Heuristic algorithm for computing reversal distance with multigene families via binary integer programming

Hannenhalli and Pevzner developed the first polynomial-time algorithm for the combinatorial problem of sorting of signed genomic data. Their algorithm solves the minimum number of reversals required for rearranging a genome to another when gene duplication is nonexisting. In this paper, we show how to extend the Hannenhalli-Pevzner approach to genomes with multigene families. We propose a new heuristic algorithm to compute the reversal distance between two genomes with multigene families via the concept of binary integer programming without removing gene duplicates. The experimental results on simulated and real biological data demonstrate that the proposed algorithm is able to find the reversal distance accurately. ©2005 IEEE

An Interactive Method of Linear Mixed Integer Multicriteria Optimization

The paper describes a learning-oriented interactive method for solving linear mixed integer problems of multicriteria optimization. The method increases the possibilities of the decision maker (DM) to describe his/her local preferences and at the same time it overcomes some computational difficulties, especially in problems of large dimension. The method is realized in an experimental decision support system for finding the solution of linear mixed integer multicriteria optimization problems.

Nonparametric tests of collectively rational consumption behavior: an integer programming procedure

We present an IP-based nonparametric (revealed preference) testing procedure for rational consumption behavior in terms of general collective models, which include consumption externalities and public consumption. An empirical application to data drawn from the Russia Longitudinal Monitoring Survey (RLMS) demonstrates the practical usefulness of the procedure. Finally, we present extensions of the testing procedure to evaluate the goodness-of-…t of the collective model subject to testing, and to quantify and improve the power of the corresponding collective rationality tests.

Allocating reforestation areas for sediment flow minimization: an integer programming formulation and a heuristic solution method

Policy and decision makers dealing with environmental conservation and land use planning often require identifying potential sites for contributing to minimize sediment flow reaching riverbeds. This is the case of reforestation initiatives, which can have sediment flow minimization among their objectives. This paper proposes an Integer Programming (IP) formulation and a Heuristic solution method for selecting a predefined number of locations to be reforested in order to minimize sediment load at a given outlet in a watershed. Although the core structure of both methods can be applied for different sorts of flow, the formulations are targeted to minimization of sediment delivery. The proposed approaches make use of a Single Flow Direction (SFD) raster map covering the watershed in order to construct a tree structure so that the outlet cell corresponds to the root node in the tree. The results obtained with both approaches are in agreement with expert assessments of erosion levels, slopes and distances to the riverbeds, which in turn allows concluding that this approach is suitable for minimizing sediment flow. Since the results obtained with the IP formulation are the same as the ones obtained with the Heuristic approach, an optimality proof is included in the present work. Taking into consideration that the heuristic requires much less computation time, this solution method is more suitable to be applied in large sized problems.

On the optimal capacity expansion of electric power systems

The analysis of investment in the electric power has been the subject of intensive research for many years. The efficient generation and distribution of electrical energy is a difficult task involving the operation of a complex network of facilities, often located over very large geographical regions. Electric power utilities have made use of an enormous range of mathematical models. Some models address time spans which last for a fraction of a second, such as those that deal with lightning strikes on transmission lines while at the other end of the scale there are models which address time horizons consisting of ten or twenty years; these usually involve long range planning issues. This thesis addresses the optimal long term capacity expansion of an interconnected power system. The aim of this study has been to derive a new, long term planning model which recognises the regional differences which exist for energy demand and which are present in the construction and operation of power plant and transmission line equipment. Perhaps the most innovative feature of the new model is the direct inclusion of regional energy demand curves in the nonlinear form. This results in a nonlinear capacity expansion model. After review of the relevant literature, the thesis first develops a model for the optimal operation of a power grid. This model directly incorporates regional demand curves. The model is a nonlinear programming problem containing both integer and continuous variables. A solution algorithm is developed which is based upon a resource decomposition scheme that separates the integer variables from the continuous ones. The decompostion of the operating problem leads to an interactive scheme which employs a mixed integer programming problem, known as the master, to generate trial operating configurations. The optimum operating conditions of each trial configuration is found using a smooth nonlinear programming model. The dual vector recovered from this model is subsequently used by the master to generate the next trial configuration. The solution algorithm progresses until lower and upper bounds converge. A range of numerical experiments are conducted and these experiments are included in the discussion. Using the operating model as a basis, a regional capacity expansion model is then developed. It determines the type, location and capacity of additional power plants and transmission lines, which are required to meet predicted electicity demands. A generalised resource decompostion scheme, similar to that used to solve the operating problem, is employed. The solution algorithm is used to solve a range of test problems and the results of these numerical experiments are reported. Finally, the expansion problem is applied to the Queensland electricity grid in Australia.

