Multi-objective integer programming: An improved recursive algorithm

This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-Objective Integer Programming (MOIP) problem. We significantly improve the earlier recursive algorithm of \"Ozlen and Azizo\u{g}lu by using the set of already solved subproblems and their solutions to avoid solving a large number of IPs. A numerical example is presented to explain the workings of the algorithm, and we conduct a series of computational experiments to show the savings that can be obtained. As our experiments show, the improvement becomes more significant as the problems grow larger in terms of the number of objectives.Comment: 11 pages, 6 tables; v2: added more details and a computational stud

An optimisation approach for fuel treatment planning to break the connectivity of high-risk regions

Uncontrolled wildfires can lead to loss of life and property and destruction of natural resources. At the same time, fire plays a vital role in restoring ecological balance in many ecosystems. Fuel management, or treatment planning by way of planned burning, is an important tool used in many countries where fire is a major ecosystem process. In this paper, we propose an approach to reduce the spatial connectivity of fuel hazards while still considering the ecological fire requirements of the ecosystem. A mixed integer programming (MIP) model is formulated in such a way that it breaks the connectivity of high-risk regions as a means to reduce fuel hazards in the landscape. This multi-period model tracks the age of each vegetation type and determines the optimal time and locations to conduct fuel treatments. The minimum and maximum Tolerable Fire Intervals (TFI), which define the ages at which certain vegetation type can be treated for ecological reasons, are taken into account by the model. Examples from previous work that explicitly disconnect contiguous areas of high fuel load have often been limited to using single vegetation types implemented within rectangular grids. We significantly extend such work by including modelling multiple vegetation types implemented within a polygon-based network to achieve a more realistic representation of the landscape. An analysis of the proposed approach was conducted for a fuel treatment area comprising 711 treatment units in the Barwon-Otway district of Victoria, Australia. The solution of the proposed model can be obtained for 20-year fuel treatment planning within a reasonable computation time of eight hours

Fuel treatment planning: Fragmenting high fuel load areas while maintaining availability and connectivity of faunal habitat

Reducing the fuel load in fire-prone landscapes is aimed at mitigating the risk of catastrophic wildfires but there are ecological consequences. Maintaining habitat for fauna of both sufficient extent and connectivity while fragmenting areas of high fuel loads presents land managers with seemingly contrasting objectives. Faced with this dichotomy, we propose a Mixed Integer Programming (MIP) model that can optimally schedule fuel treatments to reduce fuel hazards by fragmenting high fuel load regions while considering critical ecological requirements over time and space. The model takes into account both the frequency of fire that vegetation can tolerate and the frequency of fire necessary for fire-dependent species. Our approach also ensures that suitable alternate habitat is available and accessible to fauna affected by a treated area. More importantly, to conserve fauna the model sets a minimum acceptable target for the connectivity of habitat at any time. These factors are all included in the formulation of a model that yields a multi-period spatially-explicit schedule for treatment planning. Our approach is then demonstrated in a series of computational experiments with hypothetical landscapes, a single vegetation type and a group of faunal species with the same habitat requirements. Our experiments show that it is possible to fragment areas of high fuel loads while ensuring sufficient connectivity of habitat over both space and time. Furthermore, it is demonstrated that the habitat connectivity constraint is more effective than neighbourhood habitat constraints. This is critical for the conservation of fauna and of special concern for vulnerable or endangered species

Rescheduling unrelated parallel machines with total flow time and total disruption cost criteria

In this paper, we consider a rescheduling problem where a set of jobs has already been assigned to unrelated parallel machines. When a disruption occurs on one of the machines, the affected jobs are rescheduled, considering the efficiency and the schedule deviation measures. The efficiency measure is the total flow time, and the schedule deviation measure is the total disruption cost caused by the differences between the initial and current schedules. We provide polynomial-time solution methods to the following hierarchical optimization problems: minimizing total disruption cost among the minimum total flow time schedules and minimizing total flow time among the minimum total disruption cost schedules. We propose exponentialtime algorithms to generate all efficient solutions and to minimize a specified function of the measures. Our extensive computational tests on large size problem instances have revealed that our optimization algorithm finds the best solution by generating only a small portion of all efficient solutions

A spatial decomposition based math-heuristic approach to the asset protection problem

