Multi-Objective Transmission Switching

• Multi-Objective Transmission Switching is a technique that adjusts grid topology—by opening or closing line breakers and reconfiguring substations—to balance conflicting criteria like security, congestion, cost, and voltage quality.
• It employs diverse algorithmic approaches including multi-objective reinforcement learning, exact enumeration, and evolutionary optimization to derive Pareto-optimal trade-offs in power system operations.
• Empirical studies demonstrate that MOTS can significantly improve grid reliability and efficiency, offering enhanced contingency management and reduced operational costs even under complex constraints.

Multi-objective transmission switching (MOTS) denotes the use of transmission topology changes—most directly, opening or closing line breakers to take branches in or out of service—to optimize several conflicting operational criteria simultaneously. In the recent power-systems literature, MOTS is treated as part of the broader topology-control problem, which also includes substation and busbar reconfiguration. The resulting formulations balance security, congestion relief, switching effort, deviation from a reference topology, and, in some settings, operating cost, voltage quality, active-power losses, and time spent away from the reference configuration. Current research spans constrained episodic multi-objective reinforcement learning for corrective control, exact and evolutionary multi-objective optimization for sequential day-ahead planning, and deep reinforcement learning under AC power flow (Lautenbacher et al., 27 Jan 2025, Groeneveld et al., 5 May 2026, Lin et al., 15 Jul 2025).

1. Scope and relation to topology control

In the terminology used for power-grid operations, topology control encompasses corrective actions that change the electrical connectivity of the network to reroute flows and relieve congestion. Two principal classes are distinguished: Transmission switching (TS), defined as opening or closing line breakers to take branches in or out of service, and substation or busbar reconfiguration, defined as reassigning elements such as lines, transformers, and generators to busbars within node-breaker modeled substations. The recent MORL formulation for power-grid topology control explicitly notes that adjusting network topology includes both line switching and busbar changes, even though its experiments focus on substation or busbar reconfiguration in Grid2Op’s RTE 5-bus environment (Lautenbacher et al., 27 Jan 2025).

This broader framing matters because the same high-level decision problem appears in different operational timescales and with different physical abstractions. In the corrective-control setting, TS is modeled as a discrete action in an episodic environment with AC power-flow recalculation after each topology action. In the day-ahead planning setting, the decision variable is a 24-hour strategy $s=(g_t)_{t\in T}$, where each $g_t$ is a topology chosen from a finite hourly set $G_t$ derived from busbar coupler states, with the reference topology $\tilde g$ always available (Groeneveld et al., 5 May 2026). In the AC-DRL setting, TS is represented directly through binary line-status variables $x_{ij}\in\{0,1\}$, which gate the bus-admittance matrix and branch-flow equations (Lin et al., 15 Jul 2025).

The papers also distinguish TS from substation-only actions in operational consequences. For TS, the same MORL framework can be used by treating line open or close commands as discrete actions in the topology-control action space with the same vector-valued reward design and safety checks, but the data note additional protection and transient constraints, stricter feasibility checks, and potentially broader system-wide effects of line removals compared with intra-substation reassignments (Lautenbacher et al., 27 Jan 2025).

Outside power systems, the phrase “transmission switching” can denote a different problem class: in energy-harvesting broadcast communications, “transmitter switching” refers to choosing which transmitter is active so as to minimize transmission completion time and reduce the number of switches. That usage is mathematically multi-objective, but it is not a power-grid topology-control problem (Zhou et al., 2014).

2. Formal problem formulations

A central formulation models topology control as a constrained, episodic, multi-objective Markov decision process. In that setting, the state $s_t$ includes a network-topology representation, AC power-flow features, time and scenario context, and contingency status; the action $a_t$ includes discrete topology actions, including TS open or close commands and a do-nothing action; transition dynamics are given by AC power-flow recalculation via LightSim2Grid after the topology action; and feasibility is enforced by environment constraints, action masks, and expert-rule safety filters. The reward is vector-valued, with $r_t\in\mathbb{R}^d$ and $d=3$ in the reported study. Scalarization is performed with a weight vector $w\in\mathbb{R}^d$, $g_t$0, $g_t$1, and the scalarized return is $g_t$2, where (Lautenbacher et al., 27 Jan 2025)

$g_t$3

A second formulation treats day-ahead topology planning and congestion management as a sequential, multi-objective optimization problem over a finite horizon of 24 unit periods. The strategy is $g_t$4, with $g_t$5, and the Pareto objective vector is (Groeneveld et al., 5 May 2026)

$g_t$6

with

$g_t$7

Here $g_t$8 is worst-case line loading under $g_t$9 security, $G_t$0 is topological depth, $G_t$1 is the total switch count, and $G_t$2 is the total time not in the reference topology. The network model uses DC power flow for tractability, with worst-case contingency utilization computed over all single-element outages.

