309 research outputs found
Buyback Problem - Approximate matroid intersection with cancellation costs
In the buyback problem, an algorithm observes a sequence of bids and must
decide whether to accept each bid at the moment it arrives, subject to some
constraints on the set of accepted bids. Decisions to reject bids are
irrevocable, whereas decisions to accept bids may be canceled at a cost that is
a fixed fraction of the bid value. Previous to our work, deterministic and
randomized algorithms were known when the constraint is a matroid constraint.
We extend this and give a deterministic algorithm for the case when the
constraint is an intersection of matroid constraints. We further prove a
matching lower bound on the competitive ratio for this problem and extend our
results to arbitrary downward closed set systems. This problem has applications
to banner advertisement, semi-streaming, routing, load balancing and other
problems where preemption or cancellation of previous allocations is allowed
Rigorous Runtime Analysis of MOEA/D for Solving Multi-Objective Minimum Weight Base Problems
We study the multi-objective minimum weight base problem, an abstraction of
classical NP-hard combinatorial problems such as the multi-objective minimum
spanning tree problem. We prove some important properties of the convex hull of
the non-dominated front, such as its approximation quality and an upper bound
on the number of extreme points. Using these properties, we give the first
run-time analysis of the MOEA/D algorithm for this problem, an evolutionary
algorithm that effectively optimizes by decomposing the objectives into
single-objective components. We show that the MOEA/D, given an appropriate
decomposition setting, finds all extreme points within expected fixed-parameter
polynomial time in the oracle model, the parameter being the number of
objectives. Experiments are conducted on random bi-objective minimum spanning
tree instances, and the results agree with our theoretical findings.
Furthermore, compared with a previously studied evolutionary algorithm for the
problem GSEMO, MOEA/D finds all extreme points much faster across all
instances.Comment: 12 page
Parameterized Complexity Analysis of Randomized Search Heuristics
This chapter compiles a number of results that apply the theory of
parameterized algorithmics to the running-time analysis of randomized search
heuristics such as evolutionary algorithms. The parameterized approach
articulates the running time of algorithms solving combinatorial problems in
finer detail than traditional approaches from classical complexity theory. We
outline the main results and proof techniques for a collection of randomized
search heuristics tasked to solve NP-hard combinatorial optimization problems
such as finding a minimum vertex cover in a graph, finding a maximum leaf
spanning tree in a graph, and the traveling salesperson problem.Comment: This is a preliminary version of a chapter in the book "Theory of
Evolutionary Computation: Recent Developments in Discrete Optimization",
edited by Benjamin Doerr and Frank Neumann, published by Springe
Migrant Resettlement by Evolutionary Multi-objective Optimization
Migration has been a universal phenomenon, which brings opportunities as well
as challenges for global development. As the number of migrants (e.g.,
refugees) increases rapidly in recent years, a key challenge faced by each
country is the problem of migrant resettlement. This problem has attracted
scientific research attention, from the perspective of maximizing the
employment rate. Previous works mainly formulated migrant resettlement as an
approximately submodular optimization problem subject to multiple matroid
constraints and employed the greedy algorithm, whose performance, however, may
be limited due to its greedy nature. In this paper, we propose a new framework
MR-EMO based on Evolutionary Multi-objective Optimization, which reformulates
Migrant Resettlement as a bi-objective optimization problem that maximizes the
expected number of employed migrants and minimizes the number of dispatched
migrants simultaneously, and employs a Multi-Objective Evolutionary Algorithm
(MOEA) to solve the bi-objective problem. We implement MR-EMO using three
MOEAs, the popular NSGA-II, MOEA/D as well as the theoretically grounded GSEMO.
To further improve the performance of MR-EMO, we propose a specific MOEA,
called GSEMO-SR, using matrix-swap mutation and repair mechanism, which has a
better ability to search for feasible solutions. We prove that MR-EMO using
either GSEMO or GSEMO-SR can achieve better theoretical guarantees than the
previous greedy algorithm. Experimental results under the interview and
coordination migration models clearly show the superiority of MR-EMO (with
either NSGA-II, MOEA/D, GSEMO or GSEMO-SR) over previous algorithms, and that
using GSEMO-SR leads to the best performance of MR-EMO
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