Simultaneous scheduling of football games and referees using Turkish league data

Assignment decisions of referees to football (soccer) games are highly debated in sports media. Referee assignments are typically done on a weekly basis as the league progresses. However, this practice ignores important workload constraints on referees. Moreover, referees' skill levels should also be considered in determining their assignments. In this article, we first give a mixed integer linear program formulation for the problem of simultaneously generating a game schedule and assigning main referees to games by incorporating specific rules in the Turkish league. We also approach this problem using a genetic algorithm (GA) because of the computational difficulties in solving the problem. In the GA solution pool, we suggest using templates for referee assignments that follow several referee‐related workload constraints. We explain how these templates can be obtained by solving a mixed integer linear model prior to running the GA. The usage of these templates for referee assignments is conceptually similar to using a basic match schedule for game scheduling such as the one used in the Turkish Football League. We use the Turkish Football League fixtures for 2010–2013 as a case study. Experiments with the GA using real‐world data show a rather modest performance in terms of computation time and objective function value. Our numerical results indicate that the problem is extremely hard to solve.     

Solution of multiobjective optimization problems: coevolutionary algorithm based on evolutionary game theory

When attempting to solve multiobjective optimization problems (MOPs) using evolutionary algorithms, the Pareto genetic algorithm (GA) has now become a standard of sorts. After its introduction, this approach was further developed and led to many applications. All of these approaches are based on Pareto ranking and use the fitness sharing function to keep diversity. On the other hand, the scheme for solving MOPs presented by Nash introduced the notion of Nash equilibrium and aimed at solving MOPs that originated from evolutionary game theory and economics. Since the concept of Nash Equilibrium was introduced, game theorists have attempted to formalize aspects of the evolutionary equilibrium. Nash genetic algorithm (Nash GA) is the idea to bring together genetic algorithms and Nash strategy. The aim of this algorithm is to find the Nash equilibrium through the genetic process. Another central achievement of evolutionary game theory is the introduction of a method by which agents can play optimal strategies in the absence of rationality. Through the process of Darwinian selection, a population of agents can evolve to an evolutionary stable strategy (ESS). In this article, we find the ESS as a solution of MOPs using a coevolutionary algorithm based on evolutionary game theory. By applying newly designed coevolutionary algorithms to several MOPs, we can confirm that evolutionary game theory can be embodied by the coevolutionary algorithm and this coevolutionary algorithm can find optimal equilibrium points as solutions for an MOP. We also show the optimization performance of the co-evolutionary algorithm based on evolutionary game theory by applying this model to several MOPs and comparing the solutions with those of previous evolutionary optimization models. This work was presented, in part, at the 8th International Symposium on Artificial Life and Robotics, Oita, Japan, January 24#x2013;26, 2003.     

Game-theoretic static load balancing for distributed systems

In this paper, we present a game theoretic approach to solve the static load balancing problem for single-class and multi-class (multi-user) jobs in a distributed system where the computers are connected by a communication network. The objective of our approach is to provide fairness to all the jobs (in a single-class system) and the users of the jobs (in a multi-user system). To provide fairness to all the jobs in the system, we use a cooperative game to model the load balancing problem. Our solution is based on the Nash Bargaining Solution (NBS) which provides a Pareto optimal solution for the distributed system and is also a fair solution. An algorithm for computing the NBS is derived for the proposed cooperative load balancing game. To provide fairness to all the users in the system, the load balancing problem is formulated as a non-cooperative game among the users who try to minimize the expected response time of their own jobs. We use the concept of Nash equilibrium as the solution of our non-cooperative game and derive a distributed algorithm for computing it. Our schemes are compared with other existing schemes using simulations with various system loads and configurations. We show that our schemes perform near the system optimal schemes and are superior to the other schemes in terms of fairness.     

