just over 118,000 branch-and-bound nodes. When an extra 1,170
inequalities-all of the same type-were added, CPLEX took
approximately 650 seconds, with just under 3,500 nodes! Hint: SET
can be played with certain 9-card decks (the purple squiggles, for
2. In a well-known paper on cutting planes [1], Vasec Chvital present-
ed an integer programming formulation (and a cutting-plane proof
of the solution of) Moser's Cube Problem:
Let us consider the three-dimensional tick-tack-toe cube with 27
points (0,0,0), (0,0,1), ..., (2,2,2). Our objective is to select as
many of these 27 points as possible without choosing three
collinear ones.
The problem of finding a largest 'Set'less collection of purple SET cards
(a 27-card deck) is a variant of Moser's Cube Problem. Each 'Set' can
be thought of as a line. (Just as two points determine a line, two
SET cards determine a 'Set.') Construct a cutting-plane proof that a
'Set'less collection of SET cards can contain at most nine purple
3. Suppose that each SET card has five attributes instead of four.
Determine the largest number of cards in any 'Set'less collection of

0S MA63

(c, C2, C3', C4) e S4


Maximizing Vitality Revisited

rule set

example pattern

S 2.

3. 4.
7cr #

7. 8.

"'ANN", A!", M
10, in"Al -
1&k 4mM-,:`x A ,
M. W : twm 1 17 !17

VANE- `, V 1& 4, -M
mffmm: :'MMMMM I' 'K :M

ti''WE, :Jim
M, "MEN' "E., " 7, 'MEN'
V70: ow:Mmomw 10:

Figure 3. The rule set and an example pattern

In the March 1999 issue of OPTIMA, we discussed a simple one-
dimensional cellular automaton that consists of n cells (numbered from
19 0 to n-1 going from left to right) arranged in a horizontal line. Each cell i
has two neighbors: a left neighbor 1(i) and a right neighbor r(i). Cell O's
left neighbor is cell n-1, and cell n-l's right neighbor is cell 0.
Recall that at each point in time, each cell is either alive or dead. To
start up the cellular automaton, we just need to decide which cells will be
alive at time t =0 and which ones will be dead then. Then to run it, we
simply apply the rule set (displayed on the left side of Figure 3) over and
over again. The first application of the rule set determines the states of the
cells at time t =1. The second application determines the states of the cells
at time t 2. And so on. In the example pattern (displayed on the right
side of Figure 3), cell 0 is alive at time 1 because of rule 3, which states
that if cell i is alive at time t and cells 1(i) and r(i) are dead at time t, then
cell i must be alive at time t +1. Cell 1 is dead at time 1 due to rule 6,
and cell 2 is alive at time 1 due to rule 7.

At the end of the March 1999 article, we challenged readers to solve
three problems. The first was to complete our integer programming for-
mulation of the maximum average vitality problem, the problem of find-
ing an initial assignment of states to cells that maximizes the average vital-
ity of the cellular automaton over a given time interval [a,b]. (The vitality
of a cell over a time interval is the fraction of the time it is alive; the aver-
age vitality of the cellular automaton over a time interval is the average of
all its cells' vitalities over that time interval.) Our integer program had a
binary variable

1 if cell is alive at time t,
X,- 0 if not

for each 0 < i < n-1 and each 0 < t b. We presented two constraints:

-11,.: -r t "j.: + 1& 0

x ~+ x, ~+ 2,i

1 "0 1 1! 2

: .1:)

The former enforces rule 1 for cell i during the transition from time t
to time t +1; the latter enforces rules 6 and 8. Each constraint works by
prohibiting the configuration that violates the rule.
Leslie Gardner submitted constraints that enforce rules 2-5 and 7 for
cell i during the time-t-to-time-t+ transition:




.V i > .--r

... :so, t.:- o.1: EE I 0

.:,+:.. : + t, 1 2, 0 02

.ri! qi!
1+.Z +x1t t 2 2

Gardner also solved the second and third problems. The second prob-
lem was to prove that the maximum average vitality v(a,b) of the cellular
automaton over the time interval [a,b] satisfies

3 2
v(a, ) + 2-a
5 5(a-a+

Gardner began her proof by proving the validity of the following

xII"a,: + x,,. + .. + X" I + 1 l -1.


