16,197 research outputs found
Lotsize optimization leading to a -median problem with cardinalities
We consider the problem of approximating the branch and size dependent demand
of a fashion discounter with many branches by a distributing process being
based on the branch delivery restricted to integral multiples of lots from a
small set of available lot-types. We propose a formalized model which arises
from a practical cooperation with an industry partner. Besides an integer
linear programming formulation and a primal heuristic for this problem we also
consider a more abstract version which we relate to several other classical
optimization problems like the p-median problem, the facility location problem
or the matching problem.Comment: 14 page
Single-machine scheduling with stepwise tardiness costs and release times
We study a scheduling problem that belongs to the yard operations component of the railroad planning problems, namely the hump sequencing problem. The scheduling problem is characterized as a single-machine problem with stepwise tardiness cost objectives. This is a new scheduling criterion which is also relevant in the context of traditional machine scheduling problems. We produce complexity results that characterize some cases of the problem as pseudo-polynomially solvable. For the difficult-to-solve cases of the problem, we develop mathematical programming formulations, and propose heuristic algorithms. We test the formulations and heuristic algorithms on randomly generated single-machine scheduling problems and real-life datasets for the hump sequencing problem. Our experiments show promising results for both sets of problems
Single-Step Quantum Search Using Problem Structure
The structure of satisfiability problems is used to improve search algorithms
for quantum computers and reduce their required coherence times by using only a
single coherent evaluation of problem properties. The structure of random k-SAT
allows determining the asymptotic average behavior of these algorithms, showing
they improve on quantum algorithms, such as amplitude amplification, that
ignore detailed problem structure but remain exponential for hard problem
instances. Compared to good classical methods, the algorithm performs better,
on average, for weakly and highly constrained problems but worse for hard
cases. The analytic techniques introduced here also apply to other quantum
algorithms, supplementing the limited evaluation possible with classical
simulations and showing how quantum computing can use ensemble properties of NP
search problems.Comment: 39 pages, 12 figures. Revision describes further improvement with
multiple steps (section 7). See also
http://www.parc.xerox.com/dynamics/www/quantum.htm
On the Complexity of Spill Everywhere under SSA Form
Compilation for embedded processors can be either aggressive (time consuming
cross-compilation) or just in time (embedded and usually dynamic). The
heuristics used in dynamic compilation are highly constrained by limited
resources, time and memory in particular. Recent results on the SSA form open
promising directions for the design of new register allocation heuristics for
embedded systems and especially for embedded compilation. In particular,
heuristics based on tree scan with two separated phases -- one for spilling,
then one for coloring/coalescing -- seem good candidates for designing
memory-friendly, fast, and competitive register allocators. Still, also because
of the side effect on power consumption, the minimization of loads and stores
overhead (spilling problem) is an important issue. This paper provides an
exhaustive study of the complexity of the ``spill everywhere'' problem in the
context of the SSA form. Unfortunately, conversely to our initial hopes, many
of the questions we raised lead to NP-completeness results. We identify some
polynomial cases but that are impractical in JIT context. Nevertheless, they
can give hints to simplify formulations for the design of aggressive
allocators.Comment: 10 page
Order acceptance and scheduling in a single-machine environment: exact and heuristic algorithms.
In this paper, we develop exact and heuristic algorithms for the order acceptance and scheduling problem in a single-machine environment. We consider the case where a pool consisting of firm planned orders as well as potential orders is available from which an over-demanded company can select. The capacity available for processing the accepted orders is limited and orders are characterized by known processing times, delivery dates, revenues and the weight representing a penalty per unit-time delay beyond the delivery date promised to the customer. We prove the non-approximability of the problem and give two linear formulations that we solve with CPLEX. We devise two exact branch-and-bound procedures able to solve problem instances of practical dimensions. For the solution of large instances, we propose six heuristics. We provide a comparison and comments on the efficiency and quality of the results obtained using both the exact and heuristic algorithms, including the solution of the linear formulations using CPLEX.Order acceptance; Scheduling; Single machine; Branch-and-bound; Heuristics; Firm planned orders;
Breaking Instance-Independent Symmetries In Exact Graph Coloring
Code optimization and high level synthesis can be posed as constraint
satisfaction and optimization problems, such as graph coloring used in register
allocation. Graph coloring is also used to model more traditional CSPs relevant
to AI, such as planning, time-tabling and scheduling. Provably optimal
solutions may be desirable for commercial and defense applications.
Additionally, for applications such as register allocation and code
optimization, naturally-occurring instances of graph coloring are often small
and can be solved optimally. A recent wave of improvements in algorithms for
Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests
generic problem-reduction methods, rather than problem-specific heuristics,
because (1) heuristics may be upset by new constraints, (2) heuristics tend to
ignore structure, and (3) many relevant problems are provably inapproximable.
Problem reductions often lead to highly symmetric SAT instances, and
symmetries are known to slow down SAT solvers. In this work, we compare several
avenues for symmetry breaking, in particular when certain kinds of symmetry are
present in all generated instances. Our focus on reducing CSPs to SAT allows us
to leverage recent dramatic improvement in SAT solvers and automatically
benefit from future progress. We can use a variety of black-box SAT solvers
without modifying their source code because our symmetry-breaking techniques
are static, i.e., we detect symmetries and add symmetry breaking predicates
(SBPs) during pre-processing.
An important result of our work is that among the types of
instance-independent SBPs we studied and their combinations, the simplest and
least complete constructions are the most effective. Our experiments also
clearly indicate that instance-independent symmetries should mostly be
processed together with instance-specific symmetries rather than at the
specification level, contrary to what has been suggested in the literature
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