The angel wins

The angel-devil game is played on an infinite two-dimensional ``chessboard''. The squares of the board are all white at the beginning. The players called angel and devil take turns in their steps. When it is the devil's turn, he can turn a square black. The angel always stays on a white square, and when it is her turn she can fly at a distance of at most J steps (each of which can be horizontal, vertical or diagonal) to a new white square. Here J is a constant. The devil wins if the angel does not find any more white squares to land on. The result of the paper is that if J is sufficiently large then the angel has a strategy such that the devil will never capture her. This deceptively easy-sounding result has been a conjecture, surprisingly, for about thirty years. Several other independent solutions have appeared simultaneously, some of them prove that J=2 is sufficient (see the Wikipedia on the angel problem). Still, it is hoped that the hierarchical solution presented here may prove useful for some generalizations.Comment: 28 pages, 8 figure

Angel method for discrete optimization problems

In this study we present an efficient new hybrid meta-heuristic - named in other context ANGEL - for solving discrete size optimization of truss structures. ANGEL combines ant colony optimization (ACO), genetic algorithm (GA) and local search (LS) strategy. The procedures of ANGEL attempt to solve an optimization problem by repeating the following steps. First time, ACO searches the solution space and generates structure designs to provide the initial population for GA. After that, GA is executed and the pheromone set in ACO is updated when GA obtains a better solution. When GA terminates, ACO searches again by using the new pheromone set. ACO and GA search alternately and cooperatively in the solution space. In this study we propose an efficient local search procedure. The procedure, in an iterative process, tries to make a better (a lighter feasible or a less unfeasible) truss from the current truss obtained by ACO or GA. The geometrically and materially nonlinear space trusses are formulated as a large d isplacement structural model. The treatment of elastic-plastic collapse analysis is based on a path-following method \cite 6. The applied method is a combination of the perturbation technique of the stability theory and the non-linear modification of the classical linear homotopy method. With the help of the higher-order predictor-corrector terms, the method is able to follow the load- deflection path even in case of elastic-plastic material law

Stressed web environments as strategic games: risk profiles and Weltanschauung

We consider the behaviour of a set of services in a stressed web environment where performance patterns may be di cult to pre- dict. In stressed environments the performances of some providers may degrade while the performances of others, with elastic resources, may improve. The allocation of web-based providers to users (brokering) is modelled by a strategic non-cooperative angel-daemon game with risk pro les. A risk pro le speci es a bound on the number of unreliable ser- vice providers within an environment without identifying the names of these providers. Risk pro les o er a means of analysing the behaviour of broker agents which allocate service providers to users. A Nash equilib- rium is a xed point of such a game in which no user can locally improve their choice of provider { thus, a Nash equilibrium is a viable solution to the provider/user allocation problem. Angel daemon games provide a means of reasoning about stressed environments and o er the possibility of designing brokers using risk pro les and Nash equilibria.Postprint (author’s final draft

『骨董屋』におけるネルの二つの“死の意味”: “悲劇の死”と“不滅の死”

Looking similar to Oliver Twist, Pilgrim’s Progress, and TheExhibition of Humphry Clinker in the point of view of the basicstructure, The Old Curiosity Shop has one significant difference, thedeath of the virtuous heroine Nell, far from the happy endings of the rest. It must be the most controversial point and the hardest part for us readers to understand. However, closely examining Nell’s death, we find it having two aspects and roles. One is “the tragic death” as a pathetic symbol of all children of the lower classes who were the victims of avarice at that time, to show the cruelty and injustice of the Victorian industrial society built on the sacrifice of those poor, and to evoke sympathy in the contemporaries’ mind. The other is “non-death” with eternal life as an angel, the eternal good influence of her humanity among people. Love, sympathy and all other goodness Nell embodies can be a solution to the social problem Nell’s tragic death points out and can unite all the people to establish a harmonious society based on humanistic ideals.Viewed in this light, the death of Nell takes on a new meaning, the double-layer presentation of both the social problem and its solution.論

A branch-and-cut algorithm for the Orienteering Arc Routing Problem

[EN] In arc routing problems, customers are located on arcs, and routes of minimum cost have to be identified. In the Orienteering Arc Routing Problem (OARP),in addition to a set of regular customers that have to be serviced, a set of potential customers is available. From this latter set, customers have to be chosen on the basis of an associated profit. The objective is to find a route servicing the customers which maximize the total profit collected while satisfying a given time limit on the route.In this paper, we describe large families of facet-inducing inequalities for the OARP and present a branch-and-cut algorithm for its solution. The exact algorithm embeds a procedure which builds a heuristic solution to the OARP on the basis of the information provided by the solution of the linear relaxation. Extensive computational experiments over different sets of OARP instances show that the exact algorithm is capable of solving to optimality large instances, with up to 2000 vertices and 14,000 arcs, within 1 h and often within a few minutes.Authors want to thank two anonymous referees for their careful reading of the original paper and their many valuable comments and suggestions that have helped to improve the paper. Angel Corberan, Isaac Plana and Jose M. Sanchis wish to thank the Ministerio de Economia y Competitividad of Spain (MTM2012-36163-006-02) and the Generalitat Valenciana (project GVPR-OMETE02013-049) for its support.Archetti, C.; Corberán, A.; Plana, I.; Sanchís Llopis, JM.; Speranza, M. (2016). A branch-and-cut algorithm for the Orienteering Arc Routing Problem. Computers & Operations Research. 66:95-104. https://doi.org/10.1016/j.cor.2015.08.003S951046

A statistical learning based approach for parameter fine-tuning of metaheuristics

Metaheuristics are approximation methods used to solve combinatorial optimization problems. Their performance usually depends on a set of parameters that need to be adjusted. The selection of appropriate parameter values causes a loss of efficiency, as it requires time, and advanced analytical and problem-specific skills. This paper provides an overview of the principal approaches to tackle the Parameter Setting Problem, focusing on the statistical procedures employed so far by the scientific community. In addition, a novel methodology is proposed, which is tested using an already existing algorithm for solving the Multi-Depot Vehicle Routing Problem.Peer ReviewedPostprint (published version

A simheuristic for routing electric vehicles with limited driving ranges and stochastic travel times

Green transportation is becoming relevant in the context of smart cities, where the use of electric vehicles represents a promising strategy to support sustainability policies. However the use of electric vehicles shows some drawbacks as well, such as their limited driving-range capacity. This paper analyses a realistic vehicle routing problem in which both driving-range constraints and stochastic travel times are considered. Thus, the main goal is to minimize the expected time-based cost required to complete the freight distribution plan. In order to design reliable Routing plans, a simheuristic algorithm is proposed. It combines Monte Carlo simulation with a multi-start metaheuristic, which also employs biased-randomization techniques. By including simulation, simheuristics extend the capabilities of metaheuristics to deal with stochastic problems. A series of computational experiments are performed to test our solving approach as well as to analyse the effect of uncertainty on the routing plans.Peer Reviewe

Scaling Limit for the Diffusion Exit Problem in the Levinson Case

The exit problem for small perturbations of a dynamical system in a domain is considered. It is assumed that the unperturbed dynamical system and the domain satisfy the Levinson conditions. We assume that the random perturbation affects the driving vector field and the initial condition, and each of the components of the perturbation follows a scaling limit. We derive the joint scaling limit for the random exit time and exit point. We use this result to study the asymptotics of the exit time for 1-d diffusions conditioned on rare events.Comment: 13 page