Two preprocessing techniques for mixed integer quadratic programs with non-convex objective funct... more Two preprocessing techniques for mixed integer quadratic programs with non-convex objective functions are presented. The first is a convexification scheme and can be applied to problems were the continuous part of the Hessian is positive semidefinite. The second technique aims to reduce the size of the underestimating problems solved by branch-and-bound algorithms and can be applied to problems were the continuous part of the Hessian is singular. Numerical results are presented showing the effect of the preprocessing techniques.
In order to facilitate the flow of traffic in Gauteng Provence, South Africa, during peak hours t... more In order to facilitate the flow of traffic in Gauteng Provence, South Africa, during peak hours the BRT is investigating the effect of allowing minibus taxis to use the lanes presently reserved for buses either throughout the day or just during peak hours. This work represents a continuation of the work commenced at the MISG 2014 meeting where it was shown that the traffic flow through the system was improved by allowing minibus taxis to switch across to the bus lane providing the density of the traffic exceeded a critical value determined by the flow characteristics of the lanes. In the present work we investigate further the disruptions that are likely to be caused by the movement of taxis into the bus lane. Additionally we present an economic pricing model that may be used to encourage commuters to travel by bus. ∗Mathematics Department, University of Western Australia, Crawley, WA 6009, Australia email: neville.fowkes@uwa.edu.au †Mathematics and Statistics, Murdoch University, A...
Travel and Tourism as a sector has been resilient despite the diverse climatic conditions that af... more Travel and Tourism as a sector has been resilient despite the diverse climatic conditions that affect tourists. Climatic conditions prevailing in the tourist destinations determine the number of tourists visiting those destinations. In 1985, Mieczkowski developed the Tourism Climate Index (TCI) to estimate the impact of climatic conditions on tourism. A mathematical model for Tourism Climate Index South African (TCISA) is proposed. Five climatic variables such as maximum temperature, minimum temperature, precipitation, cloud cover and wind speed are used as the input to the index to estimate the values of TCISA. The model for TCISA is validated using the climate data for the Durban region. Results show Durban as one of the popular tourist destinations due to its climate suitability for various tourist activities. This is comparable with the data from TripAdvisor. This study recommends the validation of the mathematical model by using more data points and climatic variables.
In this paper, we have dealt with the solution of a two-stage stochastic programming problem usin... more In this paper, we have dealt with the solution of a two-stage stochastic programming problem using ADMM. We have formulated the problem into a deterministic three-block separable optimization problem, and then we applied ADMM to solve it. We have established the theoretical convergence of ADMM to the optimal solution based on the concept of lower semicontinuity and the Kurdyka-Lojasiewicz property. We have compared ADMM with Progressive Hedging in terms of performance criteria using five benchmark problems from the literature. The comparison shows that ADMM outperforms Progressive Hedging.
PurposeThe purpose of this paper is to consider the problem of university lecture timetabling. Ti... more PurposeThe purpose of this paper is to consider the problem of university lecture timetabling. Timetabling deals with the problem of placing certain resources into a limited number of time slots, subject to given constraints, in order to satisfy a set of stated objectives to the highest possible extent. It is a well‐known and established NP‐hard problem. University timetabling is a major administrative activity especially in the third world universities. Solving the problem requires dynamic heuristics with predictable performance especially as the number of courses increases without corresponding increase in needed resources.Design/methodology/approachA genetic algorithm metaheuristic is designed to handle a real‐life case study. Given the present structure of the case study, a modular approach to the design of the timetable schedules is adopted. The approach considers timetable in a bottom‐up fashion at the various levels of department, faculty or entire university. Simulation stud...
Asia-Pacific Journal of Operational Research, 2012
This paper presents motivations and algorithmic details of some generalized controlled random sea... more This paper presents motivations and algorithmic details of some generalized controlled random search (CRS) algorithms for global optimization. It also carries out an extensive numerical study of the generalized CRS algorithms to demonstrate their superiorities over their original counterparts. The numerical study is carried out using a set of 50 test problems many of which are inspired by practical applications. Numerical experiments indicate that the generalized algorithms are considerably better than the previous versions. The algorithms are also compared with the DIRECT algorithm (Jones et al., 1993). The comparison shows that the generalized CRS algorithms are better than the DIRECT algorithm in high dimensional problems. Thus, they offer a reasonable alternative to many currently available stochastic algorithms, especially for problems requiring "direct search type" methods.
