29 research outputs found
Solving Hard Control Problems in Voting Systems via Integer Programming
Voting problems are central in the area of social choice. In this article, we
investigate various voting systems and types of control of elections. We
present integer linear programming (ILP) formulations for a wide range of
NP-hard control problems. Our ILP formulations are flexible in the sense that
they can work with an arbitrary number of candidates and voters. Using the
off-the-shelf solver Cplex, we show that our approaches can manipulate
elections with a large number of voters and candidates efficiently
A fully polynomial time approximation scheme for packing while traveling
Understanding the interactions between different combinatorial optimisation
problems in real-world applications is a challenging task. Recently, the
traveling thief problem (TTP), as a combination of the classical traveling
salesperson problem and the knapsack problem, has been introduced to study
these interactions in a systematic way. We investigate the underlying
non-linear packing while traveling (PWT) problem of the TTP where items have to
be selected along a fixed route. We give an exact dynamic programming approach
for this problem and a fully polynomial time approximation scheme (FPTAS) when
maximising the benefit that can be gained over the baseline travel cost. Our
experimental investigations show that our new approaches outperform current
state-of-the-art approaches on a wide range of benchmark instances
A Fully Polynomial Time Approximation Scheme for Packing While Traveling
Understanding the interaction between different combinatorial optimization problems is a challenging task of high relevance for numerous real-world applications including modern computer and memory architectures as well as high performance computing. Recently, the Traveling Thief Problem (TTP), as a combination of the classical traveling salesperson problem and the knapsack problem, has been introduced to study these interactions in a systematic way. We investigate the underlying non-linear Packing While Traveling Problem (PWTP) of the TTP where items have to be selected along a fixed route. We give an exact dynamic programming approach for this problem and a fully polynomial time approximation scheme (FPTAS) when maximizing the benefit that can be gained over the baseline travel cost. Our experimental investigations show that our new approaches outperform current state-of-the-art approaches on a wide range of benchmark instances
A multi-agent system for the weighted earliness tardiness parallel machine problem
This paper studies the weighted earliness tardiness parallel machine problem where jobs have different processing times and distinct due dates. This NP hard problem arises in most just-in-time production environments. It is herein modeled as a mixed integer program, and solved using MASH, a deterministic heuristic based on multi-agent systems. MASH has three types of agents: I, G, and M. The I-agents are free jobs that need to be scheduled, whereas the G-agents are groups of jobs already assigned to machines. The M-agent acts as the system's manager of the independent intelligent I- and G-agents, which are driven by their own goals, fitness assessments, and context-dependent decision rules. The I- and G-agents employ exact and approximate approaches as part of their decisional process while the M-agent uses local search mechanisms to improve their (partial) solutions. The design of MASH is innovative in the way its intelligent agents determine bottleneck clusters and resolve conflicts for time slots. The numerical results provide computational evidence of the efficiency of MASH, whose performance on benchmark instances from the literature is superior to that of existing approaches. The success of MASH and its modularity make it a viable alternative to more complex manufacturing problems. Most importantly, they demonstrate the benefits of the hybridization of artificial intelligence and operations research. © 2013 Elsevier Ltd.S. Polyakovskiy, R.M'Halla
An intelligent framework to online bin packing in a just-in-time environment
This paper addresses a complex real life manufacturing problem that occurs in paper and wood industries: the online bin packing and cutting of small items using parallel machines in a just-in-time environment. The objective is to minimize both the unused areas of the bins and the sum of weighted earliness and tardiness penalties. This NP hard problem is herein solved using an agent-based approach A-B. The active agents of A-B interact dynamically in real time to jointly fill the bins with items, assign cutting patterns to machines, cut them, and have the items delivered on time. The application of A-B to real life instances from a manufacturing company highlights the sizeable savings induced by A-B, and demonstrates its suitability for complex online real-life situations.Sergey Polyakovskiy, and Rym M'Halla
A hybrid feasibility constraints-guided search to the two-dimensional bin packing problem with due dates
The two-dimensional non-oriented bin packing problem with due dates packs a
set of rectangular items, which may be rotated by 90 degrees, into identical
rectangular bins. The bins have equal processing times. An item's lateness is
the difference between its due date and the completion time of its bin. The
problem packs all items without overlap as to minimize maximum lateness Lmax.
The paper proposes a tight lower bound that enhances an existing bound on
Lmax for 24.07% of the benchmark instances and matches it in 30.87% cases. In
addition, it models the problem using mixed integer programming (MIP), and
solves small-sized instances exactly using CPLEX. It approximately solves
larger-sized instances using a two-stage heuristic. The first stage constructs
an initial solution via a first-fit heuristic that applies an iterative
constraint programming (CP)-based neighborhood search. The second stage, which
is iterative too, approximately solves a series of assignment low-level MIPs
that are guided by feasibility constraints. It then enhances the solution via a
high-level random local search. The approximate approach improves existing
upper bounds by 27.45% on average, and obtains the optimum for 33.93% of the
instances. Overall, the exact and approximate approaches identify the optimum
for 39.07% cases.
The proposed approach is applicable to complex problems. It applies CP and
MIP sequentially, while exploring their advantages, and hybridizes heuristic
search with MIP. It embeds a new lookahead strategy that guards against
infeasible search directions and constrains the search to improving directions
only; thus, differs from traditional lookahead beam searches