One- and two-objective approaches to an area-constrained habitat reserve site selection problem

We compare several ways to model a habitat reserve site selection problem in which an upper bound on the total area of the selected sites is included. The models are cast as optimization coverage models drawn from the location science literature. Classic covering problems typically include a constraint on the number of sites that can be selected. If potential reserve sites vary in terms of area, acquisition cost or land value, then sites need to be differentiated by these characteristics in the selection process. To address this within the optimization model, the constraint on the number of selected sites can either be replaced by one limiting the total area of the selected sites or area minimization can be incorporated as a second objective. We show that for our dataset and choice of optimization solver average solution time improves considerably when an area-constrained reserve site selection problem is modeled as a two objective rather than a single objective problem with a constraint limiting the total area of the selected sites. Computational experience is reported using a large dataset from Australia.     

Methods for reserve selection: Interior point search

Spatial reserve design concerns the planning of biological reserves for conservation. Typical reserve selection formulations operate on a large set of landscape elements, which could be grid cells or irregular sites, and selection algorithms aim to select the set of sites that achieves biodiversity target levels with minimum cost. This study presents a completely different optimization approach to reserve design. The reserve selection problem can be considerably simplified given the reasonable assumptions that: (i) maximum reserve cost is known; (ii) the approximate number of new reserves to be established is known; (iii) individual reserves need to be spatially contiguous. Further assuming the ability to construct a set of reserves in an efficient and close to optimal manner around designated reserve locations, the reserve selection problem can be turned into a search for a single interior point and area for each reserve. The utility of the proposed method is demonstrated for a data set of seven indicator species living in an conservation priority area in Southern Australia consisting of ca 73,000 selection units, with up to 10,000 cells chosen for inclusion in a reserve network. Requirements (ii) and (iii) above make interior point search computationally very efficient, allowing use with landscapes in the order of millions of elements. The method could also be used with non-linear species distribution models.     

Optimisation in reserve selection procedures—why not?

Linear programming techniques provide an appropriate tool for solving reserve selection problems. Although this has long been known, most published analyses persist in the use of intuitive heuristics, which cannot guarantee the optimality of the solutions found. Here, we dispute two of the most common justifications for the use of intuitive heuristics, namely that optimisation techniques are too slow and cannot solve the most realistic selection problems. By presenting an overview of processing times obtained when solving a diversity of reserve selection problems, we demonstrate that most of those published could almost certainly be solved very quickly by standard optimisation software using current widely available computing technology. Even for those problems that take longer to solve, solutions with low levels of sub-optimality can be obtained quite quickly, presenting a better alternative to intuitive heuristics.     

Accounting for habitat loss rates in sequential reserve selection: Simple methods for large problems

We develop reserve selection methods for maximizing either species retention in the landscape or species representation in reserve areas. These methods are developed in the context of sequential reserve selection, where site acquisition is done over a number of years, yearly budgets are limited and habitat loss may cause some sites to become unavailable during the planning period. The main methodological development of this study is what we call a site-ordering algorithm, which maximizes representation within selected sites at the end of the planning period, while accounting for habitat loss rates in optimization. Like stochastic dynamic programming, which is an approach that guarantees a globally optimal solution, the ordering algorithm generates a sequence in which sites are ideally acquired. As a distinction from stochastic dynamic programming, the ordering is generated via a relatively fast approximate process, which involves hierarchic application of the principle of maximization of marginal gain. In our comparisons, the ordering algorithm emerges a clear winner, it does well in terms of retention and is superior to simple heuristics in terms of representation within reserves. Unlike stochastic dynamic programming, the ordering algorithm is applicable to relatively large problem sizes, with reasonable computation times expected for problems involving thousands of sites.     