(To prove that it holds, take the inequality -x < -1 and add to it the two
inequalities that enforce rule 5 at cell i and cell r(i) during the time-t-to-
time-t+1 transition.) She then summed up all copies of this inequality for
i between 0 and n-1 and t between a and b, obtaining
n-1 1 -1 n-1
3 + 5 Y x + 2Zx,, 3(b- a)n.
-0 i=0 -a+l i=0

From this it follows that
n-1 b
5 Z Y x,, : 3 (b a)n + 5n


( 1 } x 3(b- a)n+ 5n 3 2
a (b- a+1)nr0, io 5(A-a++l)n 5 5(b-a+1)

The third problem asked for a solution strategy that would exploit the
fact that once values have been assigned to the variables for time 0, the
values of the remaining nb variable are completely determined. (Once we
know the values of the time-0 variables, we can run the cellular automa-
ton to obtain the values of the remaining variables.) Gardner suggested
... a genetic algorithm approach where the chromosomes are sequences
of the n binary variables for time 0." The fitness of a chromosome would
be the resulting average vitality. Simple crossover could be used as the
genetic operator.


[1] V. Chvital, Edmonds polytopes and a hierarchy ofcombinatorial prob-
lems, Discrete Mathematics 4 (1973), pp. 305-337.


0S MA63


OPTINMA wants to congratulate our distinguished colleagues on their birthdays!


celebrated his 85th birthday. A
special "Dantzig Fest" was
organized at the INFORMS
National Meeting in
Philadelphia, Nov. 7-10, 1999,
including presentations by
Arthur E Veinott, B. Curtis
Eaves, Irv Lustig, Allan J.
Hoffman, Ellis L. Johnson, and
George B. Dantzig himself.

received as a "birthday pres-
ent," the DIMACS Workshop
on the Theory andPractice of
Integer Programming in
honor ofRalph E. Gomory on
the Occasion ofhis 70th
Birthday, organized by Bill
Cook and Bill Pulleyblank.
The workshop was organized
at IBM, Yorktown Heights, on
Aug. 2-4, 1999. Main speakers
were Vasek Chvatal, Herbert
E. Scarf, Egon Balas, George
L. Nemhauser, Gerard
Cornuejols, and Ralph E.

our previous chairman, and
current vice-chairman cele-
brated his 60th birthday, and
received a dedicated issue of
SIAMJournal on OPTI-
MIZATION, a journal of
which he was the first editor.
The dedication written by
Michael L. Overton and
Robert B. Schnabel can also
be found at the following
URL: http://epubs.siam.org/







The 17th International Symposium on
Mathematical Programming (ISMP 2000)
will take place in Atlanta, Georgia, USA,
on the campus of the Georgia Institute of
Technology August 7-11, 2000. For more
information, please visit the web site

Nominations for 2000 Elections

The Constitution of the
Mathematical Programming
Society sets the terms of office for
all officers of the Society at three
years. Elections for all offices
(Chair, Treasurer, and four
At Large Members of Council) are
to be held four months prior to
each triennial International
Symposium. The seventeenth sym-
posium will take place in Atlanta
on August 7-11, 2000, so the next
election will be held in April 2000.
The new Members-at-Large of the
Council will take office at the time
of the symposium, the Chair-Elect
and the Treasurer-Elect will take
office one year later.
Candidates must be members of
the Society and may be proposed
either by Council or by any six
members of the Society. No proper
nomination may be refused, pro-
vided the candidate agrees to stand.
The following procedure will be

(1) Nomination to any office is to
be submitted to the Nomination
Committee, which consists of John
Dennis, Jan Karel Lenstra (chair,
jkl@win.tue.nl), and Clyde
Monma. Such nomination is to be
supported by the nominator and at
least five other members of the
(2) In keeping with tradition, the
next Chair should preferably be a
North American resident. The
membership is asked to consider no
residents from other continents as
candidates for the Chair.
(3) When the ballots are counted,
the four At-Large candidates for
Council having the highest number
of votes will be elected; however,
no more than two members having
permanent residence in the same
country may be elected.

Over $35,000 Collected for Fulkerson Prize

The Fulkerson Prize for outstand-
ing papers in discrete mathemat-
ics is sponsored jointly by the
Mathematical Programming
Society and the American
Mathematical Society. Since
1979, up to three awards were
presented at each International
Symposium on Mathematical
Programming. The awards were
initially paid out of a memorial
fund that was established by
friends of the late Delbert Ray
Fulkerson to encourage mathe-
matical excellence in the fields of
research exemplified by his work.
The prize fund became depleted
several years ago. MPS and AMS
appointed a fund-raising commit-
tee, consisting of Bob Bixby, Bob
Bland, and Ron Graham. In the
past year, with the help of Steve
Wright and Jan Karel Lenstra,
they raised a total amount of
$35,697.32, which should be suf-
ficient to support the prize in per-
petuity. The new prize fund will
be administered by MPS.

