Exploring the landscape of the space of heuristics for local search in SAT

Local search is a powerful technique on many combinatorial optimisation problems. However, the effectiveness of local search methods will often depend strongly on the details of the heuristics used within them. There are many potential heuristics, and so finding good ones is in itself a challenging search problem. A natural method to search for effective heuristics is to represent the heuristic as a small program and then apply evolutionary methods, such as genetic programming. However, the search within the space of heuristics is not well understood, and in particular little is known of the associated search landscapes. In this paper, we consider the domain of propositional satisfiability (SAT), and a generic class of local search methods called ‘WalkSAT’. We give a language for generating the heuristics; using this we generated over three million heuristics, in a systematic manner, and evaluated their associated fitness values. We then use this data set as the basis for an initial analysis of the landscape of the space of heuristics. We give evidence that the heuristic landscape exhibits clustering. We also consider local search on the space of heuristics and show that it can perform quite well, and could complement genetic programming methods on that space

HySST: hyper-heuristic search strategies and timetabling

9th International Conference on the Practice and Theory of Automated Timetabling, Son, Norway, 28-31 August 201

Algorithm Configuration: Learning policies for the quick termination of poor performers

One way to speed up the algorithm configuration task is to use short runs instead of long runs as much as possible, but without discarding the configurations that eventually do well on the long runs. We consider the problem of selecting the top performing configurations of the Conditional Markov Chain Search (CMCS), a general algorithm schema that includes, for examples, VNS. We investigate how the structure of performance on short tests links with those on long tests, showing that significant differences arise between test domains. We propose a "performance envelope" method to exploit the links; that learns when runs should be terminated, but that automatically adapts to the domain

Heuristic generation via parameter tuning for online bin packing

Online bin packing requires immediate decisions to be made for placing an incoming item one at a time into bins of fixed capacity without causing any overflow. The goal is to maximise the average bin fullness after placement of a long stream of items. A recent work describes an approach for solving this problem based on a ‘policy matrix’ representation in which each decision option is independently given a value and the highest value option is selected. A policy matrix can also be viewed as a heuristic with many parameters and then the search for a good policy matrix can be treated as a parameter tuning process. In this study, we show that the Irace parameter tuning algorithm produces heuristics which outperform the standard human designed heuristics for various instances of the online bin packing problem

Evolutionary squeaky wheel optimization: a new framework for analysis

Squeaky wheel optimization (SWO) is a relatively new metaheuristic that has been shown to be effective for many real-world problems. At each iteration SWO does a complete construction of a solution starting from the empty assignment. Although the construction uses information from previous iterations, the complete rebuilding does mean that SWO is generally effective at diversification but can suffer from a relatively weak intensification. Evolutionary SWO (ESWO) is a recent extension to SWO that is designed to improve the intensification by keeping the good components of solutions and only using SWO to reconstruct other poorer components of the solution. In such algorithms a standard challenge is to understand how the various parameters affect the search process. In order to support the future study of such issues, we propose a formal framework for the analysis of ESWO. The framework is based on Markov chains, and the main novelty arises because ESWO moves through the space of partial assignments. This makes it significantly different from the analyses used in local search (such as simulated annealing) which only move through complete assignments. Generally, the exact details of ESWO will depend on various heuristics; so we focus our approach on a case of ESWO that we call ESWO-II and that has probabilistic as opposed to heuristic selection and construction operators. For ESWO-II, we study a simple problem instance and explicitly compute the stationary distribution probability over the states of the search space. We find interesting properties of the distribution. In particular, we find that the probabilities of states generally, but not always, increase with their fitness. This nonmonotonocity is quite different from the monotonicity expected in algorithms such as simulated annealing

A guide to conic optimisation and its applications

Most OR academics and practitioners are familiar with linear programming (LP) and its applications. Many are however unaware of conic optimisation, which is a powerful generalisation of LP, with a prodigious array of important real-life applications. In this invited paper, we give a gentle introduction to conic optimisation, followed by a survey of applications in OR and related areas. Along the way, we try to help the reader develop insight into the strengths and limitations of conic optimisation as a tool for solving real-life problems

Immuno-inhibitory PD-L1 can be induced by a peptidoglycan/NOD2 mediated pathway in primary monocytic cells and is deficient in Crohn's patients with homozygous NOD2 mutations.

Peptidoglycan (PGN) is a ubiquitous bacterial membrane product that, despite its well known pro-inflammatory properties, has also been invoked in immuno-tolerance of the gastrointestinal tract. PGN-induced mucosal IL-10 secretion and downregulation of Toll like receptors are potential mechanisms of action in the gut but there are few data on tolerogenic adaptive immune responses and PGN. Here, using blood-derived mononuclear cells, we showed that PGN induced marked cell surface expression of PD-L1 but not PD-L2 or CD80/CD86, and specifically in the CD14(+) monocytic fraction. This was reproduced at the gene level with rapid induction (<4 h) and, unlike for LPS stimulation, was still sustained at 24 h. Using transfected and native muramyl dipeptide (MDP), which is a cleavage product of PGN and a specific NOD2 agonist, in assays with wild type cells or those from patients with Crohn's disease carrying the Leu1007 frameshift mutation of NOD2, we showed that (i) both NOD2 dependent and independent signalling (appearing TLR2 mediated) occurred for PGN upregulation of PD-L1 (ii) upregulation is lost in response to MDP in patients with the homozygous mutation and (iii) PD-L1 upregulation was unaffected in patients with heterozygous mutations as previously reported for cytokine responses to MDP. The uptake of PGN and its cleavage products by the intestinal mucosa is well recognised and further work should consider PD-L1 upregulation as one potential mechanism of the commensal flora-driven intestinal immuno-tolerance. Indeed, recent work has shown that loss of PD-L1 signalling in the gut breaks CD8(+) T cell tolerance to self antigen and leads to severe autoimmune enteritis.The authors wish to thank the Sir Halley Stewart Trust and the Dairy Council for their generous support of the research described within and the MRC for their continual suppor