On the optimal capacity expansion of electric power systems

The analysis of investment in the electric power has been the subject of intensive research for many years. The efficient generation and distribution of electrical energy is a difficult task involving the operation of a complex network of facilities, often located over very large geographical regions. Electric power utilities have made use of an enormous range of mathematical models. Some models address time spans which last for a fraction of a second, such as those that deal with lightning strikes on transmission lines while at the other end of the scale there are models which address time horizons consisting of ten or twenty years; these usually involve long range planning issues. This thesis addresses the optimal long term capacity expansion of an interconnected power system. The aim of this study has been to derive a new, long term planning model which recognises the regional differences which exist for energy demand and which are present in the construction and operation of power plant and transmission line equipment. Perhaps the most innovative feature of the new model is the direct inclusion of regional energy demand curves in the nonlinear form. This results in a nonlinear capacity expansion model. After review of the relevant literature, the thesis first develops a model for the optimal operation of a power grid. This model directly incorporates regional demand curves. The model is a nonlinear programming problem containing both integer and continuous variables. A solution algorithm is developed which is based upon a resource decomposition scheme that separates the integer variables from the continuous ones. The decompostion of the operating problem leads to an interactive scheme which employs a mixed integer programming problem, known as the master, to generate trial operating configurations. The optimum operating conditions of each trial configuration is found using a smooth nonlinear programming model. The dual vector recovered from this model is subsequently used by the master to generate the next trial configuration. The solution algorithm progresses until lower and upper bounds converge. A range of numerical experiments are conducted and these experiments are included in the discussion. Using the operating model as a basis, a regional capacity expansion model is then developed. It determines the type, location and capacity of additional power plants and transmission lines, which are required to meet predicted electicity demands. A generalised resource decompostion scheme, similar to that used to solve the operating problem, is employed. The solution algorithm is used to solve a range of test problems and the results of these numerical experiments are reported. Finally, the expansion problem is applied to the Queensland electricity grid in Australia

A new approach to automatically producing schedules for cane railways

The scheduling of locomotive movements on cane railways has proven to be a very complex task. Various optimisation methods have been used over the years to try and produce an optimised schedule that eliminates or minimises bin supply delays to harvesters and the factory, while minimising the number of locomotives, locomotive shifts and cane bins, and also the cane age. This paper reports on a new attempt to develop an automatic scheduler using a mathematical model solved using mixed integer programming and constraint programming approaches and blocking parallel job shop scheduling fundamentals. The model solution has been explored using conventional constraint programming search techniques and found to produce a reasonable schedule for small-scale problems with up to nine harvesters. While more effort is required to complete the development of the full model with metaheuristic search techniques, the work completed to date gives confidence that the metaheuristic techniques will provide near optimal solutions in reasonable time.

Scheduling techniques to optimise rail operations

In Australia, railway systems play a vital role in transporting the sugarcane crop from farms to mills. The sugarcane transport system is very complex and uses daily schedules, consisting of a set of locomotives runs, to satisfy the requirements of the mill and harvesters. The total cost of sugarcane transport operations is very high; over 35% of the total cost of sugarcane production in Australia is incurred in cane transport. Efficient schedules for sugarcane transport can reduce the cost and limit the negative effects that this system can have on the raw sugar production system. There are several benefits to formulating the train scheduling problem as a blocking parallel-machine job shop scheduling (BPMJSS) problem, namely to prevent two trains passing in one section at the same time; to keep the train activities (operations) in sequence during each run (trip) by applying precedence constraints; to pass the trains on one section in the correct order (priorities of passing trains) by applying disjunctive constraints; and, to ease passing trains by solving rail conflicts by applying blocking constraints and Parallel Machine Scheduling. Therefore, the sugarcane rail operations are formulated as BPMJSS problem. A mixed integer programming and constraint programming approaches are used to describe the BPMJSS problem. The model is solved by the integration of constraint programming, mixed integer programming and search techniques. The optimality performance is tested by Optimization Programming Language (OPL) and CPLEX software on small and large size instances based on specific criteria. A real life problem is used to verify and validate the approach. Constructive heuristics and new metaheuristics including simulated annealing and tabu search are proposed to solve this complex and NP-hard scheduling problem and produce a more efficient scheduling system. Innovative hybrid and hyper metaheuristic techniques are developed and coded using C# language to improve the solutions quality and CPU time. Hybrid techniques depend on integrating heuristic and metaheuristic techniques consecutively, while hyper techniques are the complete integration between different metaheuristic techniques, heuristic techniques, or both.

