A Survey of League Championship Algorithm: Prospects and Challenges <s> Graph Colouring <s> The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts. <s> BIB001 </s> A Survey of League Championship Algorithm: Prospects and Challenges <s> Graph Colouring <s> The resource-constrained project scheduling problem involves the determination of a schedule of the project activities, satisfying the precedence relations and resource constraints while minimizing the project duration. In practice, activity durations may be subject to variability, such that a stochastic approach to the problem is more appropriate. We propose a methodology for the determination of a project execution policy and a vector of predictive activity starting times with the objective of minimizing a cost function that consists of the weighted expected activity starting time deviations and the penalties or bonuses associated with late or early project completion. In a computational experiment, we show that our procedure greatly outperforms existing algorithms described in the literature <s> BIB002 </s> A Survey of League Championship Algorithm: Prospects and Challenges <s> Graph Colouring <s> Consider a graph with nodes, weighted links and a set of colours. In the generalised graph coloring problem GGCP, one must colour each node while minimising the total weight of monochromatic links. GGCP can model a cell site assignment problem in which nodes represent cell sites and colours represent multi-service nodes MSN. The links indicate pairs of cell sites whose geographic service areas overlap; the link weight indicates the degree of overlap. The objective is, as much as possible, to assign cell sites with overlap to different MSNs. We describe a greedy randomised adaptive search procedure GRASP for GGCP. At each replication, it builds an initial solution by randomly choosing nodes, one at a time, from a candidate list and myopically assigning a colour to each chosen node. Exchange heuristics can then improve upon the initial solution. Computational experiments indicate that the heuristic provides excellent solutions in little CPU time. <s> BIB003 </s> A Survey of League Championship Algorithm: Prospects and Challenges <s> Graph Colouring <s> Recent decades have seen a remarkable development in the use of computer systems and computer networks. With their advances our reliance on hardware and software has amplified, and so has our susceptibility to their malfunction. For fear of any major network failure, it is at all times good to recognize similar networks so that switching can be done to reduce damages. Theoretical computer science aims to model and understand the intricacy of computer systems, and thereby creates the basis for their formal verification: to mathematically prove that a system satisfies its requirement. In this paper, the decidability theory is theoretically applied to identify/decide if two different computer networks are similar (in terms of efficiency, high performance computing and scalability) or not. A finite automata is designed for each network and two different scenarios are considered for demonstration. The results show that the theory can be effectively used to make such comparisons between different computer networks. <s> BIB004 </s> A Survey of League Championship Algorithm: Prospects and Challenges <s> Graph Colouring <s> Multiple instance learning is a challenging task in supervised learning and data mining. However, algorithm performance becomes slow when learning from large-scale and high-dimensional data sets. Graphics processing units (GPUs) are being used for reducing computing time of algorithms. This paper presents an implementation of the G3P-MI algorithm on GPUs for solving multiple instance problems using classification rules. The GPU model proposed is distributable to multiple GPUs, seeking for its scalability across large-scale and high-dimensional data sets. The proposal is compared to the multi-threaded CPU algorithm with streaming SIMD extensions parallelism over a series of data sets. Experimental results report that the computation time can be significantly reduced and its scalability improved. Specifically, an speedup of up to 149$$\times $$× can be achieved over the multi-threaded CPU algorithm when using four GPUs, and the rules interpreter achieves great efficiency and runs over 108 billion genetic programming operations per second. <s> BIB005 </s> A Survey of League Championship Algorithm: Prospects and Challenges <s> Graph Colouring <s> In this paper, we present a complex-valued neuro-fuzzy inference system (CNFIS) and develop its meta-cognitive learning algorithm. CNFIS has four layers - an input layer with m rules, a Gaussian layer with K rules, a normalization layer with K rules and an output layer with n rules. The rules in the Gaussian layer map the m-dimensional complex-valued input features to a K-dimensional real-valued space. Hence, we use the Wirtinger calculus to obtain the complex-valued gradients of the real-valued function in deriving the learning algorithm of CNFIS. Next, we also develop the meta-cognitive learning algorithm for CNFIS referred to as ''meta-cognitive complex-valued neuro-fuzzy inference system (MCNFIS)''. CNFIS is the cognitive component of MCNFIS and a self-regulatory learning mechanism that decides what-to-learn, how-to-learn, and when-to-learn in a meta-cognitive framework is its meta-cognitive component. Thus, for every epoch of the learning process, the meta-cognitive component decides if each sample in the training set must be deleted or used to update the parameters of CNFIS or to be reserved for future use. The performances of CNFIS and MCNFIS are studied on a set of approximation and real-valued classification problems, in comparison to existing complex-valued learning algorithms in the literature. First, we evaluate the approximation performances of CNFIS and MCNFIS on a synthetic complex-valued function approximation problem, an adaptive beam-forming problem and a wind prediction problem. Finally, we study the decision making performance of CNFIS and MCNFIS on a set of benchmark real-valued classification problems from the UCI machine learning repository. Performance study results on approximation and real-valued classification problems show that CNFIS and MCNFIS outperform existing algorithms in the literature. <s> BIB006 </s> A Survey of League Championship Algorithm: Prospects and Challenges <s> Graph Colouring <s> Performance comparisons between algorithms have a long tradition in metaheuristic research. An early example is comparisons between Tabu Search (TS) and Simulated Annealing (SA) algorithms for tackling the Quadratic Assignment Problem (QAP). The results of these comparisons are to a certain extent inconclusive, even when focusing on only these two types of algorithms. While comparisons of SA and TS algorithms were based on rather small-sized instances, here we focus on possible dependencies of the relative performance between SA and TS algorithms on instance size. In fact, our experimental results show that the assertion whether one algorithm is better than the other can depend strongly on QAP instance size even if one focuses on instances with otherwise same characteristics. <s> BIB007
Assignment problem BIB003  . Resource Constrained Projects Resource allocation BIB001  , resource distribution 58 and scheduling BIB002 . Machine Learning Learning of classification rules BIB005 BIB004 , Learning the Structure of Bayesian Networks 62 , learning rules in a fuzzy system BIB006 and quadratic assignment problem BIB007 .