The importance of in situ site loss in nature reserve selection: Balancing notions of complementarity and robustness

Because the threat of habitat destruction can never be entirely eliminated, there is a legitimate concern that some reserve networks, especially highly complementary ones with minimal species overlap, may be predisposed to severe losses in species representation if one or more core reserve sites are destroyed. In order to address this problem in a systematic way, we propose the use of two different optimization models for designing complementary reserve networks that are also highly robust to possible site losses. Given limited budgets, the first maximizes expected species representation over all possible site loss patterns while the second maximizes a combination of representation given all sites and remaining representation following the worst-case loss of a restricted subset of reserve sites. By incorporating reserve loss in fundamentally different ways, these two models provide a range of options in terms of information requirements, assumptions about risk aversion, and structural complexity. We compare both of these methods to a more standard approach, which completely ignores the inherent risk posed by reserve site loss. Results confirm that significantly more robust solutions can be obtained for a marginal decrease in initial species representation within the reserve system.     

Heuristic algorithms vs. linear programs for designing efficient conservation reserve networks: Evaluation of solution optimality and processing time

Systematic approaches to efficient reserve network design often make use of one of two types of site selection algorithm; linear programs or heuristic algorithms. Unlike with linear programs, heuristic algorithms have been demonstrated to yield suboptimal networks in that more sites are selected in order to meet conservation goals than may be necessary or fewer features are captured than is possible. Although the degree of suboptimality is not known when using heuristics, some researchers have suggested that it is not significant in most cases and that heuristics are preferred since they are more flexible and can yield a solution more quickly. Using eight binary datasets, we demonstrate that suboptimality of numbers of sites selected and biodiversity features protected can occur to various degrees depending on the dataset, the model design, and the type of heuristic applied, and that processing time is not dramatically different between optimal and heuristic algorithms. In choosing an algorithm, the degree of suboptimality may not always be as important to planners as the perception that optimal solvers have feasibility issues, and therefore heuristic algorithms might continue to be a popular tool for conservation planning. We conclude that for many datasets, feasibility of optimal algorithms should not be a concern and that the value of heuristic results can be greatly improved by using optimal algorithms to determine the degree of suboptimality of the results.     

Two paths to a suboptimal solution - once more about optimality in reserve selection

Several studies have compared the performances of exact algorithms (integer programming) and heuristic methods in the solution of conservation resource allocation problems, with the conclusion that exact methods are always preferable. Here, I summarize a potentially major deficiency in how the relationship between exact and heuristic methods has been presented: the above comparisons have all been done using relatively simple (linear) maximum coverage or minimum set models that are by definition solvable using integer programming. In contrast, heuristic or meta-heuristic algorithms can be applied to less simplified nonlinear and/or stochastic problems. The focus of this study is two kinds of suboptimality, first-stage suboptimality caused by model simplification and second-stage suboptimality caused by inexact solution. Evidence from comparisons between integer programming and heuristic solution methods suggests a suboptimality level of around 3%-10% for well-chosen heuristics, much depending on the problem and data. There is also largely anecdotal evidence from a few studies that have evaluated results from simplified conservation resource allocation problems using more complicated (nonlinear) models. These studies have found that dropping components such as habitat loss rates or connectivity effects from the model can lead to suboptimality from 5% to 50%. Consequently, I suggest that more attention should be given to two topics, first, how the performance of a conservation plan should be evaluated, and second, what are the consequences of simplifying the ideal conservation resource allocation model? Factors that may lead to relatively complicated problem formulations include connectivity and evaluation of long-term persistence, stochastic habitat loss and availability, species interactions, and distributions that shift due to climate change.     

Replacement cost: A practical measure of site value for cost-effective reserve planning

Conservation needs are often in direct competition with other forms of land-use, and therefore protection of biodiversity must be cost-efficient. While common reserve selection algorithms address this problem, quantitative planning tools often suggest an optimal set of sites that is not necessarily convenient for practical conservation. Besides cost-effective solutions we require flexibility if land-use conflicts are to be effectively resolved. We introduce a novel concept for site value in quantitative reserve planning. Replacement cost refers to the loss in solution value given that the optimal cost-efficient solution cannot be protected and alternative solutions, with particular sites forcibly included or excluded, are needed. This cost can be defined either in terms of loss of biological value or in terms of extra economic cost, and it has clear mathematical definitions in the context of benefit-function-based reserve planning. A main difference with the much-used concept of irreplaceability is that the latter tells about the likelihood of needing a site for achieving a particular conservation target. Instead, replacement cost tells us at what cost (biological or economic) can we exclude (or include) a site from the reserve network. Here, we illustrate the concept with hypothetical examples and show that replacement-cost analysis should prove useful in an interactive planning process, improving our understanding of the importance of a site for cost-efficient conservation.     