Substantial corporate and institu-
tional donations were received:
Foundation 14th ISMP
(Amsterdam, 1991), $3,800; IBM,
$5,000; Lucent Technologies,
$5,000; Philips Research
Laboratories, $3,000; Telcordia
Technologies (formerly Bellcore),
$5,000. These sponsors will be
recognized on the MPS web site.
Individual contributions were
made by Bob Bixby, Ralph
Gomory, William Hogan, Clyde
Monma, George Nemhauser,
Lloyd Shapley, Irene and Richard
Van Slyke, David Weinberger,
Karen Aardal, Anant Balakrishnan,
Bill Cook, Pierre Courrieu, Curtis
Eaves, Kaoru Endo, Sharon
Filipowski, Robert Freund, David
Gay, Donald Hearn, T.C. Hu,
Paparrizos Konstantinos,
Siriphong Lawphongpanich, Jan
Karel Lenstra, Janny Leung, A.
Loshise, William Lucas, Charles
McCallum, Jr., Masataka
Nakamura, Michael Panik, Roman
Polyak, Herbert Scarf, Alexander
Schrijver, Bruce Shepherd, Richard
Soland, Jie Sun, Roman Sznajder,
Lakshman and Sarala Thakur,
Michael Todd, Jean-Philippe Vial,
Kevin Wayne, David Williamson,
and H. Yamano.

Online Algorithms: The State of the Art

Amos Fiat and Gerhard J. Woeginger (Eds.)

Lecture Notes in Computer Science, Vol. 1442, 1998

Springer Verlag
ISBN 3-540-64917-4

During the past years online computation has become an impor-
tant field in mathematics, computer science and operations

During the past years online computation has become an impor-
research. This is not only due to its intrinsic interest but also
to its many applications.
Typically when one solves problems and designs algorithms one assumes
that all the input data is known a priori. However, in many practical situa-
tions this assumption might not be true. Consider the following simple sce-
nario: during a ski season an enthusiastic skier goes skiing every weekend
that conditions permit. Since she does not own skis she asks herself whether
to rent a pair or buy one. Clearly, if our skier knew a priori how long the
season will last, then she could easily calculate her most inexpensive way
through the season. Unfortunately, she does not have this complete knowl-
edge but only discovers each weekend whether the season still continues or
has already ended. Each time she is faced anew with the decision whether
to rent or buy this time (unless she already bought some skies).
The area of online computation deals with the above outlined issue: an
online algorithm must decide how to process incoming pieces of informa-
tion without any knowledge of future ones. The online algorithm must
make its decisions before the next bit of information is revealed and it is not
allowed to revoke any of its past decisions. Competitive analysis has become
the standard yardstick of how to judge online algorithms: the quality of an
online algorithm is measured relative to the best possible performance of an
offlinee) algorithm that has complete knowledge of the future.
The book edited by Amos Fiat and Gerhard J. Woeginger addresses

many aspects of online computation and competitive analysis. The chapters
have been contributed by recognized experts in the field, and this has result-
ed in an excellent book about the current research in this area. Each chap-
ter examines a specific application area and summarizes the related results
in the literature.
The topics covered include classical online problems which initiated the
research on competitive analysis such as self-organizing data structures or
paging in virtual memory systems as well as more recent topics such as
searching and navigation of unknown environments or online financial
problems. The book also includes a good discussion on the applicability of
competitive analysis in practice and its limitations.
The first chapter, written by the editors Amos Fiat and Gerhard
J. Woeginger themselves, gives a brief introduction to competitive analysis
and its history. Chapter 2 by Susanne Albers and Jefferey Westbrook sur-
veys self-organizing data structures. Results and their proofs on organizing
linear lists are complemented by an overview of splay trees and applications.
In Chapter 3, Sandy Irani presents results about paging. This chapter also
includes information about variants of competitive analysis such as loose
competitiveness and access graphs.
Chapter 4 was written by Marek Chrobak and Lawrence L. Larmore. It
gives an overview of metrical task systems and the famous k-server problem.
This chapter contains many proofs, among them the celebrated theorem
about the competitiveness of the "work-function algorithm" for the k-serv-
er problem. In Chapter5, Yair Bartal gives a nice survey of distributed pag-
ing. This area includes file migration and file allocation problems which
have applications to distributed data bases and web-caching.
Chapter 6, written by James Aspnes, deals with the issue of combining
competitive (sub-) algorithms in distributed systems to a globally competi-
tive algorithm. Chapter 7 by Janos Csirik and Gerhard J. Woeginger covers
online packing and covering problems. The bin-packing problem was one
of the first problems to be studied from an online point of view. The
authors discuss the bin-packing problem, its extensions to higher dimen-
sions and geometric versions.


