The work, published in Environmental and Sustainability Indicators, is deliberately framed as a methodological proof of concept rather than a ready-to-use planning system. Even so, its findings are striking. When the algorithm was unleashed on representative model stands drawn from the university’s forest enterprise — more than 9,200 hectares divided among the Šášov, Budča and Zvolen forest districts — it consistently converged on a narrow set of management strategies, and it translated the priorities of very different stakeholders into measurably different harvesting patterns.

The technical heart of the framework is a two-way conversation between optimization and simulation. The researchers generated 120 model stands of 0.25 hectares each, spanning four geobiotope types that together cover roughly 80 percent of the enterprise: extremely dry oak–hornbeam forests, fresh oak–hornbeam forests, and two variants of floristically rich beech forests. Each stand was characterized by site productivity class, age and stocking density. The BPSO algorithm then assigned one of three fates to every tree in a stand: keep it alive, harvest and remove it, or harvest it and leave the trunk behind as deadwood. A simple logical rule ensured that no living tree could be declared deadwood without first being selected for harvest.

For every candidate solution, the framework calculated standardized scores for four groups of values: production, regulation, cultural ecosystem services and biodiversity. Indicators included harvested volume and timber revenues, water quantity and quality, stand density, aesthetic value, visibility, longevity, seasonality and species diversity. These group scores were combined into a single multicriteria utility function whose weights came not from the researchers’ imaginations but from real stakeholder interviews previously conducted in Slovak Paradise National Park. Six profiles were tested, ranging from a production-minded economist, who assigned 36.4 percent weight to production, to a “do nothing” conservationist, who gave biodiversity a dominant 64.1 percent.

The algorithm then searched the vast decision space using swarm intelligence. Each tree was treated as a particle moving through a binary hyperspace, guided by its own best past position and by the best solution found by the whole swarm. The configuration used an inertia of 0.9, a cognitive factor of 0.8 and a social factor of 1.6, with runs capped at 100 iterations and an early stopping rule after 50 fruitless rounds. Once an optimal decision vector was found, the updated stand was handed back to Sibyla, which simulated five years of growth, mortality and competition. The cycle repeated across a 20-year planning horizon divided into four decision periods, and the whole process was run for nine predefined management schedules, from near-continuous intervention to complete non-intervention.

The results revealed a strong asymmetry in the optimizer’s preferences. Schedule V, meaning no intervention at all, and Schedule III, a single intervention in the first period, together accounted for roughly three-quarters of all selected schedules across geobiotopes, stakeholder profiles and stand ages. Schedules involving repeated or delayed interventions were rarely or never chosen. Some solutions also accumulated implausibly large volumes of deadwood, because the unconstrained algorithm was free to maximize utility without any operational guardrails. The authors are candid about what this means: maximizing multicriteria utility alone is insufficient when ecological and economic feasibility are not written into the problem as explicit constraints.

Yet the framework also produced ecologically coherent and genuinely interesting patterns. In the oak–hornbeam geobiotopes, oak declined while beech and hornbeam increased, mirroring the natural competitive dynamics of Central European mixed forests where shade-tolerant species replace oak under reduced disturbance. In the beech forests, spruce consistently declined while broadleaves and sometimes fir increased — a trajectory that echoes field observations of Norway spruce struggling outside its optimal range under warming temperatures and prolonged drought. Crucially, these successional directions were driven mainly by site conditions and initial stand composition rather than by stakeholder preferences, suggesting that the growth simulator kept the optimization anchored in ecological reality.

Where stakeholder preferences did matter was in the intensity and distribution of management. Conservation-oriented profiles retained a greater share of dominant trees as deadwood, concentrating large retained trunks in the canopy class that matters most for saproxylic beetles, cavity-nesting birds and nutrient cycling. Economically oriented profiles directed more harvesting toward those same dominant trees. The framework was therefore sensitive enough to reflect contrasting societal priorities without prescribing a single universal solution — a property the authors see as essential for participatory forest planning.

The study also exposes the hard problems that stand between prototype and practice. The multicriteria utility depends on a two-stage standardization procedure whose scaling choices shape the outcome, yet no formal sensitivity analysis was performed. The deadwood indicator carried a disproportionately high inherent weight, and the stand-volume indicator inflated the appeal of doing nothing. The regulation indicators for water rely on expert-assigned values available only for common species, masking differences among rarer ones. The authors recommend converting volume and deadwood into constraining conditions rather than freely optimized objectives, extending the regulation group with erosion control, noise reduction and carbon sequestration, and refining the deadwood mechanism by linking it to Sibyla’s natural-mortality module with explicit retention bounds and decomposition dynamics.

