Jeffrey D. Camm

A COMPARISON OF RESERVE SELECTION ALGORITHMS USING DATA ON TERRESTRIAL VERTEBRATES IN OREGON

We compare the number of species represented and the spatial pattern of reserve networks derived using five types of reserve selection algorithms on a set of vertebrate distribution data for the State of Oregon (USA). The algorithms compared are: richness-based heuristic algorithms (four variations), weighted rarity-based heuristic algorithms (two variations), progressive rarity-based heuristic algorithms (11 variations), simulated annealing, and a linear programming-based branch-and-bound algorithm. The linear programming algorithm provided optimal solutions to the reserve selection problem, finding either the maximum number of species for a given number of sites or the minimum number of sites needed to represent all species. Where practical, we recommend the use of linear programming algorithms for reserve network selection. However, several simple heuristic algorithms provided near-optimal solutions for these data. The near-optimality, speed and simplicity of heuristic algorithms suggests that they are acceptable alternatives for many reserve selection problems, especially when dealing with large data sets or complicated analyses.

Choosing reserve networks with incomplete species information

Existing methods for selecting reserve networks require data on the presence or absence of species at various sites. This information, however, is virtually always incomplete. In this paper, we analyze methods for choosing priority conservation areas when there is incomplete information about species distributions. We formulate a probabilistic model and find the reserve network that represents the greatest expected number of species. We compare the reserve network chosen using this approach with reserve networks chosen when the data is treated as if presence/absence information is known and traditional approaches are used. We find that the selection of sites differs when using probabilistic data to maximize the expected number of species represented versus using the traditional approaches. The broad geographic pattern of which sites are chosen remains similar across these different methods but some significant differences in site selection emerge when probabilities of species occurrences are not near 0 or 1.

A note on optimal algorithms for reserve site selection

A recent note by Underhill (Biol. Conserv., 70, 85-7, 1994) points out the need for the use of optimization models and a closer working relationship with mathematicians for the solution of biological management problems such as the reserve site selection problem. In this note we give the mathematical formulation of what he terms ‘the more realistic’ version of the reserve selection problem, namely, the problem of maximizing the number of species preserved given a fixed budget for reserve sites. We also discuss some straight-forward data reduction schemes which may reduce the solution time for these problems when they are solved using general off-the-shelf optimization code as mentioned by Underhill.

Nature Reserve Site Selection to Maximize Expected Species Covered

We analyze the problem of maximizing the expected number of species in a nature reserve network, subject to a constraint on the number of sites in the network, given probabilistic information about species occurrences. The problem is a nonlinear binary integer program that is NP-hard. We develop a linear integer programming approximation that may be solved with standard integer programming software. We compare the approximation with two other approaches, an expected greedy approach and a probability hurdle approach, using probabilistic data on occurrences of terrestrial vertebrates in the state of Oregon. Results of the approximation and an exact algorithm are compared by using samples from the North American Breeding Bird Survey.

WEIGHING CONSERVATION OBJECTIVES: MAXIMUM EXPECTED COVERAGE VERSUS ENDANGERED SPECIES PROTECTION

Decision makers involved in land acquisition and protection often have mul- tiple conservation objectives and are uncertain about the occurrence of species or other features in candidate sites. Models informing decisions on selection of sites for reserves need to provide information about cost-efficient trade-offs between objectives and account for incidence uncertainty. We describe a site selection model with two important conser- vation objectives: maximize expected number of species represented, and maximize the likelihood that a subset of endangered species is represented. The model uses probabilistic species occurrence data in a linear-integer formulation solvable with commercial software. The model is illustrated using probabilistic occurrence data for 403 terrestrial vertebrates in 147 candidate sites in western Oregon, USA. The trade-offs between objectives are explicitly measured by incrementally varying the threshold probability for endangered species representation and recording the change in expected number of species represented. For instance, in the example presented here, we found that under most budget constraints, the probability of representing three endangered species can be increased from 0.00 (i.e., no guaranteed protection) to 0.90 while reducing expected species representation ;2%. However, further increasing the probability of endangered species representation from 0.90 to 0.99 results in a much larger reduction in species representation of ;14%. Although the numerical results from our analysis are specific to the species and area studied, the meth- odology is general and applicable elsewhere.

Conjoint Optimization: An Exact Branch-and-Bound Algorithm for the Share-of-Choice Problem

Conjoint analysis is a statistical technique used to elicit partworth utilities for product attributes from consumers to aid in the evaluation of market potential for new products. The objective of the share-of-choice problem (a common approach to new product design) is to find the design that maximizes the number of respondents for whom the new products utility exceeds a specific hurdle (reservation utility). We present an exact branch-and-bound algorithm to solve the share-of-choice problem. Our empirical results, based on several large commercial data sets and simulated data from a controlled experiment, suggest that the approach is useful for finding provably optimal solutions to realistically sized problems, including cases where partworths contain estimation error.

An exact algorithm for the maximal covering problem

This article develops a robust, exact algorithm for the maximal covering problem (MCP) using dual-based solution methods and greedy heuristics in branch and bound. Based on tests using randomly generated problems with problem parameters similar to those in the existing literature, the hybrid approach developed in this work appears to be effective over a wide range of MCP model parameters. The method is further validated on problems constructed from three real-world data sets. The extensive computational study compares the new method with other existing exact methods using problems that are as big, or larger than, those used in previous work on MCP. The results show that the proposed method is effective in most instances of MCP. In particular, it is shown that bounding schemes using Lagrangian relaxation are effective on MCP as a method of obtaining both exact and heuristic solutions.

The unit learning curve approximation of total cost

Abstract Learning curve theory has been integrated into mathematical models which previously did not take learning into account. Researchers have in general used one of two approximations of total cost based on the integral of the unit learning curve when developing larger models. An error analysis of the two approximations is presented.

A Branch-and-Price Approach to the Share-of-Choice Product Line Design Problem

We develop a branch-and-price algorithm for constructing an optimal product line using partworth estimates from choice-based conjoint analysis. The algorithm determines the specific attribute levels for each multiattribute product in a set of products to maximize the resulting product lines share of choice, i.e., the number of respondents for whom at least one new products utility exceeds the respondents reservation utility. Computational results using large commercial and simulated data sets demonstrate that the algorithm can identify provably optimal, robust solutions to realistically sized problems.

Effect of process learning on manufacturing schedules

Abstract The capacity constrained lot sizing problem with learning is modeled as a nonlinear mixed integer program. Three solution techniques for solving the model are investigated. A nonlinear programming package together with the branch and bound technique is used to obtain a solution to the exact problem. The issue of nonconvexity is discussed. In the piecewise linearization of the learning curve, the problem is represented by a mixed integer programming model. Finally, a heuristic that gives near optimal solutions in minimal computer time is developed. Process learning results in a reduction in the number of setups and an increase in inventory level.