Chapter 8 by Yossi Azar is about online load balancing. This chapter is
tightly connected to Chapter 11 on online network routing. The latter
chapter was written by Stefano Leonardi and contains an enjoyable survey
and some nice proofs. The also related area of scheduling is treated in great
detail in Chapter 9 by Jiri Sgall.
The use of competitive analysis for online searching and navigation is
discussed in Chapter 10 which was written by Piotr Berman. Chapter 12
by Bala Kalyanasundaram and Kirk Pruhs covers online network design
problems. The authors also give pointers to online versions of the traveling
salesperson problem. In Chapterl3, Hal A.Kierstead surveys online graph-
coloring problems. This chapter is an excellent source for results as well as
applications of online graph coloring.
Chapter 14 was written by Avrim Blum and provides thorough infor-
mation about online problems from Computational Learning Theory. The
chapter also contains a nice list of open problems from this area. Online
financial problems are the topic of Chapter 15 by Ran El-Yaniv. These
problems have interesting applications in portfolio selection, search and
leasing. In Chapterl6, Anna Karlin comments on the performance of com-
petitive algorithms in practice.
The last chapter is again written by the two editors, Amos Fiat and
Gerhard J. Woeginger. In this chapter they indicate the limits of competi-
tive analysis and comment on ways around some competitive odds and
ends. Often "standard" competitive analysis fails to provide a theoretical
explanation of behavior that is observed in practice. One such example is
the fact that a number of paging algorithms (First-In-First-Out, Least-
Recently-Used, etc.) all have the same competitive ratio k, where k equals
the number of page slots in memory, but their performance in practice is
quite different. Another problem with competitive analysis is that for some
problems it only allows extremely weak positive results. The best possible
competitive ratio is totally disappointing and is achieved by a trivial algo-
rithm. An example is provided again by the paging problem: the First-In-
First-Out page replacement strategy hits the "triviality barrier" of k.
In conclusion, Amos Fiat and Gerhard J. Woeginger as well as their
guests have done an excellent job in producing a comprehensive survey of
the most relevant results in online computation. There is one grain of salt
that has to be added: The reader would probably like to see more proofs in
the book (such as in Chapter 4 instance). However, due to the immense
material covered in the book it was apparently not possible to include even
I strongly recommend the book edited by Amos Fiat and Gerhard
J. Woeginger as a reference for researchers in the area of online computa-
tion. For readers new to the area, the reading should be supplemented by a
study of a good textbook on online algorithms such as the recent book by
Allan Borodin and Ran El-Yaniv [BEY98].

Konrad-Zuse-Zentrum fur Informationstechnik Berlin


[BEY98] A. Borodin and R. El-Yaniv, Online computation and competi-
tive analysis, Cambridge University Press, 1998.

[FW98] A. Fiat and G. J. Woeginger (eds.), Online algorithms: The state
of the art, Lecture Notes in Computer Science, vol. 1442,
Springer, 1998.


