8,117 research outputs found
High-dimensional Black-box Optimization via Divide and Approximate Conquer
Divide and Conquer (DC) is conceptually well suited to high-dimensional
optimization by decomposing a problem into multiple small-scale sub-problems.
However, appealing performance can be seldom observed when the sub-problems are
interdependent. This paper suggests that the major difficulty of tackling
interdependent sub-problems lies in the precise evaluation of a partial
solution (to a sub-problem), which can be overwhelmingly costly and thus makes
sub-problems non-trivial to conquer. Thus, we propose an approximation
approach, named Divide and Approximate Conquer (DAC), which reduces the cost of
partial solution evaluation from exponential time to polynomial time.
Meanwhile, the convergence to the global optimum (of the original problem) is
still guaranteed. The effectiveness of DAC is demonstrated empirically on two
sets of non-separable high-dimensional problems.Comment: 7 pages, 2 figures, conferenc
Negatively Correlated Search
Evolutionary Algorithms (EAs) have been shown to be powerful tools for
complex optimization problems, which are ubiquitous in both communication and
big data analytics. This paper presents a new EA, namely Negatively Correlated
Search (NCS), which maintains multiple individual search processes in parallel
and models the search behaviors of individual search processes as probability
distributions. NCS explicitly promotes negatively correlated search behaviors
by encouraging differences among the probability distributions (search
behaviors). By this means, individual search processes share information and
cooperate with each other to search diverse regions of a search space, which
makes NCS a promising method for non-convex optimization. The cooperation
scheme of NCS could also be regarded as a novel diversity preservation scheme
that, different from other existing schemes, directly promotes diversity at the
level of search behaviors rather than merely trying to maintain diversity among
candidate solutions. Empirical studies showed that NCS is competitive to
well-established search methods in the sense that NCS achieved the best overall
performance on 20 multimodal (non-convex) continuous optimization problems. The
advantages of NCS over state-of-the-art approaches are also demonstrated with a
case study on the synthesis of unequally spaced linear antenna arrays
A Parallel Divide-and-Conquer based Evolutionary Algorithm for Large-scale Optimization
Large-scale optimization problems that involve thousands of decision
variables have extensively arisen from various industrial areas. As a powerful
optimization tool for many real-world applications, evolutionary algorithms
(EAs) fail to solve the emerging large-scale problems both effectively and
efficiently. In this paper, we propose a novel Divide-and-Conquer (DC) based EA
that can not only produce high-quality solution by solving sub-problems
separately, but also highly utilizes the power of parallel computing by solving
the sub-problems simultaneously. Existing DC-based EAs that were deemed to
enjoy the same advantages of the proposed algorithm, are shown to be
practically incompatible with the parallel computing scheme, unless some
trade-offs are made by compromising the solution quality.Comment: 12 pages, 0 figure
A Link-based Mixed Integer LP Approach for Adaptive Traffic Signal Control
This paper is concerned with adaptive signal control problems on a road
network, using a link-based kinematic wave model (Han et al., 2012). Such a
model employs the Lighthill-Whitham-Richards model with a triangular
fundamental diagram. A variational type argument (Lax, 1957; Newell, 1993) is
applied so that the system dynamics can be determined without knowledge of the
traffic state in the interior of each link. A Riemann problem for the
signalized junction is explicitly solved; and an optimization problem is
formulated in continuous-time with the aid of binary variables. A
time-discretization turns the optimization problem into a mixed integer linear
program (MILP). Unlike the cell-based approaches (Daganzo, 1995; Lin and Wang,
2004; Lo, 1999b), the proposed framework does not require modeling or
computation within a link, thus reducing the number of (binary) variables and
computational effort.
The proposed model is free of vehicle-holding problems, and captures
important features of signalized networks such as physical queue, spill back,
vehicle turning, time-varying flow patterns and dynamic signal timing plans.
The MILP can be efficiently solved with standard optimization software.Comment: 15 pages, 7 figures, current version is accepted for presentation at
the 92nd Annual Meeting of Transportation Research Boar
Lagrangian-based Hydrodynamic Model: Freeway Traffic Estimation
This paper is concerned with highway traffic estimation using traffic sensing
data, in a Lagrangian-based modeling framework. We consider the
Lighthill-Whitham-Richards (LWR) model (Lighthill and Whitham, 1955; Richards,
1956) in Lagrangian-coordinates, and provide rigorous mathematical results
regarding the equivalence of viscosity solutions to the Hamilton-Jacobi
equations in Eulerian and Lagrangian coordinates. We derive closed-form
solutions to the Lagrangian-based Hamilton-Jacobi equation using the Lax-Hopf
formula (Daganzo, 2005; Aubin et al., 2008), and discuss issues of fusing
traffic data of various types into the Lagrangian-based H-J equation. A
numerical study of the Mobile Century field experiment (Herrera et al., 2009)
demonstrates the unique modeling features and insights provided by the
Lagrangian-based approach.Comment: 17 pages, 7 figures, current version submitted to Transportation
Research Part
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