Species specific connectivity in reserve-network design using graphs

Systematic conservation planning applications based solely on the presence/absence of a large number of species are not sufficient to guarantee their persistence in highly fragmented landscapes. Recent developments have thus incorporated much desired spatial design considerations, and reserve-network connectivity has received increased attention. Nonetheless, connectivity is often determined without regard to species-specific responses to habitat fragmentation. But species differ in their dispersal ability and habitat requirements, making proximate priority areas necessary for some species, while undesirable for others. We present a novel approach that incorporates species-specific connectivity needs in reserve-network design. Importantly, our method differs from previous approaches in that connectivity is not part of the objective function, but part of the constraints, thus avoiding typical undesirable trade-off that may result in high connectivity for some species but null connectivity for others. We use graphs to describe the dispersal pattern of each species and our goal is to identify minimum sets of reserves with connected sites for each of the species. This is not a trivial problem and we present three algorithms, one heuristic and two integer cutting algorithms that guarantee optimality, based on different 0-1 linear programming formulations. Applications to simulated data show that one of the algorithms that guarantee optimality is superior to the other, although both have limited application due to the number of sites and species they can manage. Remarkably, the heuristic can obtain very satisfactory solutions in short computational times, surpassing the limitations of the exact algorithms.     

Designing spatially-explicit reserve networks in the presence of mandatory sites

In the selection of reserve networks there are special sites whose ecologic, strategic or morphologic values dictate their inclusion. The existence of regional rare or confined-distribution species is one among other reasons that often determines the existence of such mandatory sites. Moreover, quite often these mandatory sites are located far apart. Although several methods have been proposed to accommodate structural connectivity in reserve selection, they were not devised to deal specifically with such mandatory sites. Those that encourage aggregation of sites by means of criteria incorporated in the objective function do not seem suitable to acquire consistent connectivity levels in the presence of mandatory sites. Methods that enforce “full connectivity” tend to produce long and narrow solutions, which results in efficiency deficits and biological unsuitability, as they force the selection of more sites of less quality to ensure connectivity. Hence specific methods to select ecological reserves when mandatory sites exist are needed. Here we discuss and propose a 0-1 linear programming model to deal with this issue. The model was applied in two data sets of forest breeding birds and butterflies. Its solutions and computational performances are discussed.     

Landscape Zonation, benefit functions and target-based planning: Unifying reserve selection strategies

The most widespread reserve selection strategy is target-based planning, as specified under the framework of systematic conservation planning. Targets are given for the representation levels of biodiversity features, and site selection algorithms are employed to either meet the targets with least cost (the minimum set formulation) or to maximize the number of targets met with a given resource (maximum coverage). Benefit functions are another recent approach to reserve selection. In the benefit function framework the objective is to maximize the value of the reserve network, however value is defined. In one benefit function formulation value is a sum over species-specific values, and species-specific value is an increasing function of representation. This benefit function approach is computationally convenient, but because it allows free tradeoffs between species, it essentially makes the assumption that species are acting as surrogates, or samples from a larger regional species pool. The Zonation algorithm is a recent computational method that produces a hierarchy of conservation priority through the landscape. This hierarchy is produced via iterative removal of selection units (cells) using the criterion of least marginal loss of conservation value to decide which cell to remove next. The first variant of Zonation, here called core-area Zonation, has a characteristic of emphasizing core-areas of all species. Here I separate the Zonation meta-algorithm from the cell removal rule, the definition of marginal loss of conservation value utilized inside the algorithm. I show how additive benefit functions and target-based planning can be implemented into the Zonation framework via the use of particular kinds of cell removal rules. The core-area, additive benefit function and targeting benefit function variants of Zonation have interesting conceptual differences in how they treat and trade off between species in the planning process.     