A flexible optimisation model for the railway crew scheduling problem

Addressing the Crew Scheduling Problem (CSP) in transportation systems can be too complex to capture all details. The designed models usually ignore or simplify features which are difficult to formulate. This paper proposes an alternative formulation using a Mixed Integer Programming (MIP) approach to the problem. The optimisation model integrates the two phases of pairing generation and pairing optimisation by simultaneously sequencing trips into feasible duties and minimising total elapsed time of any duty. Crew scheduling constraints in which the crew have to return to their home depot at the end of the shift are included in the model. The flexibility of this model comes in the inclusion of the time interval of relief opportunities, allowing the crew to be relieved during a finite time interval. This will enhance the robustness of the schedule and provide a better representation of real-world conditions.

Integrated approach to optimize open-pit mine block sequencing

Critical stage in open-pit mining is to determine the optimal extraction sequence of blocks, which has significant impacts on mining profitability. In this paper, a more comprehensive block sequencing optimisation model is developed for the open-pit mines. In the model, material characteristics of blocks, grade control, excavator and block sequencing are investigated and integrated to maximise the short-term benefit of mining. Several case studies are modeled and solved by CPLEX MIP and CP engines. Numerical investigations are presented to illustrate and validate the proposed methodology.

An open pit multistage mine production scheduling model for drilling, blasting and excavating operations

This paper proposes a new multi-resource multi-stage scheduling problem for optimising the open-pit drilling, blasting and excavating operations under equipment capacity constraints. The flow process is analysed based on the real-life data from an Australian iron ore mine site. The objective of the model is to maximise the throughput and minimise the total idle times of equipment at each stage. The following comprehensive mining attributes and constraints have been considered: types of equipment; operating capacities of equipment; ready times of equipment; speeds of equipment; block-sequence-dependent movement times of equipment; equipment-assignment-dependent operation times of blocks; distances between each pair of blocks; due windows of blocks; material properties of blocks; swell factors of blocks; and slope requirements of blocks. It is formulated by mixed integer programming and solved by ILOG-CPLEX optimiser. The proposed model is validated with extensive computational experiments to improve mine production efficiency at the operational level. The model also provides an intelligent decision support tool to account for the availability and usage of equipment units for drilling, blasting and excavating stages.

A quay crane scheduling methodology for multimodal container terminals

This thesis develops an operational decision support tool for container terminal managements. The tool generates efficient schedules for shore cranes handling containers carried by mega container vessels.

New graph-based algorithms to efficiently solve large scale open pit mining optimisation problems

In the mining optimisation literature, most researchers focused on two strategic-level and tactical-level open-pit mine optimisation problems, which are respectively termed ultimate pit limit (UPIT) or constrained pit limit (CPIT). However, many researchers indicate that the substantial numbers of variables and constraints in real-world instances (e.g., with 50-1000 thousand blocks) make the CPIT’s mixed integer programming (MIP) model intractable for use. Thus, it becomes a considerable challenge to solve the large scale CPIT instances without relying on exact MIP optimiser as well as the complicated MIP relaxation/decomposition methods. To take this challenge, two new graph-based algorithms based on network flow graph and conjunctive graph theory are developed by taking advantage of problem properties. The performance of our proposed algorithms is validated by testing recent large scale benchmark UPIT and CPIT instances’ datasets of MineLib in 2013. In comparison to best known results from MineLib, it is shown that the proposed algorithms outperform other CPIT solution approaches existing in the literature. The proposed graph-based algorithms leads to a more competent mine scheduling optimisation expert system because the third-party MIP optimiser is no longer indispensable and random neighbourhood search is not necessary.

A new open-pit multi-stage mine production timetabling model for drilling, blasting and excavating operations

This paper proposes a new multi-resource multi-stage mine production timetabling problem for optimising the open-pit drilling, blasting and excavating operations under equipment capacity constraints. The flow process is analysed based on the real-life data from an Australian iron ore mine site. The objective of the model is to maximise the throughput and minimise the total idle times of equipment at each stage. The following comprehensive mining attributes and constraints are considered: types of equipment; operating capacities of equipment; ready times of equipment; speeds of equipment; block-sequence-dependent movement times; equipment-assignment-dependent operational times; etc. The model also provides the availability and usage of equipment units at multiple operational stages such as drilling, blasting and excavating stages. The problem is formulated by mixed integer programming and solved by ILOG-CPLEX optimiser. The proposed model is validated with extensive computational experiments to improve mine production efficiency at the operational level.