Deconstructing the Big Valley Search Space Hypothesis

The big valley hypothesis suggests that, in combinatorial optimisation, local optima of good quality are clustered and surround the global optimum. We show here that the idea of a single valley does not always hold. Instead the big valley seems to de-construct into several valleys, also called ‘funnels’ in theoretical chemistry. We use the local optima networks model and propose an effective procedure for extracting the network data. We conduct a detailed study on four selected TSP instances of moderate size and observe that the big valley decomposes into a number of sub-valleys of different sizes and fitness distributions. Sometimes the global optimum is located in the largest valley, which suggests an easy to search landscape, but this is not generally the case. The global optimum might be located in a small valley, which offers a clear and visual explanation of the increased search difficulty in these cases. Our study opens up new possibilities for analysing and visualising combinatorial landscapes as complex networks

Coarse-Grained Barrier Trees of Fitness Landscapes

Recent literature suggests that local optima in fitness landscapes are clustered, which offers an explanation of why perturbation-based metaheuristics often fail to find the global optimum: they become trapped in a sub-optimal cluster. We introduce a method to extract and visualize the global organization of these clusters in form of a barrier tree. Barrier trees have been used to visualize the barriers between local optima basins in fitness landscapes. Our method computes a more coarsely grained tree to reveal the barriers between clusters of local optima. The core element is a new variant of the flooding algorithm, applicable to local optima networks, a compressed representation of fitness landscapes. To identify the clusters, we apply a community detection algorithm. A sample of 200 NK fitness landscapes suggests that the depth of their coarse-grained barrier tree is related to their search difficulty

Understanding Phase Transitions with Local Optima Networks: Number Partitioning as a Case Study

Phase transitions play an important role in understanding search difficulty in combinatorial optimisation. However, previous attempts have not revealed a clear link between fitness landscape properties and the phase transition. We explore whether the global landscape structure of the number partitioning problem changes with the phase transition. Using the local optima network model, we analyse a number of instances before, during, and after the phase transition. We compute relevant network and neutrality metrics; and importantly, identify and visualise the funnel structure with an approach (monotonic sequences) inspired by theoretical chemistry. While most metrics remain oblivious to the phase transition, our results reveal that the funnel structure clearly changes. Easy instances feature a single or a small number of dominant funnels leading to global optima; hard instances have a large number of suboptimal funnels attracting the search. Our study brings new insights and tools to the study of phase transitions in combinatorial optimisation

A narrative review on the similarities and dissimilarities between myalgic encephalomyelitis/chronic fatigue syndrome (me/cfs) and sickness behavior

It is of importance whether myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS) is a variant of sickness behavior. The latter is induced by acute infections/injury being principally mediated through proinflammatory cytokines. Sickness is a beneficial behavioral response that serves to enhance recovery, conserves energy and plays a role in the resolution of inflammation. There are behavioral/symptomatic similarities (for example, fatigue, malaise, hyperalgesia) and dissimilarities (gastrointestinal symptoms, anorexia and weight loss) between sickness and ME/CFS. While sickness is an adaptive response induced by proinflammatory cytokines, ME/CFS is a chronic, disabling disorder, where the pathophysiology is related to activation of immunoinflammatory and oxidative pathways and autoimmune responses. While sickness behavior is a state of energy conservation, which plays a role in combating pathogens, ME/CFS is a chronic disease underpinned by a state of energy depletion. While sickness is an acute response to infection/injury, the trigger factors in ME/CFS are less well defined and encompass acute and chronic infections, as well as inflammatory or autoimmune diseases. It is concluded that sickness behavior and ME/CFS are two different conditions