ACO算法及其在铰接车辆优化设计中的应用

为了缩短工程设计周期和提高产品的质量,针对协同优化（CO）算法存在的计算量大、协调困难等问题进行了改善性研究。改善后的协同优化（ACO）算法采取了无约束的系统级,排除了单一雅克比方程式问题,使用了L1范数改进了CO算法的学科一致性约束,另外子系统增加了一些优化参数和约束模型。通过算例验证,ACO算法在计算效率上比CO算法提高了2.6倍,优化结果也更加逼近标准解。最后,将ACO算法应用到铰接车辆设计中,车辆的燃油经济性提高了2.596%,车辆速度从零到最高车速所需要的时间也减少了6.051 s。该算法有助于提高复杂工程系统优化设计中计算的效率和准确性。     

Probabilistic approaches to scheduling reserve selection

Most existing reserve selection algorithms are static in that they assume that a reserve network is designed and patches are selected by decision-makers at a single point in time. In reality, however, selection processes are often dynamic and patches are selected one by one or in several groups because for example there are insufficient funds at the beginning of the process to put all the patches under protection. Finding an optimal dynamic selection strategy is tricky since due to the complementarity principle the value of a particular patch depends on the presence of other patches in the network - including those that have not yet been selected. As unprotected patches may be lost, e.g., through development, the long-term value of selecting a particular patch is uncertain. Existing dynamic selection algorithms are either ‘myopic’ and consider only those patches that have already been protected, totally ignoring future uncertainty, or they are based on stochastic dynamic programming, which delivers the optimal strategy taking uncertainty into account but is numerically too complex to be employed in actual selection problems. In this paper, a ‘foresighted’ selection strategy as well as a number of variants are developed using probability theory. The different strategies are compared for a large number of selection problems. All variants outperform the myopic strategy and perform close to the optimal strategy. However, the performances of all strategies, including the optimal and the myopic one, are not dramatic.     

喷灌系统加压泵的优化选型

该文根据系统分析原理，分析了水泵优化选型问题的目标函数和约束条件，选用适合于水泵直接加压式喷灌工程特点的大系统层次分析优化研究方法，建立了数学模型、并探讨解决了具体计算方法，为喷灌工程规划设计提供了快速、准确地水泵优化选型方法     

Locating and protecting critical reserve sites to minimize expected and worst-case losses

There has been much recent interest in the development of systematic reserve selection methods that are capable of incorporating uncertainty associated with site destruction. This paper makes a contribution to this line of research by presenting two different optimization models for minimizing species losses within a planning region. Given limited acquisition budgets, the first minimizes expected species losses over all possible site loss patterns outside the reserve network while the second minimizes maximum species losses following the worst-case loss of a restricted subset of nonreserve sites. By incorporating the uncertainty of site destruction directly into the decision planning process, these models allow a conservation planner to take a less defensive and more strategic view of reserve selection that seeks to minimize species losses through the targeted acquisition of high-value/high-risk sites. We compare both of these methods to a more standard approach, which simply maximizes within reserve representation without regard for the varied level of threat faced by different sites and species. Results on a realistic dataset show that significant reductions in species losses can be achieved using either of these more intelligent modeling frameworks.     

Reserve selection with minimum contiguous area restrictions: An application to open space protection planning in suburban Chicago

Conservation efforts often require site or parcel selection strategies that lead to spatially cohesive reserves. Although habitat contiguity is thought to be conducive to the persistence of many sensitive species, availability of funding and suitable land may restrict the extent to which this spatial attribute can be pursued in land management or conservation. Using optimization modeling, we explore the economic and spatial tradeoffs of retaining or restoring grassland habitat in contiguous patches of various sizes near the Chicago metropolitan area. The underlying mathematical construct is the first exact, generalized formulation that directly models spatial contiguity in optimal reserve selection. The construct allows conservation planners to analyze and weigh different minimum contiguous habitat size requirements that are to be used in specific land acquisition or retention projects.     

