About Yasol
Yasol is a search based solver for so called 'Quantified
integer linear programs with minimax objective‘ (QIP).
As we additionally allow continuous decision variables in
the final stage, the solver is able to deal with very
specific Quantified mixedinteger linear programs (QMIP).
The aim is to support optimization under uncertainty in a
new way, based upon rigorous formal models of quantification
and linear constraints.
Our mission is research. The reason why we open the sources
of this solver is in order to intensify the discussion
whether multistage optimization is possible and maybe
even practical.
While the solver is new in the sense that there are no other
QIP solver at this time (October 2022), most basic ingredients
of Yasol are not new at all. The heart of the search algorithm
is an arithmetic linear constraint database together with
the Alphabeta algorithm which has been successfully used in
gaming programs like in chess programs since many years. In
order to realize fast back jumps as typically performed in
SAT and QBF solvers, we have extended the Alphabeta
algorithm as roughly described in [1]. Yasol deals with
constraint learning on the so called primal side as known
from SAT and QBFsolving, as well as with constraint
learning on the so called dual side, as is known from
Mathematical Programming. Yasol solves multistage quantified
programs with the following properties:

all constraints are linear

quantifiers are either existential or universal

the objective is minmax (more exactly: min max min … max
min max) and is linear for any single game

integer variables are allowed on all existstages and must
be greater or equal to zero

only integer variables are allowed on universal stages

continuous variables are allowed only on the last stage,
assuming it is an existential stage

all variables must be bounded from below and above, and
the range between upper and lower bounds of integer
variables must not exceed 40 bits
In a recent computational study we showed that solving robust
discrete problems with multiple stages is well within the
reach of our solver [2]. It makes intensive use of a linear
program solver like clp or the lpsolver of cplex.
For some historical notes on Quantified Programming, Linear
Programming and personal credits, we refer to our
history page.
For details of how to use the solver and about details of input
formats etc. we refer to our
download page.
[1] Thorsten Ederer, Michael Hartisch, Ulf Lorenz, Thomas
Opfer, Jan Wolf.
Yasol: An Open Source Solver for Quantified Mixed Integer
Programs. ACG 2017: 224233
[2] Marc Goerigk, Michael Hartisch.
Multistage Robust Discrete Optimization via
Quantified Integer Programming. Computers & Operations
Research, 135:105434, 202
[3] Michael Hartisch, Ulf Lorenz.
A general modelandrun solver for multistage
robust discrete linear optimizationi. Submitted to
INFORMS Journal on Computing, 2023

Downloads
Yasol for Mac OS
Yasol for Linux
Yasol for Windows
Instances