Formulation of customers’ shopping path in shelf space planning: A simulation-optimization approach

Numerous studies confirm that customers’ shopping behavior can highly be managed by many in-store factors such that retail managers try to systematically consider them in order to achieve a well-established solution for shelf-space allocation problem (SSAP). To assist them, we develop an approach based on two artificial intelligence techniques to facilitate well-designed shelf space management. We propose an iterative simulation-optimization approach that integrates customers’ shopping path in the potential demand and introduces it by simulation in the optimization. A profit-based integer programming is also presented that the related computer program, being able to solve small-sized instances, applies important factors including shelf level utility, attraction of store’ zones, allocated shelf space, number of product facings, and demand substitution effects. The problem is inherently a complex and large-sized problem; therefore, we develop two algorithms: GA and hybrid GA with imperialist competitive algorithm. The experimental results prove good performance of hybrid algorithm in terms of both the solution quality and computation time. By embedding this flexible and powerful framework in an expert tool, retail managers are capable of making effective decisions.     

Data Generation for Path Testing

We present two stochastic search algorithms for generating test cases that execute specified paths in a program. The two algorithms are: a simulated annealing algorithm (SA), and a genetic algorithm (GA). These algorithms are based on an optimization formulation of the path testing problem which include both integer- and real-value test cases. We empirically compare the SA and GA algorithms with each other and with a hill-climbing algorithm, Korel's algorithm (KA), for integer-value-input subject programs and compare SA and GA with each other on real-value subject programs. Our empirical work uses several subject programs with a number of paths. The results show that: (a) SA and GA are superior to KA in the number of executed paths, (b) SA tends to perform slightly better than GA in terms of the number of executed paths, and (c) GA is faster than SA; however, KA, when it succeeds in finding the solution, is the fastest.     

基于PSO信息传递模式的混合算法

粒子群优化算法（Particle Swarm Optimization，PSO）是一种基于群智能（Swarm Intelligence）的随机优化计算技术。PSO和遗传算法这两种算法相比较，PSO收敛快速准确，但编码形式单一，局限于解决实优化问题，而遗传算法编码形式灵活，解决问题广泛，但执行效率低于PS00。将粒子群算法的信息传递模式与遗传算法的编码和遗传操作相结合，提出一种混合算法。并推导了两个算法之间的密切联系。并通过组合优化和函数优化的基准测试集对算法进行测试，试验结果表明，该算法在收敛精度和速度优于传统遗传算法。同时，也观察到该算法取得了与粒子群算法一致的收敛现象。     

知识驱动的游戏攻略自动标注算法

为了帮助用户快速检索感兴趣的游戏攻略,提出了知识驱动的游戏攻略自动标注算法。首先,对每款游戏的多个资讯网站进行融合,自动构建游戏领域知识库;然后,再通过游戏领域词汇发现算法和决策树分类模型,抽取游戏攻略中的游戏术语;由于游戏术语在攻略中大多以简称的形式存在,故最后将攻略中游戏术语和知识库进行链接得到该术语所对应的全称即语义标签对攻略进行标注。在多款游戏上的实验结果表明,所提出的游戏攻略标注方法的准确率高达90%。同时,游戏领域词汇发现算法与其他术语抽取方法n-gram语言模型相比取得了更好的效果。     

