Wenxiang Chen

Large-scale global optimization using cooperative coevolution with variable interaction learning

In recent years, Cooperative Coevolution (CC) was proposed as a promising framework for tackling high-dimensional optimization problems. The main idea of CC-based algorithms is to discover which decision variables, i.e, dimensions, of the search space interact. Non-interacting variables can be optimized as separate problems of lower dimensionality. Interacting variables must be grouped together and optimized jointly. Early research in this area started with simple attempts such as one-dimension based and splitting-in-half methods. Later, more efficient algorithms with new grouping strategies, such as DECCG and MLCC, were proposed. However, those grouping strategies still cannot sufficiently adapt to different group sizes. In this paper, we propose a new CC framework named Cooperative Coevolution with Variable Interaction Learning (CCVIL), which initially considers all variables as independent and puts each of them into a separate group. Iteratively, it discovers their relations and merges the groups accordingly. The efficiency of the newly proposed framework is evaluated on the set of large-scale optimization benchmarks.

Benchmarking Optimization Algorithms: An Open Source Framework for the Traveling Salesman Problem

We introduce an experimentation procedure for evaluating and comparing optimization algorithms based on the Traveling Salesman Problem (TSP). We argue that end-of-run results alone do not give sufficient information about an algorithms performance, so our approach analyzes the algorithms progress over time. Comparisons of performance curves in diagrams can be formalized by comparing the areas under them. Algorithms can be ranked according to a performance metric. Rankings based on different metrics can then be aggregated into a global ranking, which provides a quick overview of the quality of algorithms in comparison. An open source software framework, the TSP Suite, applies this experimental procedure to the TSP. The framework can support researchers in implementing TSP solvers, unit testing them, and running experiments in a parallel and distributed fashion. It also has an evaluator component, which implements the proposed evaluation process and produces detailed reports. We test the approach by using the TSP Suite to benchmark several local search and evolutionary computation methods. This results in a large set of baseline data, which will be made available to the research community. Our experiments show that the tested pure global optimization algorithms are outperformed by local search, but the best results come from hybrid algorithms.

Constant time steepest descent local search with lookahead for NK-landscapes and MAX-kSAT

A modified form of steepest descent local search is proposed that displays an average complexity of O(1) time per move for NK-Landscape and MAX-kSAT problems. The algorithm uses a Walsh decomposition to identify improving moves. In addition, it is possible to compute a Hamming distance 2 statistical lookahead: if x is the current solution and y is a neighbor of x, it is possible to compute the average evaluation of the neighbors of y. The average over the Hamming distance 2 neighborhood can be used as a surrogate evaluation function to replace f. The same modified steepest descent can be executed in O(1) time using the Hamming distance 2 neighborhood average as the fitness function. In practice, the modifications needed to prove O(1) complexity can be relaxed with little or no impact on runtime performance. Finally, steepest descent local search over the mean of the Hamming distance 2 neighborhood yields superior results compared to using the standard evaluation function for certain types of NK-Landscape problems.

Impact of problem decomposition on Cooperative Coevolution

Variable Interaction Learning (VIL) is an emerging technique regarding detecting interacting variables so that Cooperative Coevolutionary Evolutionary Algorithms (CCEAs) can decompose problems accordingly and tackle subproblems of smaller sizes. While previous approaches are developed to efficiently perform VIL, no study has been on the actual usefulness of the detected variable interactions in terms of the performance of CCEAs. Since VIL is a computationally expensive task by itself, overly spending time on VIL without notable benefits for CCEAs should be avoided. It is hence critical to study the real impact of problem decomposition on CCEAs. We conduct empirical studies to address three closely related questions: 1) will a better problem decomposition lead to better performance of CCEAs, 2) when will improving problem decomposition benefit CCEAs, and 3) to what extent will improving problem decomposition enhance the performance of CCEAs.

Second order partial derivatives for NK-landscapes

Local search methods based on explicit neighborhood enumeration require at least

Hyperplane initialized local search for MAXSAT

O(n)

An empirical evaluation of o(1) steepest descent for NK-Landscapes

time to identify all possible improving moves. For k-bounded pseudo-Boolean optimization problems, recent approaches have achieved

Decomposing SAT Instances with Pseudo Backbones

O(k^2*2^{k})

Selecting Optimal Models Based on Efficiency and Robustness in Multi-valued Biological Networks

runtime cost per move, where

Tunneling between plateaus: improving on a state-of-the-art MAXSAT solver using partition crossover

n