Multi-objective volleyball premier league algorithm

This paper proposes a novel optimization algorithm called the Multi-Objective Volleyball Premier League (MOVPL) algorithm for solving global optimization problems with multiple objective functions. The algorithm is inspired by the teams competing in a volleyball premier league. The strong point of this study lies in extending the multi-objective version of the Volleyball Premier League algorithm (VPL), which is recently used in such scientific researches, with incorporating the well-known approaches including archive set and leader selection strategy to obtain optimal solutions for a given problem with multiple contradicted objectives. To analyze the performance of the algorithm, ten multi-objective benchmark problems with complex objectives are solved and compared with two well-known multiobjective algorithms, namely Multi-Objective Particle Swarm Optimization (MOPSO) and Multi-Objective Evolutionary Algorithm Based on Decomposition (MOEA/D). Computational experiments highlight that the MOVPL outperforms the two state-of-the-art algorithms on multi-objective benchmark problems. In addition, the MOVPL algorithm has provided promising results on well-known engineering design optimization problems

A multi objective volleyball premier league algorithm for green scheduling identical parallel machines with splitting jobs

Parallel machine scheduling is one of the most common studied problems in recent years, however, this classic optimization problem has to achieve two conflicting objectives, i.e. minimizing the total tardiness and minimizing the total wastes, if the scheduling is done in the context of plastic injection industry where jobs are splitting and molds are important constraints. This paper proposes a mathematical model for scheduling parallel machines with splitting jobs and resource constraints. Two minimization objectives - the total tardiness and the number of waste - are considered, simultaneously. The obtained model is a bi-objective integer linear programming model that is shown to be of NP-hard class optimization problems. In this paper, a novel Multi-Objective Volleyball Premier League (MOVPL) algorithm is presented for solving the aforementioned problem. This algorithm uses the crowding distance concept used in NSGA-II as an extension of the Volleyball Premier League (VPL) that we recently introduced. Furthermore, the results are compared with six multi-objective metaheuristic algorithms of MOPSO, NSGA-II, MOGWO, MOALO, MOEA/D, and SPEA2. Using five standard metrics and ten test problems, the performance of the Pareto-based algorithms was investigated. The results demonstrate that in general, the proposed algorithm has supremacy than the other four algorithms

A multi objective volleyball premier league algorithm for green scheduling identical parallel machines with splitting jobs

Parallel machine scheduling is one of the most common studied problems in recent years, however, this classic optimization problem has to achieve two conflicting objectives, i.e. minimizing the total tardiness and minimizing the total wastes, if the scheduling is done in the context of plastic injection industry where jobs are splitting and molds are important constraints. This paper proposes a mathematical model for scheduling parallel machines with splitting jobs and resource constraints. Two minimization objectives - the total tardiness and the number of waste - are considered, simultaneously. The obtained model is a bi-objective integer linear programming model that is shown to be of NP-hard class optimization problems. In this paper, a novel Multi-Objective Volleyball Premier League (MOVPL) algorithm is presented for solving the aforementioned problem. This algorithm uses the crowding distance concept used in NSGA-II as an extension of the Volleyball Premier League (VPL) that we recently introduced. Furthermore, the results are compared with six multi-objective metaheuristic algorithms of MOPSO, NSGA-II, MOGWO, MOALO, MOEA/D, and SPEA2. Using five standard metrics and ten test problems, the performance of the Pareto-based algorithms was investigated. The results demonstrate that in general, the proposed algorithm has supremacy than the other four algorithms

Proceedings of Mathsport international 2017 conference

Proceedings of MathSport International 2017 Conference, held in the Botanical Garden of the University of Padua, June 26-28, 2017. MathSport International organizes biennial conferences dedicated to all topics where mathematics and sport meet. Topics include: performance measures, optimization of sports performance, statistics and probability models, mathematical and physical models in sports, competitive strategies, statistics and probability match outcome models, optimal tournament design and scheduling, decision support systems, analysis of rules and adjudication, econometrics in sport, analysis of sporting technologies, financial valuation in sport, e-sports (gaming), betting and sports