A simple and effective evolutionary algorithm for the vehicle routing problem

The vehicle routing problem (VRP) plays a central role in the optimization of distribution networks. Since some classical instances with 75 nodes resist the best exact solution methods, most researchers concentrate on metaheuristics for solving real-life problems. Contrary to the VRP with time windows, no genetic algorithm (GA) can compete with the powerful tabu search (TS) methods designed for the VRP. This paper bridges the gap by presenting a relatively simple but effective hybrid GA. In terms of average solution cost, this algorithm outperforms most published TS heuristics on the 14 classical Christofides instances and becomes the best solution method for the 20 large-scale instances generated by Golden et al.Scope and purposeThe framework of this research is the development of effective metaheuristics for hard combinatorial optimization problems met in vehicle routing. It is surprising to notice in the literature the absence of effective genetic algorithms (GA) for the vehicle routing problem (VRP, the main capacitated node routing problem), contrary to node routing problems with time windows or arc routing problems. Earlier attempts were based on chromosomes with trip delimiters and needed a repair procedure to get feasible children after each crossover. Such procedures are known to weaken the genetic transmission of information from parents to children. This paper proposes a GA without trip delimiters, hybridized with a local search procedure. At any time, a chromosome can be converted into an optimal VRP solution (subject to chromosome sequence), thanks to a special splitting procedure. This design choice avoids repair procedures and enables the use of classical crossovers like OX. The resulting algorithm is flexible, relatively simple, and very effective when applied to two sets of standard benchmark instances ranging from 50 to 483 customers.     

Benchmarking hybrid algorithms for distributed constraint optimisation games

In this paper, we consider algorithms for distributed constraint optimisation problems (DCOPs). Using a potential game characterisation of DCOPs, we decompose eight DCOP algorithms, taken from the game theory and computer science literatures, into their salient components. We then use these components to construct three novel hybrid algorithms. Finally, we empirical evaluate all eleven algorithms, in terms of solution quality, timeliness and communication resources used, in a series of graph colouring experiments. Our experimental results show the existence of several performance trade-offs (such as quick convergence to a solution, but with a cost of high communication needs), which may be exploited by a system designer to tailor a DCOP algorithm to suit their mix of requirements.     

An incremental genetic algorithm approach to multiprocessor scheduling

We have developed a genetic algorithm (GA) approach to the problem of task scheduling for multiprocessor systems. Our approach requires minimal problem specific information and no problem specific operators or repair mechanisms. Key features of our system include a flexible, adaptive problem representation and an incremental fitness function. Comparison with traditional scheduling methods indicates that the GA is competitive in terms of solution quality if it has sufficient resources to perform its search. Studies in a nonstationary environment show the GA is able to automatically adapt to changing targets.     

基于自适应邻域模拟退火算法的非合作对策求解

对有多个Nash平衡点的非合作n人有限对策问题进行了研究。首先构造了其非合作n人有限对策的数学规划模型,证明了此模型的解与对策问题的解的等价性;然后提出了求解此类问题的一种自适应邻域模拟退火算法,基于此算法,在不减少问题解的条件下,解决了多解的非合作n人对策问题。通过数值实验说明了此算法的收敛性及稳定性;通过与粒子群算法、免疫粒子群算法、传统模拟退火算法的比较,说明了本文算法的优越性。     

Multi-objective optimization of stochastic disassembly line balancing with station paralleling

One of the major activities performed in product recovery is disassembly. Disassembly line is the most suitable setting to disassemble a product. Therefore, designing and balancing efficient disassembly systems are important to optimize the product recovery process. In this study, we deal with multi-objective optimization of a stochastic disassembly line balancing problem (DLBP) with station paralleling and propose a new genetic algorithm (GA) for solving this multi-objective optimization problem. The line balance and design costs objectives are simultaneously optimized by using an AND/OR Graph (AOG) of the product. The proposed GA is designed to generate Pareto-optimal solutions considering two different fitness evaluation approaches, repair algorithms and a diversification strategy. It is tested on 96 test problems that were generated using the benchmark problem generation scheme for problems defined on AOG as developed in literature. In addition, to validate the performance of the algorithm, a goal programming approach and a heuristic approach are presented and their results are compared with those obtained by using GA. Computational results show that GA can be considered as an effective and efficient solution algorithm for solving stochastic DLBP with station paralleling in terms of the solution quality and CPU time.     