Two preprocessing techniques for mixed integer quadratic programs with non-convex objective funct... more Two preprocessing techniques for mixed integer quadratic programs with non-convex objective functions are presented. The first is a convexification scheme and can be applied to problems were the continuous part of the Hessian is positive semidefinite. The second technique aims to reduce the size of the underestimating problems solved by branch-and-bound algorithms and can be applied to problems were the continuous part of the Hessian is singular. Numerical results are presented showing the effect of the preprocessing techniques.
In order to facilitate the flow of traffic in Gauteng Provence, South Africa, during peak hours t... more In order to facilitate the flow of traffic in Gauteng Provence, South Africa, during peak hours the BRT is investigating the effect of allowing minibus taxis to use the lanes presently reserved for buses either throughout the day or just during peak hours. This work represents a continuation of the work commenced at the MISG 2014 meeting where it was shown that the traffic flow through the system was improved by allowing minibus taxis to switch across to the bus lane providing the density of the traffic exceeded a critical value determined by the flow characteristics of the lanes. In the present work we investigate further the disruptions that are likely to be caused by the movement of taxis into the bus lane. Additionally we present an economic pricing model that may be used to encourage commuters to travel by bus. ∗Mathematics Department, University of Western Australia, Crawley, WA 6009, Australia email: neville.fowkes@uwa.edu.au †Mathematics and Statistics, Murdoch University, A...
Travel and Tourism as a sector has been resilient despite the diverse climatic conditions that af... more Travel and Tourism as a sector has been resilient despite the diverse climatic conditions that affect tourists. Climatic conditions prevailing in the tourist destinations determine the number of tourists visiting those destinations. In 1985, Mieczkowski developed the Tourism Climate Index (TCI) to estimate the impact of climatic conditions on tourism. A mathematical model for Tourism Climate Index South African (TCISA) is proposed. Five climatic variables such as maximum temperature, minimum temperature, precipitation, cloud cover and wind speed are used as the input to the index to estimate the values of TCISA. The model for TCISA is validated using the climate data for the Durban region. Results show Durban as one of the popular tourist destinations due to its climate suitability for various tourist activities. This is comparable with the data from TripAdvisor. This study recommends the validation of the mathematical model by using more data points and climatic variables.
In this paper, we have dealt with the solution of a two-stage stochastic programming problem usin... more In this paper, we have dealt with the solution of a two-stage stochastic programming problem using ADMM. We have formulated the problem into a deterministic three-block separable optimization problem, and then we applied ADMM to solve it. We have established the theoretical convergence of ADMM to the optimal solution based on the concept of lower semicontinuity and the Kurdyka-Lojasiewicz property. We have compared ADMM with Progressive Hedging in terms of performance criteria using five benchmark problems from the literature. The comparison shows that ADMM outperforms Progressive Hedging.
PurposeThe purpose of this paper is to consider the problem of university lecture timetabling. Ti... more PurposeThe purpose of this paper is to consider the problem of university lecture timetabling. Timetabling deals with the problem of placing certain resources into a limited number of time slots, subject to given constraints, in order to satisfy a set of stated objectives to the highest possible extent. It is a well‐known and established NP‐hard problem. University timetabling is a major administrative activity especially in the third world universities. Solving the problem requires dynamic heuristics with predictable performance especially as the number of courses increases without corresponding increase in needed resources.Design/methodology/approachA genetic algorithm metaheuristic is designed to handle a real‐life case study. Given the present structure of the case study, a modular approach to the design of the timetable schedules is adopted. The approach considers timetable in a bottom‐up fashion at the various levels of department, faculty or entire university. Simulation stud...
Asia-Pacific Journal of Operational Research, 2012
This paper presents motivations and algorithmic details of some generalized controlled random sea... more This paper presents motivations and algorithmic details of some generalized controlled random search (CRS) algorithms for global optimization. It also carries out an extensive numerical study of the generalized CRS algorithms to demonstrate their superiorities over their original counterparts. The numerical study is carried out using a set of 50 test problems many of which are inspired by practical applications. Numerical experiments indicate that the generalized algorithms are considerably better than the previous versions. The algorithms are also compared with the DIRECT algorithm (Jones et al., 1993). The comparison shows that the generalized CRS algorithms are better than the DIRECT algorithm in high dimensional problems. Thus, they offer a reasonable alternative to many currently available stochastic algorithms, especially for problems requiring "direct search type" methods.
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