The validity, reliability and sensitivity of utilising a wearable GPS based IMU to determine goalkeeper specific training demands

Despite the plethora of football focused literature, there is still very little known about the training practices of the goalkeeper (GK). The development of portable Global Positioning System (GPS) and Inertial Measurement Unit (IMU) devices ensured physical activities can be accurately measured within the training environment. The integration of inertial sensor fusion algorithms has allowed the IMU the ability to also detect non-locomotive activities that are specific to a sport. This technology is shown to be a valid method of analysis for the demands of an outfield football player, however, similar research into the GK position is required. Thus, the aim of this study was to investigate the validity, reliability and sensitivity of utilizing a wearable GPS based IMU to determine goalkeeper specific training demands. A total of 123 event variables were recorded via OptimEye G5 GPS units over 14 sessions from 6 professional GKs during the 2017-2018 Scottish Premiership season. GPS data was collected as part of normal daily monitoring and compared against corresponding computerized notational analysis of the same training sessions. Event variables were split into specific IMU events by a GK specific algorithm: Total Dives (TD), Dives Right (DvR), Dives Left (DvL), Dive Returns (DR) and Jumps. The intra-unit variation was derived from reproducibility of trends within the difference between GPS and corresponding Video Analysis (VA) counts. Unit sensitivity was investigated according to the relationship between average DR times and countermovement jump (CMJ) and ballistic press-up (BP) results which corresponded to lower and upper body velocity at peak power (m/s) respectively. There was no significant difference (p0.05). Bland Altman 95% Limits of Agreement (LOA) show minimal variation for TD (-3.6 to 5.6), DvL (-1.75 to 4.04) and DvR (-3.38 to 3.13). However, DR (-13 to 12.6) and Jumps (-8.8 to 15.7) showed much wider LOA and variation from VA counts. Intra-unit variability was significantly different across all metrics with GPS units, over-estimating movement event counts compared to VA counts. Inter-unit sensitivity suggested that CMJ and lower body velocity at peak power (m/s) performance had the greatest correlation (r=0.992) with average DR times compared to BP and upper body velocity at peak power (r=0.684) and CMJ + BP combined (r=0.603). Based on these findings, the sensitivity of the OptimEye G5 GPS to count GK specific events was almost perfect (r = 903), however, the specificity of the IMU algorithm to distinguish the different movements was questionable. Jumps were significantly over- estimated, and in the meantime, we would suggest using video footage to compliment GPS data for accurate longitudinal analysis. This study provided novel information regarding the DR action, of which the lower body muscular profile plays the dominant part in. Although there are limitations within this study, these investigations should only act as the first step in understanding if the GPS coupled IMU has a place in accurately determining the training demands of a goalkeeper

Determining, scoring and presenting successful performance in professional rugby league

