74,928 research outputs found
Submodular memetic approximation for multiobjective parallel test paper generation
Parallel test paper generation is a biobjective distributed resource optimization problem, which aims to generate multiple similarly optimal test papers automatically according to multiple user-specified assessment criteria. Generating high-quality parallel test papers is challenging due to its NP-hardness in both of the collective objective functions. In this paper, we propose a submodular memetic approximation algorithm for solving this problem. The proposed algorithm is an adaptive memetic algorithm (MA), which exploits the submodular property of the collective objective functions to design greedy-based approximation algorithms for enhancing steps of the multiobjective MA. Synergizing the intensification of submodular local search mechanism with the diversification of the population-based submodular crossover operator, our algorithm can jointly optimize the total quality maximization objective and the fairness quality maximization objective. Our MA can achieve provable near-optimal solutions in a huge search space of large datasets in efficient polynomial runtime. Performance results on various datasets have shown that our algorithm has drastically outperformed the current techniques in terms of paper quality and runtime efficiency
Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control
Constrained optimization of high-dimensional numerical problems plays an
important role in many scientific and industrial applications. Function
evaluations in many industrial applications are severely limited and no
analytical information about objective function and constraint functions is
available. For such expensive black-box optimization tasks, the constraint
optimization algorithm COBRA was proposed, making use of RBF surrogate modeling
for both the objective and the constraint functions. COBRA has shown remarkable
success in solving reliably complex benchmark problems in less than 500
function evaluations. Unfortunately, COBRA requires careful adjustment of
parameters in order to do so.
In this work we present a new self-adjusting algorithm SACOBRA, which is
based on COBRA and capable to achieve high-quality results with very few
function evaluations and no parameter tuning. It is shown with the help of
performance profiles on a set of benchmark problems (G-problems, MOPTA08) that
SACOBRA consistently outperforms any COBRA algorithm with fixed parameter
setting. We analyze the importance of the several new elements in SACOBRA and
find that each element of SACOBRA plays a role to boost up the overall
optimization performance. We discuss the reasons behind and get in this way a
better understanding of high-quality RBF surrogate modeling
Flexible Multi-layer Sparse Approximations of Matrices and Applications
The computational cost of many signal processing and machine learning
techniques is often dominated by the cost of applying certain linear operators
to high-dimensional vectors. This paper introduces an algorithm aimed at
reducing the complexity of applying linear operators in high dimension by
approximately factorizing the corresponding matrix into few sparse factors. The
approach relies on recent advances in non-convex optimization. It is first
explained and analyzed in details and then demonstrated experimentally on
various problems including dictionary learning for image denoising, and the
approximation of large matrices arising in inverse problems
Energy efficiency optimization in MIMO interference channels: A successive pseudoconvex approximation approach
In this paper, we consider the (global and sum) energy efficiency
optimization problem in downlink multi-input multi-output multi-cell systems,
where all users suffer from multi-user interference. This is a challenging
problem due to several reasons: 1) it is a nonconvex fractional programming
problem, 2) the transmission rate functions are characterized by
(complex-valued) transmit covariance matrices, and 3) the processing-related
power consumption may depend on the transmission rate. We tackle this problem
by the successive pseudoconvex approximation approach, and we argue that
pseudoconvex optimization plays a fundamental role in designing novel iterative
algorithms, not only because every locally optimal point of a pseudoconvex
optimization problem is also globally optimal, but also because a descent
direction is easily obtained from every optimal point of a pseudoconvex
optimization problem. The proposed algorithms have the following advantages: 1)
fast convergence as the structure of the original optimization problem is
preserved as much as possible in the approximate problem solved in each
iteration, 2) easy implementation as each approximate problem is suitable for
parallel computation and its solution has a closed-form expression, and 3)
guaranteed convergence to a stationary point or a Karush-Kuhn-Tucker point. The
advantages of the proposed algorithm are also illustrated numerically.Comment: submitted to IEEE Transactions on Signal Processin
Decomposition by Successive Convex Approximation: A Unifying Approach for Linear Transceiver Design in Heterogeneous Networks
We study the downlink linear precoder design problem in a multi-cell dense
heterogeneous network (HetNet). The problem is formulated as a general
sum-utility maximization (SUM) problem, which includes as special cases many
practical precoder design problems such as multi-cell coordinated linear
precoding, full and partial per-cell coordinated multi-point transmission,
zero-forcing precoding and joint BS clustering and beamforming/precoding. The
SUM problem is difficult due to its non-convexity and the tight coupling of the
users' precoders. In this paper we propose a novel convex approximation
technique to approximate the original problem by a series of convex
subproblems, each of which decomposes across all the cells. The convexity of
the subproblems allows for efficient computation, while their decomposability
leads to distributed implementation. {Our approach hinges upon the
identification of certain key convexity properties of the sum-utility
objective, which allows us to transform the problem into a form that can be
solved using a popular algorithmic framework called BSUM (Block Successive
Upper-Bound Minimization).} Simulation experiments show that the proposed
framework is effective for solving interference management problems in large
HetNet.Comment: Accepted by IEEE Transactions on Wireless Communicatio
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