An efficient memetic, permutation-based evolutionary algorithm for real-world train timetabling

Train timetabling is a difficult and very tightly constrained combinatorial problem that deals with the construction of train schedules. We focus on the particular problem of local reconstruction of the schedule following a small perturbation, seeking minimisation of the total accumulated delay by adapting times of departure and arrival for each train and allocation of resources (tracks, routing nodes, etc.). We describe a permutation-based evolutionary algorithm that relies on a semi-greedy heuristic to gradually reconstruct the schedule by inserting trains one after the other following the permutation. This algorithm can be hybridised with ILOG commercial MIP programming tool CPLEX in a coarse-grained manner: the evolutionary part is used to quickly obtain a good but suboptimal solution and this intermediate solution is refined using CPLEX. Experimental results are presented on a large real-world case involving more than one million variables and 2 million constraints. Results are surprisingly good as the evolutionary algorithm, alone or hybridised, produces excellent solutions much faster than CPLEX alone

An Empirical Study on Collective Intelligence Algorithms for Video Games Problem-Solving

Computational intelligence (CI), such as evolutionary computation or swarm intelligence methods, is a set of bio-inspired algorithms that have been widely used to solve problems in areas like planning, scheduling or constraint satisfaction problems. Constrained satisfaction problems (CSP) have taken an important attention from the research community due to their applicability to real problems. Any CSP problem is usually modelled as a constrained graph where the edges represent a set of restrictions that must be verified by the variables (represented as nodes in the graph) which will define the solution of the problem. This paper studies the performance of two particular CI algorithms, ant colony optimization (ACO) and genetic algorithms (GA), when dealing with graph-constrained models in video games problems. As an application domain, the "Lemmings" video game has been selected, where a set of lemmings must reach the exit point of each level. In order to do that, each level is represented as a graph where the edges store the allowed movements inside the world. The goal of the algorithms is to assign the best skills in each position on a particular level, to guide the lemmings to reach the exit. The paper describes how the ACO and GA algorithms have been modelled and applied to the selected video game. Finally, a complete experimental comparison between both algorithms, based on the number of solutions found and the levels solved, is analysed to study the behaviour of those algorithms in the proposed domain

A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems

Tour recommendation for groups

Consider a group of people who are visiting a major touristic city, such as NY, Paris, or Rome. It is reasonable to assume that each member of the group has his or her own interests or preferences about places to visit, which in general may differ from those of other members. Still, people almost always want to hang out together and so the following question naturally arises: What is the best tour that the group could perform together in the city? This problem underpins several challenges, ranging from understanding people’s expected attitudes towards potential points of interest, to modeling and providing good and viable solutions. Formulating this problem is challenging because of multiple competing objectives. For example, making the entire group as happy as possible in general conflicts with the objective that no member becomes disappointed. In this paper, we address the algorithmic implications of the above problem, by providing various formulations that take into account the overall group as well as the individual satisfaction and the length of the tour. We then study the computational complexity of these formulations, we provide effective and efficient practical algorithms, and, finally, we evaluate them on datasets constructed from real city data

Hybrid artificial intelligence technique for solving large, highly constrained timetabling problems

Timetabling problems are often hard and time-consuming to solve. Profits from full automatization of this process can be invaluable. Although over the years many solutions have been proposed, most of the methods concern only one problem instance or class. This paper describes a possibly universal method for solving large, highly constrained timetabling problems from different areas. The solution is based on evolutionary algorithm's framework, with specialized genetic operators and penalty-based evaluation function, and uses hyper-heuristics to establish its operating parameters. The method has been used to solve three different timetabling problems, which are described in detail, along with some results of preliminary experiments

Solving the Resource Constrained Project Scheduling Problem with Generalized Precedences by Lazy Clause Generation

The technical report presents a generic exact solution approach for minimizing the project duration of the resource-constrained project scheduling problem with generalized precedences (Rcpsp/max). The approach uses lazy clause generation, i.e., a hybrid of finite domain and Boolean satisfiability solving, in order to apply nogood learning and conflict-driven search on the solution generation. Our experiments show the benefit of lazy clause generation for finding an optimal solutions and proving its optimality in comparison to other state-of-the-art exact and non-exact methods. The method is highly robust: it matched or bettered the best known results on all of the 2340 instances we examined except 3, according to the currently available data on the PSPLib. Of the 631 open instances in this set it closed 573 and improved the bounds of 51 of the remaining 58 instances.Comment: 37 pages, 3 figures, 16 table