Performance indicators allow for the objective quantification of performance (Vogelbein, Nopp & Hokelmann, 2014). However, limited PI research for professional rugby league exists, with just one paper published (Woods, Sinclair and Robertson, 2017) although this was conducted on teams from the Australian elite competition, the NRL, with no similar attempts for Europe’s Super League competition. Therefore, this thesis aimed to identify robust indicators of success for professional rugby league teams in super league, which would subsequently allow performances to be scored and assessed graphically through performance profiles. Data from all 27 rounds of the 2012, 2013 and 2014 European Super League seasons were collected by Opta, amounting to 567 matches. Data for 45 action variables was extracted from spreadsheets using Visual Basic for Applications in Microsoft Excel (Excel, v2013, Microsoft Inc., Redmond, USA). To enable clear comparisons between winning and losing teams, draws (n=22) were excluded. Study 1 assessed twenty-four relative variables (home value minus away) using backwards logistic (match outcome) and linear (points difference) regression models alongside exhaustive Chi-Square Automatic Interaction Detection (CHAID) decision trees to identify performance indicators (PIs) and key performance indicators (KPIs). However, some variables which were thought to be important (as identified by previous literature) were removed from the analysis as they did not contribute to the model’s predictive ability as much as others thus calling into question the appropriateness of stepwise methods. Furthermore, unusual results were evident which lead to the conclusion that a suitable dimension reduction technique could be more appropriate to analyse large datasets with multiple variables that could be related to each other. Study 2 utilised principal component analysis to reduce 45 action variables into 10 orthogonal principle components. These components were analysed using backwards and enter methods in logistic and linear regression models alongside CHAID decision trees. This method provided a relevant guide on how teams could improve their performance by improving a collection of variables as opposed to traditional methods which described individual variables. Furthermore, the use of stepwise methods was argued to be less appropriate for sporting performances as some principal components that could relate to success may be removed. Results from both regression models indicated large variations on confidence intervals for beta coefficients and odds ratios, suggesting that the variation of a set of values are more representative of the data analysed, when assessing multiple teams. Therefore, idiographic assessments of performances were suggested to provide relevant information for practitioners, which can be lost through traditional nomothetic approaches, as evidenced in this study. Study 3 utilised the principle component scores to create idiographic performance profiles, according to match venue and match closeness. In addition, a case study was produced assessing two teams’ previous performances, prior to an upcoming game, providing a practical example of how practitioners could utilise this information in their respective environments. Although large variations were evident on profiles, it was suggested that team performances may never stabilise due to the unpredictability of complex sports involving multiple players like rugby league. However it was clear that idiographic profiles provided meaningful and informative assessments of performance which were arguably more relevant for practitioners compared to traditional nomothetic methods. Overall, this thesis facilitated a greater understanding of how rugby league teams perform in Super League, through the use of practical and relevant methodologies that can be utilised by practitioners and coaches who are constantly striving to improve sporting performance. Future research must consider the ‘theory-practice’ gap identified by McKenzie and Cushion (2013) in order to provide simple and relevant answers that practitioners require, which seems to be a principle that has remained elusive thus far

A Multi–Objective Gaining–Sharing Knowledge-Based Optimization Algorithm for Solving Engineering Problems

Metaheuristics in recent years has proven its effectiveness; however, robust algorithms that can solve real-world problems are always needed. In this paper, we suggest the first extended version of the recently introduced gaining–sharing knowledge optimization (GSK) algorithm, named multiobjective gaining–sharing knowledge optimization (MOGSK), to deal with multiobjective optimization problems (MOPs). MOGSK employs an external archive population to store the nondominated solutions generated thus far, with the aim of guiding the solutions during the exploration process. Furthermore, fast nondominated sorting with crowding distance was incorporated to sustain the diversity of the solutions and ensure the convergence towards the Pareto optimal set, while the e- dominance relation was used to update the archive population solutions. e-dominance helps provide a good boost to diversity, coverage, and convergence overall. The validation of the proposed MOGSK was conducted using five biobjective (ZDT) and seven three-objective test functions (DTLZ) problems, along with the recently introduced CEC 2021, with fifty-five test problems in total, including power electronics, process design and synthesis, mechanical design, chemical engineering, and power system optimization. The proposed MOGSK was compared with seven existing optimization algorithms, including MOEAD, eMOEA, MOPSO, NSGAII, SPEA2, KnEA, and GrEA. The experimental findings show the good behavior of our proposed MOGSK against the comparative algorithms in particular real-world optimization problems

Designing Sports Player’s Valuation Indices (Case Study: Volleyball Players)

The purpose of the present article is to design indicators and variables that represent the value of volleyball players. This research method is applied, which was done in a quantitative and qualitative way. The research tool was a semi-structured interview with experts in the field of player valuation. In this research, the statistical population included all the experts and specialists in human resources and financial management issues in sports, and also volleyball experts. The sample size included a number of volleyball sports experts who expressed their ideas to determine the variables. A total of 60 variables were extracted, of which 40 are quantitative indicators and 20 are qualitative indicators. These indicators are not only effective in the selection of players, but can also determine the price and final value of the players