The researchers also sketch the road ahead: integrating an economic-evaluation module, embedding climate-change scenarios into the growth simulations, testing modern BPSO variants for more reliable convergence, and validating the framework against operational management strategies. Planning horizons of 10 to 50 years appear most appropriate, balancing predictive accuracy against the rising risk of windthrow, insect outbreaks and climatic extremes. If those challenges can be met, the payoff could extend beyond better harvest plans. Because the infrastructure is flexible in scale and transparent in its ecosystem-service accounting, the authors suggest it could one day support payment schemes for ecosystem-service providers and give communities a structured, quantified voice in how their forests are managed. For now, the message is clear: the mathematics exists to plan a forest for everything it provides, not just its timber — the task now is to teach the algorithm the rules that foresters, and forests themselves, cannot break.

Subject of Research: Simulation–optimization framework for ecosystem-service-oriented forest management planning

Article Title: New approach in forest management planning

Article References: Kúdela, P., & Sedmák, R. (2026). New approach in forest management planning. Environmental and Sustainability Indicators, 32, Article 101564. https://doi.org/10.1016/j.indic.2026.101564

Image Credits: AI Generated

DOI: 10.1016/j.indic.2026.101564

Keywords: forest management, ecosystem services, particle swarm optimization, forest growth simulation, biodiversity, deadwood, Sibyla, Slovakia, multicriteria optimization, stakeholder preferences, decision support systems, silviculture

Multi-criteria decision analysis, or MCDA, is the mathematical backbone of countless real-world decisions, from selecting suppliers and infrastructure projects to ranking medical treatments and environmental policies. Methods such as TOPSIS or PROMETHEE combine performance scores across several criteria—cost, quality, delivery time, reliability—into a single ranking. But every one of these methods requires weights that express how important each criterion is relative to the others. In practice, these weights are frequently unavailable, disputed among stakeholders, or expected to drift over time. When a ranking rests on weights nobody truly measured, its apparent precision can be misleading. Version 1.0 of PySensMCDA tackled this with classical perturbation analysis: adjust an element of the decision problem and observe how the ranking responds. Version 2.0 adds the inverse direction, along with a suite of tools designed to summarise many rankings at once, regardless of how they were produced.

The update is organised around four new submodules. The first handles weight space sampling, separating the assumptions made about criterion weights from the analyses that consume them. It offers uniform and Dirichlet sampling of the weight simplex, analytic sampling under an ordinal ranking of criteria, exhaustive simplex grids, and the Hit-And-Run algorithm for sampling under arbitrary linear constraints—a technique originally developed for efficient Monte Carlo generation of points over bounded regions. Decision-makers often hold only partial preference information: an ordering of criteria importance, bounds on individual weights, bounds on trade-off ratios, or general linear constraints. Version 2.0 expresses all four types through a single constraint builder, producing plain numerical arrays that can feed any downstream analysis in the package.

The second submodule implements the stochastic multicriteria acceptability analysis family, better known as SMAA, a methodology developed for group decision-making under uncertain or missing weight information. SMAA works by drawing millions of random weight vectors from the admissible space and computing, for each alternative, the share of weight space in which it attains each possible rank. These are the rank acceptability indices, reported with Monte Carlo standard errors. The implementation goes considerably further, offering central weight vectors that describe the “typical” preference profile supporting each alternative, favourable weight ranges, confidence and cross-confidence factors, holistic and k-best-ranks measures, and support for ordinal criteria through SMAA-O.

Perhaps the most technically striking addition is an exact route for deterministic problems. For an additive value function with fixed criteria values, the acceptability index is not estimated by simulation but computed exactly, as a ratio of polytope volumes—the volumes of geometric regions defined by linear inequalities. This serves two purposes. It provides a reference free of sampling error against which the required number of simulation iterations can be judged: in validation tests, the Monte Carlo and exact routes agree to 0.003 percentage points at 200,000 iterations. More importantly, it resolves a case that random sampling can never reach. An alternative whose favourable weight set is lower-dimensional—confined to a slice of zero volume within the weight space—has an acceptability of exactly zero, yet possesses a well-defined central weight vector. Simulation will never visit such a region, but the exact computation identifies it, distinguishing an alternative that can never win from one that wins only under a degenerate weight configuration. Two components of this exact route remain computationally inexpensive regardless of problem size: a linear-programming feasibility test that eliminates dominated alternatives, and the true favourable weight ranges obtained from just twice as many linear programs as there are criteria.