This paper addresses the highly critical task of planning asset protection activities during uncontrollable wildfires known in the literature as the Asset Protection Problem (APP). In the APP each asset requires a protective service to be performed by a set of emergency response vehicles within a specific time period defined by the spread of fire. We propose a new spatial decomposition based math-heuristic approach for the solution of large-scale APPs. The heuristic exploits the property that time windows are geographically correlated as fire spreads across a landscape. Thus an appropriate division of the landscape allows the problem to be decomposed into smaller more tractable sub-problems. The main challenge then is to minimise the difference between the final locations of vehicles from one division to the optimal starting locations of the next division. The performance of the proposed approach is tested on a set of benchmark instances from the literature and compared to the most recent Adaptive Large Neighborhood Search (ALNS) algorithm developed for the APP. The results show that our proposed solution approach outperforms the ALNS algorithm on all instances with comparable computation time. We also see a trend with the margin of out-performance becoming more significant as the problems become larger

A mixed integer programming approach for asset protection during escaped wildfires

Incident management teams (IMTs) are responsible for managing the response to wildfires. One of the objectives of IMTs is the protection of assets and infrastructure. In this paper, we develop a mathematical model to assist IMTs in assigning resources to asset protection activities during wildfires. We present a mixed integer programming model for resource allocation with the aim of protecting the maximum possible total value of assets. The model allows for mixed vehicle types with interchangeable capabilities and with travel times determined by vehicle-specific speed and road network information. We define location-specific protection requirements in terms of vehicle capabilities. The formulated model extends classic variants of the team orienteering problem with time windows. The model capabilities are demonstrated using a hypothetical fire scenario impacting South Hobart, Tasmania, Australia. Computational testing shows that realistically sized problems can be solved within a reasonable time

Dynamic rerouting of vehicles during cooperative wildfire response operations

Incident managers assigning wildfire response vehicles to provide protection to community assets may experience disruptions to their plans arising from factors such as changes in weather, vehicle breakdowns or road closures. We develop an approach to rerouting wildfire response vehicles once a disruption has occurred. The aim is to maximise the total value of assets protected while minimising changes to the original vehicle assignments. A number of functions to measure deviations from the original plans are proposed. The approach is demonstrated using a realistic fire scenario impacting South Hobart, Tasmania, Australia. Computational testing shows that realistic sized problems can be solved within a reasonable time using a commercial solver

Using improved climate forecasting in cash crop planning

Developments in meteorology over the last couple of decades have enabled significant improvements to be made in the accuracy of seasonal forecasts. This paper focuses on developing a model for cash crop planning that utilises these forecasts. It does this by determining the rate of growth of each crop as a function of heat units accumulated. This enables time to maturity to be determined and used in planning, particularly for planting new crops, removing unprofitable immature crops, and harvesting mature crops for profits. The proposed model is solved on a rolling horizon basis. To illustrate the advantage to be gained from improved seasonal forecasts the model is first applied to a problem using long-term temperature averages (climatology). Solutions to the same problem utilising improved seasonal forecasts for temperature are then obtained. This forecast proves to be a valuable input to the model and makes the second approach outperform the first consistently in our simulations

Multi-objective integer programming: A general approach for generating all nondominated solutions

In this paper we develop a general approach to generate all non-dominated solutions of the multi-objective integer programming (MOIP) Problem. Our approach, which is based on the identification of objective efficiency ranges, is an improvement over classical e-constraint method. Objective efficiency ranges are identified by solving simpler MOIP problems with fewer objectives. We first provide the classical e-constraint method on the bi-objective integer programming problem for the sake of completeness and comment on its efficiency. Then present our method on tri-objective integer programming problem and then extend it to the general MOIP problem with k objectives. A numerical example considering tri-objective assignment problem is also provided

Generating all efficient solutions of a rescheduling problem on unrelated parallel machines

In this paper, we consider a rescheduling problem where a set of jobs has already been assigned to unrelated parallel machines. When a disruption occurs on one of the machines, the affected jobs are rescheduled, considering the efficiency and stability measures. Our efficiency measure is the total flow time and stability measure is the total reassignment cost caused by the differences in the machine allocations in the initial and new schedules. We propose a branch and bound algorithm to generate all efficient solutions with respect to our efficiency and stability measures. We improve the efficiency of the algorithm by incorporating powerful reduction and bounding mechanisms. Our computational tests on large sized problem instances have revealed the satisfactory behaviour of our algorithm