A third formulation embeds TS in AC network equations with binary line-status variables. Decision variables include generator active and reactive power, bus voltage magnitudes and angles, and line statuses $G_t$3. AC nodal power-balance constraints and branch-flow equations are evaluated on the topology induced by $G_t$4, and the multi-objective criterion is scalarized as (Lin et al., 15 Jul 2025)

$G_t$5

In the reinforcement-learning implementation, the instantaneous reward is $G_t$6, with an additional large penalty if islanding occurs or AC power flow diverges. This formulation uses an AC simulator rather than a DC approximation during learning.

These formulations differ in timescale, physics model, and optimization architecture, but they share a common structural feature: topology decisions are not evaluated against a single scalar criterion. Instead, they are embedded in explicitly competing objective systems.

3. Objective systems and characteristic trade-offs

The recent literature defines MOTS through objective vectors rather than through a single economic optimum. The main objective families are summarized below.

Setting	Decision scope	Objective set
MORL topology control (Lautenbacher et al., 27 Jan 2025)	Corrective control	Line loading, topological deviation, switching frequency
Sequential topology planning (Groeneveld et al., 5 May 2026)	Day-ahead, 24-hour horizon	Worst-case $G_t$7 line loading, topological depth, number of switching actions, time off reference
AC-DRL TS (Lin et al., 15 Jul 2025)	TS under AC power flow	Operating cost, voltage violations, line overload, active-power losses, switching penalty

In the MORL formulation, the reward vector consists of three components. The line-loading reward $G_t$8 is based on thermal margins, with per-line margin defined as (Lautenbacher et al., 27 Jan 2025)

$G_t$9

and

$\tilde g$0

Topological deviation is measured relative to the default, fully meshed topology; for TS, the distance from the base topology is

$\tilde g$1

summing both line-state differences and busbar-assignment differences. Switching frequency counts actions within an operator-relevant interval such as an hour or a day (Lautenbacher et al., 27 Jan 2025).

In the day-ahead planning formulation, the objective system explicitly reflects “real TSO decision criteria”: worst-case line loading under $\tilde g$2 security, topological depth, number of switching actions, and time spent in non-reference topologies over a 24-hour horizon. Topological depth is

$\tilde g$3

the switch count is

$\tilde g$4

and time off reference is

$\tilde g$5

This objective design distinguishes instantaneous structural complexity from cumulative deviation over time (Groeneveld et al., 5 May 2026).

In the AC-DRL formulation, the scalarized objective combines operating cost, voltage-magnitude violations beyond bounds, line overload beyond thermal limits, active-power losses, and a switching penalty $\tilde g$6, which penalizes removing lines from service. On IEEE 118-bus, the weights are reported as

$\tilde g$7

The data note that the cost term is computed as a difference relative to the all-lines-in-service baseline to balance scales (Lin et al., 15 Jul 2025).

Empirical trade-offs reported in the MORL study are consistent with the objective definitions. The $\tilde g$8–$\tilde g$9 projection shows conflict: improving margins often requires deviating from the default topology. The $x_{ij}\in\{0,1\}$0–$x_{ij}\in\{0,1\}$1 projection is generally aligned at low switching, but some switching is required to further increase margins. The $x_{ij}\in\{0,1\}$2–$x_{ij}\in\{0,1\}$3 projection shows that lower switching frequency can sustain higher deviation because the topology remains altered longer. The paper notes a directly relevant TS interpretation: a few decisive line actions can significantly reduce loading, but persistent line outages increase deviation (Lautenbacher et al., 27 Jan 2025).