Optimizing capacity allocation in semiconductor manufacturing photolithography area – Case study: Robert Bosch

In this paper, we advance the state of the art for capacity allocation and scheduling models in a semiconductor manufacturing front-end fab (SMFF). In SMFF, a photolithography process is typically considered as a bottleneck resource. Since SMFF operational planning is highly complex (re-entrant flows, high number of jobs, etc.), there is only limited research on assignment and scheduling models and their effectiveness in a photolitography toolset. We address this gap by: (1) proposing a new mixed integer linear programming (MILP) model for capacity allocation problem in a photolithography area (CAPPA) with maximum machine loads minimized, subject to machine process capability, machine dedication and maximum reticles sharing constraints, (2) solving the model using CPLEX and proofing its complexity, and (3) presenting an improved genetic algorithm (GA) named improved reference group GA (IRGGA) biased to solve CAPPA efficiently by improving the generation of the initial population. We further provide different experiments using real data sets extracted from a Bosch fab in Germany to analyze both proposed algorithm efficiency and solution sensitivity against changes in different conditional parameters.     

Extending the effectiveness of simulation-based DSS through genetic algorithms

Many real life ill-structured problems involve high uncertainty and complexity preventing application of analytical optimization techniques in building effective decision support systems (DSS). These systems may employ simulation method and search for a “good” solution through “what-if” analysis. However, this method is very time consuming and often overlooks the consideration of many promising alternative solutions. A genetic algorithm (GA) automates the search for “good” solutions by finding near-optimal solutions and increases effectiveness of DSS. This paper introduces a hybrid method based on the combination of Monte-Carlo simulation and genetic algorithms. The combined method is illustrated through application to the marketing mix problem to improve the process for searching and evaluating alternatives for decisional support. The paper compares two methods: MC and MC+GA. It also discusses ways for dealing with crisp and soft constraints contained in the example problem. A business game environment is chosen for experiments. The results of the experiments show that the GA-based approach outperforms human “what-if” method in terms of effectiveness and efficiency.     

Using differential evolution for fine tuning naïve Bayesian classifiers and its application for text classification

The Naive Bayes (NB) learning algorithm is simple and effective in many domains including text classification. However, its performance depends on the accuracy of the estimated conditional probability terms. Sometimes these terms are hard to be accurately estimated especially when the training data is scarce. This work transforms the probability estimation problem into an optimization problem, and exploits three metaheuristic approaches to solve it. These approaches are Genetic Algorithms (GA), Simulated Annealing (SA), and Differential Evolution (DE). We also propose a novel DE algorithm that uses multi-parent mutation and crossover operations (MPDE) and three different methods to select the final solution. We create an initial population by manipulating the solution generated by a method used for fine tuning the NB. We evaluate the proposed methods by using their resulted solutions to build NB classifiers and compare their results with the results of obtained from classical NB and Fine-Tuning Naïve Bayesian (FTNB) algorithm, using 53 UCI benchmark data sets. We name these obtained classifiers NBGA, NBSA, NBDE, and NB-MPDE respectively. We also evaluate the performance NB-MPDE for text-classification using 18 text-classification data sets, and compare its results with the results of obtained from FTNB, BNB, and MNB. The experimental results show that using DE in general and the proposed MPDE algorithm in particular are more convenient for fine-tuning NB than all other methods, including the other two metaheuristic methods (GA, and SA). They also indicate that NB-MPDE achieves superiority over classical NB, FTNB, NBDE, NBGA, NBSA, MNB, and BNB.     

Avoiding game‐tree pathology in 2‐player adversarial search

Adversarial search, or game‐tree search, is a technique for analyzing an adversarial game to determine what moves a player should make in order to win a game. Until recently, lookahead pathology (in which deeper game‐tree search results in worse play) has been thought to be quite rare. We provide an analysis that shows that every game should have some sections that are locally pathological, assuming that both players can potentially win the game. We also modify the minimax algorithm to recognize local pathologies in arbitrary games and cut off search accordingly (shallower search is more effective than deeper search when local pathologies occur). We show experimentally that our modified search procedure avoids local pathologies and consequently provides improved performance, in terms of decision accuracy, when compared with the minimax algorithm. In addition, we provide an experimental evaluation on the African game of Kalah, which shows the improved performances of our suggested error‐minimizing minimax algorithm when there is a large degree of pathology.     