The third submodule implements the Exhaustive Objective Ranking Solution, or EORS, a recently proposed method that explores the admissible weight space systematically rather than by sampling. For each alternative it reports the preference value attained most often across the explored space, together with degrees of confidence describing how concentrated that outcome is. The release also incorporates a newly published local sensitivity extension, based on simplex-projected finite differences around the weight configuration supporting each global result, aggregated into a criterion-level sensitivity index and an alternative-level fragility index. The fourth submodule collects robustness metrics that summarise a distribution of ranking outcomes: ranking stability and balance point coefficients, pairwise winning indices, and decision entropy for both choice and ranking problems.

The architectural decision that ties the update together is a single, method-agnostic calling convention: any decision method can be supplied as a simple function taking a decision matrix, a weight vector, and a list of criterion types, and returning preference values. Any method from the companion pymcdm library satisfies this contract directly, as does any plain callable, with no inheritance or adapter code required. The consequence is significant. Because the ranking machinery underlying SMAA compares preference values and nothing else, substituting an arbitrary method yields SMAA-TOPSIS, SMAA-PROMETHEE, or SMAA applied to any user-defined method without additional code. Reference implementations of SMAA in R and Java are restricted to the additive value model, so this generalisation extends the reach of the entire SMAA family rather than merely reimplementing it. One caveat is documented explicitly: for methods with internal normalisation, the acceptability indices retain their probabilistic interpretation, but the central weight vector becomes a descriptive centre of gravity rather than an estimate of utility weights.

The power of the approach is illustrated with a supplier selection problem involving five alternatives and four criteria: unit cost and lead time, both of cost type, and quality audit score and delivery reliability, both of profit type. Evaluated with TOPSIS under equal weights, the problem yields the ranking A3 first, followed by A1, A5, A2 and A4. But suppose decision-makers cannot agree on weights, and instead agree only that quality is the most important criterion, followed by cost, reliability and lead time, with quality carrying between 25 and 50 percent of the total weight, and criteria values known only within 5 percent. Under these more realistic assumptions, the conclusion changes dramatically. Alternative A2, only fourth under equal weights, emerges as the most preferred option for 64 percent of the admissible weight vectors, with a confidence factor of 89 percent indicating the measurements are accurate enough to sustain that conclusion. Alternative A4 is never preferred at all. The recommended alternative under equal weights is not the one supported by the majority of plausible preferences.

The robustness metrics sharpen this picture further. When the entire weight simplex is explored without any preference constraints, every alternative eventually visits every position, and the ranking stability coefficient is zero throughout—under complete ignorance, no position is stable. Restricting the analysis to the preferences the decision-makers consider plausible separates the alternatives meaningfully. Decision entropy quantifies the same gain from a different angle: normalised choice entropy falls from 0.585 to 0.393, and ranking entropy from 0.625 to 0.315, once the stated preference information is imposed. This provides a direct, quantitative answer to a question decision analysts are often asked—whether further effort to elicit preferences is actually worth it.

Validation of the new implementation is unusually rigorous for scientific software. Both founding SMAA papers report complete input data and results, allowing them to serve as regression fixtures: the implementation reproduces their acceptability indices, confidence factors, central weight vectors, full rank acceptability matrices and holistic indices to within one percentage point, and this agreement is enforced as an automated test rather than reported once. The constrained Hit-And-Run sampler reproduces the distribution of the analytic ordered-simplex sampler with which it shares no code. The test suite comprises 371 tests covering 98 percent of the new modules. The software is released under the MIT licence on GitHub, with full documentation hosted online, requiring Python 3.10 or newer along with standard scientific libraries including numpy, scipy and pandas.

The broader impact is a shift in what a practitioner can honestly state about a recommendation. Instead of presenting a ranking derived from weights that were never measured, analysts can now report how much of the admissible weight space supports each alternative, which preference profiles would justify it, and whether the underlying measurements are precise enough to distinguish candidates at all. For methodological researchers, the update makes two recently introduced method families—EORS and the stability coefficients—available in a maintained implementation alongside established methods, on a common interface permitting direct comparison. Future releases may extend the framework toward outranking-based SMAA variants using ELECTRE-type methods, and may bring fuzzy variants of iterative compromise ranking analysis into the same interface. For a field in which weight elicitation has long been the weakest link between mathematical rigour and practical credibility, version 2.0 of PySensMCDA offers something close to a completeness check: a way of knowing not just which alternative wins, but how much of the decision space actually agrees.