Graphs, Networks andAlgorithms

by Dieter Jugnickel

Springer Verlag, 1999
ISBN 3-540-63760-5

his book is the translation of a revised version of the third edi-
tion of the German text book 'Graphen, Netzwerke und
Algorithmen' by Dieter Jungnickel. The first German edition
appeared in 1987 and it was followed by other revised editions
in 1990 and 1994. This is to say that the text has had the time to evolve and
reach maturity and this English version is a well written and balanced text-
The chosen topics are in accordance with the title. As the author points
out in the preface, "the present book concerns mainly that part of
Combinatorial Optimization which can be formulated and treated by graph
theoretical methods; neither the theory of Linear Programming nor
Polyhedral Combinatorics are considered. Simultaneously, the book gives
an introduction into Graph Theory." The list of chapter titles will better
outline the scope of the book (the number of pages of each chapter is in
parentheses): 1. Basic Graph Theory (34), 2. Algorithms and Complexity
(28), 3. Shortest Paths (36), 4. Spanning Trees (30), 5. The Greedy
Algorithm (26), 6. Flows (54), 7. Applications in Combinatorics (30), 8.
Colourings (14), 9. Circulations (52), 10. Synthesis of Networks (26), 11.
Connectivity (24), 12. Matchings (34), 13. Weighted Matchings (34), 14.
A Hard Problem: the TSP (48). Then there is an appendix with the solu-
tions of the exercises and an appendix with the list of symbols. In total the
book comprises 590 pages. I would also say that sometimes the author is not
able to stay within the self-inflicted bounds, as in Chapter 5, where
matroids are presented as abstract combinatorial objects, or in Chapter 13
where he cannot refrain from introducing the matching polytope.
Given these data, it is not surprising that the topics are treated quite in
depth and extensively. Indeed there is a wealth of material which could be
suited for some advanced courses in graph or network theory. Ph.D. stu-
dents could benefit a lot from the book. However, there is probably too
much material for a typical Master's student. The book is a mathematical
one. Definitions are carefully phrased (though not explicitly stated as such)
and Theorems, Lemmas, and Corollaries go along with their proofs.
Moreover, the text is interspersed with exercises which stimulate the reader
to a more active understanding of the material. Figures are pervasive and
quite welcome.
To convey a more detailed idea on the scope and depth of the book, here
are some examples of topics which are rarely included in Graph Theory
books and can be found in Jungnickel's book: path algebras in Chapter 3;
the Matrix Tree Theorem (how to compute the number of spanning trees of
a graph) and Steiner trees in Chapter 4; greedoids in Chapter 5; preflow
ideas for maximal flows in Chapter 6; Cayley graphs in Chapter 7; edge col-
oring in Chapter 8, and so on. Clearly the basic material is always covered.
As a reference text this is a highly recommendable book to anyone work-
ing in this field. It is highly valuable and quite up-to-date. If you have to
find a result together with its proof and background, then there is a good
chance you will find it in this book. Of course this implies that it is not easy
reading for the newcomer. In the preface the author says that this book has
been used as a textbook in several universities and even at a special work-

0S MA63


shop for high school students. Well, I am full of admiration for the German
students and their preparation if they can really go through these topics at
ease. Personally I would recommend this book as a first course textbook to
Mathematics (Master's) students (using the material to cover two semesters
or even three semesters) and as an advanced (second course) textbook to
Computer Science or Engineering students.

University di Udine
E-mail: serafini@dimi.uniud.it

Stochastic Linear Programming Algorithms:

A comparison based on a model management system

Jinos Meyer

Gordon and Breach Science Publishers, 1998
ISBN 90-5699-144-2

During the past decade there has been a lot of focus in the sto-
chastic programming community on teaching the philosophy
and tools of the field and several textbooks have appeared
recently (see, e.g., the books by Birge & Louveaux [1], Kall &
Wallace [2], and Prekopa [3]. This book by Janos Meyer focuses on a spe-
cific but important aspect of stochastic linear programming (SLP), namely
algorithms for solving two-stage and chance-constrained SLP problems.
The book consists of six chapters discussing, respectively, general mathe-
matical programming concepts, SLP models and algorithms, implementa-
tion and testing issues, and finally computational results.
The first part of the book is devoted to a survey of SLP models and algo-
rithms. Chapter 1 begins by reviewing a number of results from convex and
linear programming. Next, in Chapter 2, a number of SLP models are pre-
sented. The exposition is limited to two-stage and jointly chance-
constrained models. On the one hand, this choice may seem restrictive and
indeed rules out both interesting and relevant stochastic programming
models, but these models are on the other hand very well studied and a
number of solvers and algorithms are available for comparison. Finally,
Chapter 3 reviews a number of SLP solution approaches with emphasis on
decomposition and approximation/bounding results.
The second part of the book presents the implementation and testing
environment used for carrying out computational experiments. Chapter 4
briefly describes the implementation and origin of the algorithms being
tested. Many of these algorithms belong to the "classics" of stochastic pro-
gramming, but implementations are, except for a few extensions, due to the
author, and carried out in a testing environment which has been specifical-
ly developed to manage SLP problems. This model management system,
which also has been described in numerous scientific articles by the book
author and Peter Kall, is the topic of Chapter 5. The 6th and last chapter
finally contains an extensive report on computational experiments using test
problems from the literature as well as randomly generated and/or per-
turbed problems.
Overall, Meyer's book gives a well balanced introduction to stochastic
linear programming algorithms with emphasis on computational topics.
Although a revision of the author's Habilitationsschrift (postdoctoral


