## 2 State-Space Network (SSN) Superstructure for Diesel Conditioning Pathways  
The State-Space Network (SSN) method represents complex process systems by decomposing them into task nodes (representing processing operations) and state nodes (representing material conditions), connected by directed flows. In the context of emergency diesel conditioning, the SSN superstructure explicitly enumerates all feasible fuel flow paths--for example, from an Initial-State (raw diesel) through pumps and conditioning units to a Final-State (treated diesel). This graphical representation allows engineers to visualize and adjust alternative process routes more clearly [21]. Compared to traditional superstructure methods, SSNs significantly reduce computational complexity and improve modeling flexibility. When combined with modern optimization techniques (e.g., Genetic Algorithms), designers can efficiently explore various conditioning strategies and rapidly identify optimal solutions. As illustrated in Figure 1, each processing unit in the SSN--such as a pump, conditioning unit, or pipeline--is modeled as a task that links an input state to an output state (e.g., transitions in fuel quality or pressure). For example, a pump task connects a \"low-pressure diesel\" state to a \"high-pressure diesel\" state, while a conditioning task converts \"untreated diesel\" into \"conditioned diesel.\" The SSN allows multiple units of the same type to appear in parallel or in series. For instance, different pumps with varying capacities can feed into a common downstream route, or the diesel may bypass one conditioning unit and follow an alternative treatment path. By modeling these units as nodes, the SSN captures all feasible combinations of operations [12]. Path Definition: In an SSN, a path is defined as a sequence of connected tasks leading from an initial material state to a final treated state. In emergency diesel conditioning systems, a typical path might begin at the raw diesel tank, proceed through one or more pumps and conditioning units, and ultimately deliver fuel to a usable diesel state. The SSN framework enforces interface constraints, ensuring that fuel only flows through physically compatible connections--for example, fuel exiting a high-pressure state must enter tasks that accept high-pressure input. Common assumptions include steady-state operation (constant flow through each path, with no accumulation) and pump capacity limits (maximum allowable flow for each pump). All flows must also be balanced at each state node to ensure fuel conservation. These assumptions simplify the model while accurately representing normal operating conditions in emergency systems. Optimization Objectives: The SSN superstructure is embedded within an optimization framework to achieve operational objectives. In emergency diesel conditioning, the primary goals are to minimize total conditioning time and maximize fuel quality, under safety and reliability constraints. [PERSON] et al. demonstrated that optimizing SSN paths can significantly enhance system performance--for example, achieving a 7.9% reduction in processing time while improving output quality. The SSN framework naturally supports multi-objective optimization, such as minimizing energy consumption (e.g., pump work), minimizing total residence time, or minimizing residual impurity levels. Because the SSN enumerates all feasible configurations, the optimizer can evaluate trade-offs between different routing strategies such as a slower single-pass path versus a faster recirculating scheme to meet target criteria. In emergency applications, system reliability is also an implicit objective, and the SSN helps identify and preserve critical paths that must remain functional under all conditions. Figure 1: State-space network (SSN) superstructure for diesel conditioning pathway optimization. The system links initial and final diesel states via transport and processing routes. DN: decision nodes for inlet–outlet configurations; PO: process modules.