Designing an Optimization Model for Biodiversity Funding: Variables, Goals, Constraints

1 Optimization Model

The 2020 B problem "Funding Biodiversity Conservation" is essentially an optimization problem : find variable values that maximize or minimize an objective under given constraints.

Based on the objective function and constraints, optimization problems can be classified as:

Linear programming problem

Nonlinear programming problem

According to the number of objective functions:

Single‑objective programming

Multi‑objective programming

According to the presence of constraints:

Unconstrained programming

Constrained programming

For the 2020 B problem, goals such as minimizing cost, maximizing efficiency, and maximizing benefit make it a multi‑objective problem, which can be aggregated into a single objective for easier solving. The model is typically nonlinear and constrained, requiring suitable algorithms like Monte‑Carlo or genetic algorithms.

Besides the overall optimization model, sub‑problems may use evaluation models for objective functions or forecasting models for future funding.

2 Elements of the Optimization Model

The basic elements include:

Decision variables : quantities that can be changed, e.g., production amount or path choice.

Objective function : quantifies the goal, either maximization or minimization.

Constraints : limits on time, space, manpower, resources, etc.

2.1 Decision Variables

For the B problem, the decision variable is the "schedule" of funding—i.e., the start year of each species' protection plan. With 48 species over 30 years, we define 48 integer variables ranging from 1 to 30.

2.2 Objective Function

The problem is multi‑objective: minimize total funds while maximizing the number of protected species, stabilizing yearly investment, and shortening the total protection period. Common strategies include converting some objectives into constraints or combining them into a single weighted objective, such as maximizing a benefit‑cost ratio.

Maximize benefit while keeping cost below a given threshold.

Minimize cost while ensuring a minimum number of species saved.

Combine benefit and cost with weights, or maximize the benefit/cost ratio.

2.3 Constraints

Assumptions simplify the real world. For example, once a species' rescue starts, funding must continue for the required number of years without interruption. Another assumption is that the feasibility of success decreases as the start time is delayed.

Specific constraints may include:

Annual funding cannot exceed a given limit.

Number of species rescued must meet a minimum.

Yearly funding volatility (standard deviation) must stay below a threshold.

Total funding years must not exceed a given bound.

2.4 Optimization Model

The general form of a nonlinear programming model is:

Examples from O‑award papers illustrate concrete objective functions such as the benefit‑cost ratio, with variables representing start times, costs, benefits, success rates, and depreciation coefficients.

Data Download

The referenced papers can be obtained by replying with 2020B10997 , 2020B10876 , or 2020B10839 in the public account chat.