Equivalentsgoal

Equivalentsgoal is a term used in planning and optimization to describe a relationship between goals that makes them interchangeable under a given model or context. In this use, two goals are considered equivalentsgoal when substituting one for the other does not change the feasibility or the value of the resulting plan.

Formally, for a domain with goals G and states S, G1 and G2 are equivalent under goal equivalence if, for every state s in S, any feasible plan that achieves G1 from s can be transformed into a plan that achieves G2 from s with no increase in cost or decrease in utility, and vice versa. The relation is intended to be reflexive, symmetric, and transitive, partitioning the goal set into equivalence classes.

Detection and analysis of equivalentsgoal are typically approximate and rely on heuristic analysis, automata-based model checking, or solving subproblems to compare costs and plan structures. In practice, exact equivalence is rare; analysts often identify near-equivalences to guide pruning and abstraction in planners.

Examples can arise in logistics, where delivering to two nearby destinations with identical distances and penalties may form an equivalence class, allowing a single plan to represent both goals. In reinforcement learning, two reward locations that provide the same return under the current policy may be treated as equivalentsgoal, simplifying policy evaluation.

Applications include reduction of search space, goal-space pruning, and state aggregation in planning tools. Limitations include dependence on model fidelity, as changes in reward, dynamics, or constraints can invalidate equivalence, and the risk that over-aggregation hides important strategic differences. See also goal equivalence, planning, abstraction, and heuristic pruning.