degree) from the University of Ziirich, the text is accessible to any person
with some knowledge of mathematical (linear) programming, since the
emphasis has been put on computational comparison. However, it is not an
introductory stochastic programming textbook in the same sense as the pre-
viously mentioned books [1, 2, 3], since its scope is much too narrow in
comparison. A possible limitation is also that the scope of the book is not
development of new algorithms or solution methods, but rather a descrip-
tion and a comparison of already existing algorithms. This is also the
strength of the book. Probably one of the most useful assets of the book is
not actually a part of the book, but is the SLP-IOR model management sys-
tem utilized for performing the computational experiments, manipulating
model data and carrying out the testing. It should be mentioned that SLP-
IOR is freely available for academic use from the authors. Thus this
book/SLP-IOR may provide something which no textbook can do alone:
giving hands-on modeling experience in classroom teaching.
In short, I find the book useful, both for readers already familiar with
stochastic programming concepts -as it serves as a convenient (computa-
tional) documentation of algorithms and test problems which are otherwise
scattered around in the scientific literature -and for newcomers and poten-
tial users of SLP techniques who are looking for descriptions of algorithms
and their computational performance and characteristics and who do not
wish to start right away reading journal articles.


[1] J.R. Birge and F.V. Louveaux, Introduction to Stochastic
Programming (Springer-Verlag, New York, 1997).

[2] P Kall and S.W. Wallace, Stochastic Programming (Wiley-
Interscience, New York, 1994).

[3] A. Prekopa, Stochastic Programming (Kluwer Academic Publishers,
Dordrecht, 1995).



C o n f e r e n c e

) APMOD 2000
April 17-19, 2000,London,UK
) Seventh International Workshop on Project Management and Scheduling (PMS 2000)
April 17-19, 2000,University of Osnabrueck,Germany
URL: http://www.mathematik.uni-osnabrueck.de/research/OR/pms2000/
) Applied Mathematical Programming and Modelling Conference (APMOD 2000)
17-19 April 2000, Brunel University, London
) INFORMS Spring 2000
May 7-10, 2000, Salt Lake City, Utah,USA
URL: http://www. informs.org/Conf/SaltLake2000/
) STOC 2000
May 21-23, 2000, Portland,Oregon,USA
) Tenth SIAM Conference on Discrete Mathematics
June 12-15, 2000,Minneapolis,Minnesota,USA
June 18-21, 2000,Seoul, Korea
) SIAM Annual Meeting
July 10-14, 2000, Rio Grande, Puerto Rico
URL: http://www.siam.org/meetings/an00/
) ISMP 2000 17th International Symposium on Mathematical Programming
August 7-11, 2000,Georgia Institute of Technology, Atlanta,GA,USA
) First SIAM Conference on Computational Science and Engineering
September 21-23, Washington,DC,USA
URL: http://www.siam.org/meetings/cse00/
) INFORMS Fall 2000
November 3-7, 2000, San Antonio, Texas,USA
) IPCO 2001
Utrecht, The Netherlands
URL: http://www.cs.uu.nl/events/ipco2001/


First Announcement and Call for Papers

HPOPT 2000
5th International Conference on High Performance Optimization Techniques

Rotterdam, The Netherlands
June 7-9, 2000

HPOPT 2000 will take place in the context of the
Dutch research project "High Performance
Models for Mathematical Optimization." In this
project, funded by the Dutch Organization for
Scientific Research (NWO), research teams
cooperate from four universities in the
Netherlands: Delft University of Technology,
Erasmus University, Eindhoven University of
Technology, and University of Utrecht.
The aim of the conference is to bring together
some of the most active researchers working on
the design and implementation of optimization
algorithms. We aim to cover the latest algorith-
mic developments, complexity results and imple-
mentation aspects, including the required tools
from numerical algebra. Much attention will be
given to the recent developments in semidefinite
optimization and its relevance for a wide range
of practical applications in fields such as combi-
natorial optimization, engineering design, matrix
inequalities in systems and control theory, and
matrix completion problems.
The meeting will consist of a one-day tutorial
and a two-day conference. Along with invited
presentations there will be sessions with con-
tributed lectures.
Conference Organizers: Dick den Hertog
(CQM, Eindhoven), Cor Hurkens (Eindhoven
University of Technology), Jan Karel Lenstra
(Eindhoven University of T.. I -..... ..'WI),
Leen Stougie (Eindhoven University of
Technology), and Tjark Vredeveld (Eindhoven
University of Technology).
Program Committee: Jan Brinkhuis (Erasmus
University Rotterdam), Dick den Hertog
(CQM, Eindhoven), Cor Hurkens (Eindhoven
of University Technology), Jan Karel Lenstra
(Eindhoven University of T.. I -..... ..'WI),
Kees Roos (Delft University of Technology),
Leen Stougie (Eindhoven University of
Technology), Henk van der Vorst (University of
Utrecht), and Tjark Vredeveld (Eindhoven
University of Technology).
Invited Speakers: Karen Aardal (University of
Utrecht, The Netherlands), Aharon Ben-Tal
(Technion, Haifa, Israel), N.G. de Bruijn
(Eindhoven University of Technology, The