The importance of traditional meadow management techniques for conservation of vascular plant species richness in Norway

Using information from a regional survey of vascular plants of 130 sites in western Norway, a selection of sites based on a heuristic iterative complementarity-based nature reserve selection procedure was performed. The results indicate that conservation of traditionally managed hay meadows is of major importance as they contributed 60.1% of all native species recorded; afforested grasslands (deciduous woodlands < 70 years old) contributed 26.8%, whereas artificially fertilized hay meadows and intensively cultivated grasslands taken together contributed 13.1% of the species. The species composition of the meadows was significantly nested. Thus, if you conserve the most species-rich meadows, you also conserve most of the species in the less species-rich meadows. Nestedness in meadows was significantly correlated with within-meadow habitat diversity and soil pH. The most species-rich meadows were traditional meadows, characterized by high habitat diversity and high soil pH. These meadows will support nearly all species including habitat specialists and regionally rare species, whilst artificially fertilized hay meadows only support the generalist subset, i.e. common species. Area was not significantly correlated with nestedness suggesting that it is more important to cover many habitats than to preserve large traditional meadows just because they are large.     

Efficiency and effectiveness in representative reserve design in Canada: The contribution of existing protected areas

To be effective, reserve networks should represent all target species in protected areas that are large enough to ensure species persistence. Given limited resources to set aside protected areas for biodiversity conservation, and competing land uses, a prime consideration for the design of reserve networks is efficiency (the maximum biodiversity represented in a minimum number of sites). However, to be effective, networks may sacrifice efficiency. We used reserve selection algorithms to determine whether collections of existing individual protected areas in Canada were efficient and/or effective in terms of representing the diversity of disturbance-sensitive mammals in Canada in comparison to (1) an optimal network of reserves, and (2) sites selected at random. Unlike previous studies, we restricted our analysis to individual protected areas that met a criterion for minimum reserve size, to address issues of representation and persistence simultaneously. We also tested for effectiveness and efficiency using historical and present-day data to see whether protected area efficiency and/or effectiveness varied over time. In general, existing protected areas did not effectively capture the full suite of mammalian species diversity, nor are most existing protected areas part of a near-optimal solution set. To be effective, Canada’s network of reserves will require at minimum 22 additional areas of >2700 km². This study shows that even when only those reserves large enough to be effective are considered, protected areas systems may not be representative, nor were they representative at the time of establishment.     

Co-clustering Spatial Data Using a Generalized Linear Mixed Model With Application to the Integrated Pest Management

Co-clustering has been broadly applied to many domains such as bioinformatics and text mining. However, model-based spatial co-clustering has not been studied. In this paper, we develop a co-clustering method using a generalized linear mixed model for spatial data. To avoid the high computational demands associated with global optimization, we propose a heuristic optimization algorithm to search for a near optimal co-clustering. For an application pertinent to Integrated Pest Management, we combine the spatial co-clustering technique with a statistical inference method to make assessment of pest densities more accurate. We demonstrate the utility and power of our proposed pest assessment procedure through simulation studies and apply the procedure to studies of the persea mite (Oligonychus perseae), a pest of avocado trees, and the citricola scale (Coccus pseudomagnoliarum), a pest of citrus trees.     

Simulating the effects of using different types of species distribution data in reserve selection

In a perfect world, systematic conservation planning would use complete information on the distribution of biodiversity. However, information on most species is grossly incomplete. Two main types of distribution data are frequently used in conservation planning: observed and predicted distribution data. A fundamental question that planners face is - which kind of data is better under what circumstances? We used simulation procedures to analyse the effects of using different types of distribution data on the performance of reserve selection algorithms in scenarios using different reserve selection problems, amounts of species distribution known, conservation targets and costs. To compare these scenarios we used occurrence data from 25 amphibian and 41 reptile species of the Iberian Peninsula and assumed the available data represented the whole truth. We then sampled fractions of these data and either used them as they were, or converted them to modelled predicted distributions. This enabled us to build three other types of species distribution data sets commonly used in conservation planning: “predicted”, “transformed predicted” and “mixed”. Our results suggest that reserve selection performance is sensitive to the type of species distribution data used and that the most cost-efficient decision depends most on the reserve selection problem and on how much we have of the species distribution data. Choosing the most appropriate type of distribution data should start by evaluating the scenario circumstances. While there is no one best approach for every scenario, we discovered that using a mixed approach usually provides an acceptable compromise between species representation and cost.