Exact and approximate algorithms for the longest induced path problem

The longest induced path problem consists in finding a maximum subset of vertices of a graph such that it induces a simple path. We propose a new exact enumerative algorithm that solves problems with up to 138 vertices and 493 edges and a heuristic for larger problems. Detailed computational experiments compare the results obtained by the new algorithms with other approaches in the literature and investigate the characteristics of the optimal solutions.

An enumerative algorithm for de novo design of proteins with diverse pocket structures

To create new enzymes and biosensors from scratch, precise control over the structure of small-molecule binding sites is of paramount importance, but systematically designing arbitrary protein pocket shapes and sizes remains an outstanding challenge. Using the NTF2-like structural superfamily as a model system, we developed an enumerative algorithm for creating a virtually unlimited number of de novo proteins supporting diverse pocket structures. The enumerative algorithm was tested and refined through feedback from two rounds of large-scale experimental testing, involving in total the assembly of synthetic genes encoding 7,896 designs and assessment of their stability on yeast cell surface, detailed biophysical characterization of 64 designs, and crystal structures of 5 designs. The refined algorithm generates proteins that remain folded at high temperatures and exhibit more pocket diversity than naturally occurring NTF2-like proteins. We expect this approach to transform the design of small-molecule sensors and enzymes by enabling the creation of binding and active site geometries much more optimal for specific design challenges than is accessible by repurposing the limited number of naturally occurring NTF2-like proteins.

Research on the Single-Model Stochastic Assembly Line Balancing Problems of Type-1: A Task-Oriented Enumerative Algorithm

In this paper, the optimal assembly sequence is considered as precedence graph which reduces the complexity of the problem, and an exact algorithm named task-oriented enumeration is proposed to solve the single-model stochastic assembly line balancing problems of type-1. The results show the proposed algorithm can solve the single-model stochastic assembly line balancing problems of type-1.

Slope Optimization Design Based on Improved Response Surface

Due to lacking of explicitly analytical model, optimization design of complex slope is often consulted to enumerative algorithm which generally results huge computation efforts. To overcome this problem, a new optimization method based on improved response surface (IRS) is proposed. The IRS, constructed by uniform design (UD) and non-parametric regression (NR), provides a regressed and explicitly analytical model through a few trial computations without prior assumed sliding surface. The optimization process is explained and a slope is optimized to verify the feasibility of the proposed method. The results show that the provided method can optimize a slope with multiple sliding surfaces and provide an optimum result under the safety constraints of the slope. Meanwhile, the introduction of UD and NR to construct the IRS can provide a better regression effect with fewer computational costs.