Netherlands to be confirmed), Martin Dyer
(University of Leeds, Great Britain), Andrzej
Ruszczynski (Rutgers University, New
Brunswick, USA), Robert Vanderbei (Princeton
University, USA), and Maarten van der Vlerk
(University of Groningen, The Netherlands).
Submission of Papers: For contributed lectures,
authors are kindly requested to submit a one-
page abstract including title, author's name, affil-
iation, e-mail and postal address. Abstracts
should be sent in LaTeX format to
Registration: Pre-registration can be done
through the web site or by sending an e-mail
with your name and affiliation to
. Upon pre-registration you
will be kept up-to-date with any further
announcements about the conference.
Registration can be done in the same way as pre-
registration. Early registration is due on the 30th
of April 2000. The conference fees for early reg-
istration are: For the one-day seminar on
Wednesday, 7 June, Dgl 100; or the conference
on 8 and 9 June, Dgl 200; For both, Dgl 300.
For late registration, the fees for the two separate
parts are augmented with Dgl 50 and for the
three days with 100.
The conference fees include an abstract book,
free lunches in the restaurant of the World Trade
Center, coffee and tea with cookies during the
breaks, a get-together on Wednesday evening
and the conference dinner on Thursday evening.
Upon cancellation before the 30th of April
2000, your conference fee will be refunded com-
pletely, up to bank costs. Upon cancellation
before the 31st of May 2000, only half of your
fee will be refunded. After that date no refund-
ing is possible.
Important Dates: March 1, 2000 Deadlinefor
abstracts, March 31, 2000 Acceptance or rejection
notification; April 30, 2000 Deadline for early reg-
istration; June 7-9, 2000 HPOPT 2000.
Information: Information about the conference
can be found on the Conference Web Site:
mation can be obtained by sending an e-mail to:


Call for Papers for Theme
Issue of The Arabian Journal
for Science and Engineering
on Optimization Theory and

The Editorial Board of the Arabian
Journal for Science and Engineering
(AJSE) plans to publish, in June 2000, a
Theme Issue in Optimization Theory
and Applications. The AJSE hopes to
bring together in a single issue research
papers that represent the state of the art
in this vast and rapidly growing area.
The scope of this theme issue encom-
passes, but is not limited to, the follow-
ing areas: linear programming; interior
and exterior methods; quadratic pro-
gramming; large scale optimization; sto-
chastic programming; nonsmooth opti-
mization; nonconvex programming;
semidefinite programming; integer and
combinatorial optimization; LCP; varia-
tional inequalities; heuristic-based opti-
mization; and industrial applications.
Guest Editors Professor Katta G.
Murty, Department of Industrial and
Operations Engineering, University of
Michigan; Professor Hanif D. Sherali,
Department of Industrial and Systems
Engineering, Virginia Polytechnic
Institute and State University.
Publication Schedule
Deadline forsubmission of manu-
scripts: January 10, 2000; Notification
of acceptance of papers: March 31,
2000; Publication of the theme issue:
June 2000.
Note to Authors: Four copies of the
manuscript should be submitted to:
Professor Harry Mavromatis, Managing
Editor, The Arabian Journal for Science
and Engineering, King Fahd University
of Petroleum & Minerals KFUPM, Box
5033, Dhahran 31261, Saudi Arabia;
Telephone: (+966) 3 8605418; Fax:
(+966) 3 8605458; e-mail:
Authors may obtain details of the for-
mat and style adopted by the AJSE by
contacting the Managing Editor at the
above address or by e-mail.



Call for Nominations:

Optimization Prize for

Young Researchers

Principal Guideline The Optimization Prize
for Young Researchers, established in 1998 and
administered by the Optimization Section
(OS) within the Institute for Operations
Research and Management Science
(INFORMS), is awarded annually at the
INFORMS Fall National Meeting to one (or
more) young researchers for the most outstand-
ing paper in optimization that is submitted to
or published in a refereed professional journal.
The prize serves as an esteemed recognition of
promising colleagues who are at the beginning
of their academic or industrial career.
Description of the Award The optimization
award includes a cash amount of US$1,000
and a citation certificate. The award winners
will be invited to give a one-hour lecture of the
winning paper at the INFORMS Fall National
Meeting in the year the award is made. It is
expected that the winners will be responsible
for the travel expenses to present the paper at
the INFORMS meeting.
Eligibility The authors and paper must satisfy
the following three conditions to be eligible for
the prize:
(a) The paper must either be published in a
refereed professional journal no more than
three years before the closing date of
nomination, or be submitted to and
received by a refereed professional journal
no more than three years before the clos-
ing date of nomination;
(b) All authors must have been awarded their
terminal degree within five years of the
closing date of nomination;
(c) The topic of the paper must belong to the
field of optimization in its broadest sense.
Nomination Nominations should be sent
before July 15, 2000 to
Robert J. Vanderbei
Dept. of Operations Research and Financial
Princeton University
Princeton, NJ 08544
Nominations should be accompanied by
a supporting letter.


