Constrained Optimization of an Integral Security Indicator for Adaptive Management of Hazardous Facilities

The subject matter of the article is quantitative assessment and adaptive decision-making for managing the safety state of potentially hazardous facilities using an integral security indicator. The goal is to develop a mathematical framework for selecting an optimal management action that maximizes the indicator under resource, time, and acceptable risk constraints. The tasks are: (i) to formalize the facility state as a normalized vector of indicators and construct the integral indicator A (t) ; (ii) to formulate a constrained optimization model for selecting the optimal action v* (t) based on maximizing A (t) ; (iii) to define a periodic update and feedback mechanism and an effectiveness measure η for evaluating actions across decision cycles. The methods used are multi-criteria aggregation in a normalized indicator space, constrained optimization, argmax-based decision rules, and iterative feedback evaluation. The following results were obtained: an indicator-based state model and integral security indicator were constructed for compact decision support; a constrained selection problem was defined for a discrete action set with cost, implementation time, and risk admissibility constraints; and an operational loop of reassessment, action application, and feedback was specified, enabling adaptive refinement of decisions and visualization of A (tₖ) dynamics. Conclusions. Scientific novelty: 1) an integrated constrained-optimization scheme that maximizes an integral security indicator while jointly accounting for cost, time, and risk constraints; 2) a feedback-enabled adaptive control loop with η and periodic reassessment to improve action selection under changing conditions.