81,499 research outputs found
Fair task allocation in transportation
Task allocation problems have traditionally focused on cost optimization.
However, more and more attention is being given to cases in which cost should
not always be the sole or major consideration. In this paper we study a fair
task allocation problem in transportation where an optimal allocation not only
has low cost but more importantly, it distributes tasks as even as possible
among heterogeneous participants who have different capacities and costs to
execute tasks. To tackle this fair minimum cost allocation problem we analyze
and solve it in two parts using two novel polynomial-time algorithms. We show
that despite the new fairness criterion, the proposed algorithms can solve the
fair minimum cost allocation problem optimally in polynomial time. In addition,
we conduct an extensive set of experiments to investigate the trade-off between
cost minimization and fairness. Our experimental results demonstrate the
benefit of factoring fairness into task allocation. Among the majority of test
instances, fairness comes with a very small price in terms of cost
On Correcting Inputs: Inverse Optimization for Online Structured Prediction
Algorithm designers typically assume that the input data is correct, and then
proceed to find "optimal" or "sub-optimal" solutions using this input data.
However this assumption of correct data does not always hold in practice,
especially in the context of online learning systems where the objective is to
learn appropriate feature weights given some training samples. Such scenarios
necessitate the study of inverse optimization problems where one is given an
input instance as well as a desired output and the task is to adjust the input
data so that the given output is indeed optimal. Motivated by learning
structured prediction models, in this paper we consider inverse optimization
with a margin, i.e., we require the given output to be better than all other
feasible outputs by a desired margin. We consider such inverse optimization
problems for maximum weight matroid basis, matroid intersection, perfect
matchings, minimum cost maximum flows, and shortest paths and derive the first
known results for such problems with a non-zero margin. The effectiveness of
these algorithmic approaches to online learning for structured prediction is
also discussed.Comment: Conference version to appear in FSTTCS, 201
Profit-oriented disassembly-line balancing
As product and material recovery has gained importance, disassembly volumes have increased, justifying construction of disassembly lines similar to assembly lines. Recent research on disassembly lines has focused on complete disassembly. Unlike assembly, the current industry practice involves partial disassembly with profit-maximization or cost-minimization objectives. Another difference between assembly and disassembly is that disassembly involves additional precedence relations among tasks due to processing alternatives or physical restrictions. In this study, we define and solve the profit-oriented partial disassembly-line balancing problem. We first characterize different types of precedence relations in disassembly and propose a new representation scheme that encompasses all these types. We then develop the first mixed integer programming formulation for the partial disassembly-line balancing problem, which simultaneously determines (1) the parts whose demand is to be fulfilled to generate revenue, (2) the tasks that will release the selected parts under task and station costs, (3) the number of stations that will be opened, (4) the cycle time, and (5) the balance of the disassembly line, i.e. the feasible assignment of selected tasks to stations such that various types of precedence relations are satisfied. We propose a lower and upper-bounding scheme based on linear programming relaxation of the formulation. Computational results show that our approach provides near optimal solutions for small problems and is capable of solving larger problems with up to 320 disassembly tasks in reasonable time
TopCom: Index for Shortest Distance Query in Directed Graph
Finding shortest distance between two vertices in a graph is an important
problem due to its numerous applications in diverse domains, including
geo-spatial databases, social network analysis, and information retrieval.
Classical algorithms (such as, Dijkstra) solve this problem in polynomial time,
but these algorithms cannot provide real-time response for a large number of
bursty queries on a large graph. So, indexing based solutions that pre-process
the graph for efficiently answering (exactly or approximately) a large number
of distance queries in real-time is becoming increasingly popular. Existing
solutions have varying performance in terms of index size, index building time,
query time, and accuracy. In this work, we propose T OP C OM , a novel
indexing-based solution for exactly answering distance queries. Our experiments
with two of the existing state-of-the-art methods (IS-Label and TreeMap) show
the superiority of T OP C OM over these two methods considering scalability and
query time. Besides, indexing of T OP C OM exploits the DAG (directed acyclic
graph) structure in the graph, which makes it significantly faster than the
existing methods if the SCCs (strongly connected component) of the input graph
are relatively small
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