Second Announcement

Seventh DIMACS Implementation Challenge
Semidefinite and Related Optimization Problems
The workshop of the Seventh DIMACS Challenge has been postponed to
September 13-15, 2000. We have received many excellent proposals (see
the web site address below), but also a fair number of requests to allow
more time for projects which were otherwise unlikely to finish before
January. New proposals are still welcome.
For up-to-date information on the workshop, please see the Challenge
web site at . For the collection of test
problems, visit .


Version 2 of the NEOS Server was de-com-
missioned on March 4, 1999, after having
processed 39,900 submissions. Version 3 of
the NEOS Server (NEOS 99) went into
operation the same day, and is continually
being improved. The new server can be
found at .
NEOS 99 is a major improvement. This
version is portable, faster, more reliable,
allows submissions from the local file space,
and accepts compressed data. We have also
added a considerable number of new
solvers. In particular, for integer program-
ming: MINLP (Roger Fletcher and Sven
Associates and Dash Optimization); for
complementarity problems: MILES
(GAMS Development Corporation and T
Rutherford), PATH (GAMS Development
Corporation and S. Dirkse, M. Ferris and
T Munson); for nonlinearly constrained
optimization: DONLP2 (Hans Mittelmann
and Peter Spellucci), FILTER (Roger
Fletcher and Sven L. .II. . LANCELOT

(Andy Conn, Nick Gould and Philippe
Toint), LOQO (Robert Vanderbei),
MINOS (Bruce Murtagh and Michael
Saunders), SNOPT (Philip Gill, Walter
Murray and Michael Saunders); for bound-
constrained optimization: L-BFGS-B
(Ciyou Zhu, Richard Byrd, Peihuang Lu,
and Jorge Nocedal), TRON (Chih-Jen Lin
and Jorge More); and for positive semidefi-
nite programming: DSDP (Steve Benson,
Yinyu Ye, and Xiong Zhang). Many of the
solvers accept input in AMPL format, and
we have recently added solvers that accept
input in GAMS format.
We welcome comments and suggestions.
In particular, we are seeking comments
from NEOS users who support our contin-
uing effort to offer this service to the pub-
lic. The easiest way to provide user feedback
is by sending e-mail to

0S MA63

IANU "i; l
jJ rJUiW 0"
1'..1. .


SThe deadline >i [he neX\ Issue of OPTINIA is Nihl\ 5. 200.

For the electronic version of OPTIMA, please see:


Application for Membership

I wish to enroll as a member of the Society.

My subscription is for my personal use and not for the benefit of any library or institution.

O I will pay my membership dues on receipt of your invoice.

E I wish to pay by credit card (Master/Euro or Visa).








Mail to:

Mathematical Programming Society
3600 University City Sciences Center
Philadelphia PA 19104-2688 USA

Cheques or money orders should be made
payable to The Mathematical Programming
Society, Inc. Dues for 1999, including sub-
scription to the journal Mathematical
Programming, are US $75.
Student applications: Dues are one-half the
above rate. Have a faculty member verify your
student status and send application with dues
to above address.

Faculty verifying status


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Center for Applied Optimization
371 Weil
PO Box 116595
Gainesville FL 32611-6595 USA


Karen Aardal
Department of Computer Science
Utrecht University
PO Box 80089
3508 TB Utrecht
The Netherlands
e-mail: aardal@cs.ruu.nl
URL: http://www.cs.ruu.nl/staff/aardal.html

Sebastian Ceria
417 Uris Hall
Graduate School of Business
Columbia University
New York, NY 10027-7004
e-mail: sebas@cumparsita.gsb.columbia.edu
URL: http://www.columbia.edu/~sc244/

Robert Weismantel
Universitat Magdeburg
Fakultat fur Mathematik
Universitatsplatz 2
D-39106 Magdeburg
e-mail: weismant@math.uni-magdeburg.de

Elsa Drake, DESIGNER
University of Florida

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