Optimizing Polynomial-Time Solutions to a Network Weighted Vertex Cover Game

Weighted vertex cover (WVC) is one of the most important combinatorial optimization problems. In this paper, we provide a new game optimization to achieve efficiency and time of solutions for the WVC problem of weighted networks. We first model the WVC problem as a general game on weighted networks. Under the framework of a game, we newly define several cover states to describe the WVC problem. Moreover, we reveal the relationship among these cover states of the weighted network and the strict Nash equilibriums (SNEs) of the game. Then, we propose a game-based asynchronous algorithm (GAA), which can theoretically guarantee that all cover states of vertices converging in an SNE with polynomial time. Subsequently, we improve the GAA by adding 2-hop and 3-hop adjustment mechanisms, termed the improved game-based asynchronous algorithm (IGAA), in which we prove that it can obtain a better solution to the WVC problem than using a the GAA. Finally, numerical simulations demonstrate that the proposed IGAA can obtain a better approximate solution in promising computation time compared with the existing representative algorithms.      

基于改进遗传与模拟退火融合的RISP软硬件划分

软硬件划分是可重构指令集处理器在软硬件协同设计中的关键问题,通过对比遗传算法和经典模拟退火算法的优缺点,提出改进遗传算法的适应度函数,同时将Tsallis接受准则引入到经典模拟退火当中;其思路是用遗传算法的结果来制约模拟退火算法产生的随机状态,然后由模拟退火的接受准则以及产生的随机状态函数对遗传算法的种群进行更新,从而找到全局近似最优解;实验结果证明,改进算法与单一遗传算法以及经典模拟退火算法相比,其收敛速度和适应度更好,找到全局近似最优解的概率更大。     

An improved hybrid particle swarm optimization algorithm for fuzzy p-hub center problem

The p-hub center problem is useful for the delivery of perishable and time-sensitive system such as express mail service and emergency service. In this paper, we propose a new fuzzy p-hub center problem, in which the travel times are uncertain and characterized by normal fuzzy vectors. The objective of our model is to maximize the credibility of fuzzy travel times not exceeding a predetermined acceptable efficient time point along all paths on a network. Since the proposed hub location problem is too complex to apply conventional optimization algorithms, we adapt an approximation approach (AA) to discretize fuzzy travel times and reformulate the original problem as a mixed-integer programming problem subject to logic constraints. After that, we take advantage of the structural characteristics to develop a parametric decomposition method to divide the approximate p-hub center problem into two mixed-integer programming subproblems. Finally, we design an improved hybrid particle swarm optimization (PSO) algorithm by combining PSO with genetic operators and local search (LS) to update and improve particles for the subproblems. We also evaluate the improved hybrid PSO algorithm against other two solution methods, genetic algorithm (GA) and PSO without LS components. Using a simulated data set of 10 nodes, the computational results show that the improved hybrid PSO algorithm achieves the better performance than GA and PSO without LS in terms of runtime and solution quality.     

拉丁超立方体抽样遗传算法求解图的二划分问题

图的二划分问题是一个典型的NP-hard组合优化问题, 在许多领域都有重要应用. 近年来, 传统遗传算法等各种智能优化方法被引入到该问题的求解中来, 但效果不理想. 基于理想浓度模型的机理分析, 利用拉丁超立方体抽样的理论和方法, 对遗传算法中的交叉操作进行了重新设计, 并在分析图二划分问题特点的基础上, 结合局部搜索策略, 给出了一个解决图二划分问题的新的遗传算法, 称之为拉丁超立方体抽样遗传算法. 通过将该算法与简单遗传算法和佳点集遗传算法进行求解图二划分问题的仿真模拟比较, 可以看出新的算法提高了求解的质量、速度和精度.