The exact day-ahead study sharpens this trade-off structure. For the congested Dutch high-voltage day analyzed there, achieving approximately $x_{ij}\in\{0,1\}$4 worst-case line loading requires depth $x_{ij}\in\{0,1\}$5, five switches, and zero use of the reference topology. The same study reports that any solution with $x_{ij}\in\{0,1\}$6 necessarily abandons the reference topology during congested hours, although moderate schedules with depth $x_{ij}\in\{0,1\}$7 and at most two switches can still achieve $x_{ij}\in\{0,1\}$8 if they leave the reference topology during those intervals (Groeneveld et al., 5 May 2026). This suggests that “few switches” and “small deviation” are not interchangeable constraints: one may be reduced only by increasing the other.

4. Algorithmic approaches

One research line uses multi-objective reinforcement learning to approximate a Pareto front of corrective topology-control policies. The reported approach combines Deep Optimistic Linear Support (DOL) with Multi-Objective PPO (MOPPO). DOL approximates the Pareto front by iteratively solving scalarized RL problems at weight vectors $x_{ij}\in\{0,1\}$9 and building a convex coverage set of supported solutions. It starts from simplex-extrema weights, trains a single-policy RL method for each selected $s_t$0, evaluates the resulting value vector, adds improving solutions to the convex coverage set, computes new corner weights where the piecewise-linear convex support changes slope, and can reuse parameters from nearby trained models for faster convergence. MOPPO adapts PPO to vector rewards using a multi-head critic, with one head per objective, vector advantages obtained by GAE per objective, and scalarized policy updates using $s_t$1 inside the PPO clipped surrogate objective (Lautenbacher et al., 27 Jan 2025).

A second line uses exact multi-objective optimization for sequential planning. The block algorithm exploits temporal block structure: a block is a contiguous interval during which topology is constant, switches occur only at block boundaries, and the horizon is partitioned into consecutive non-overlapping blocks. For each block, the method precomputes the best achievable worst-case loading over the intersection of topologies available throughout that block, optionally subject to a depth bound. It then enumerates triples $s_t$2 consisting of a depth bound $s_t$3, a block configuration $s_t$4, and a non-consecutive set $s_t$5 of blocks assigned to the reference topology; computes the corresponding objective values; and performs nondominated filtering. For fixed operational bounds on depth and switch count, the evaluation count grows polynomially with the planning horizon, with overall complexity stated as $s_t$6 (Groeneveld et al., 5 May 2026).

The same study complements exact enumeration with a tailored NSGA-III heuristic. Chromosomes are direct encodings of hourly topology sequences $s_t$7. Initialization is structure-guided to enhance diversity in depth and switch count. Variation operators are problem-specific but simple: $s_t$8-point crossover with $s_t$9 preserves temporal contiguity and feasibility, and random-reset mutation replaces $a_t$0 by a random element of $a_t$1, again preserving feasibility. Selection uses NSGA-III with 100 uniformly distributed reference directions generated by Riesz $a_t$2-energy minimization (Groeneveld et al., 5 May 2026).

A third line uses deep reinforcement learning under AC power flow. The reported method is DDSAC, a dueling-based discrete Soft Actor-Critic. The critic uses the dueling decomposition

$a_t$3

together with twin Q-networks, target networks updated by Polyak averaging, and entropy regularization. The state includes generator outputs, bus voltages, line apparent flows, losses, loads, topology, and optionally a time or load-scenario index. The paper defines the action as a joint selection of line statuses $a_t$4, notes that the joint discrete action space has size $a_t$5, and states that practical tractability may require restricted actions or action masking. The architecture uses MLPs with two hidden layers of 256 units, Adam with learning rate $a_t$6, discount factor $a_t$7, mini-batch size 32, and soft-update rate $a_t$8 (Lin et al., 15 Jul 2025).

Across these approaches, combinatorial action growth is a recurrent issue. The MORL study addresses it through candidate-action pruning via expert rules, action masking, and a do-nothing action that remains available. The AC-DRL study notes the same issue from the perspective of the exponential joint action space. The exact day-ahead study circumvents online action selection by shifting computational effort into offline blockwise precomputation (Lautenbacher et al., 27 Jan 2025, Lin et al., 15 Jul 2025, Groeneveld et al., 5 May 2026).

5. Empirical results and comparative evidence

The MORL study reports quantitative gains in Pareto-front approximation and operational robustness. Against a random-sampling baseline that feeds random weight vectors to MOPPO, DOL achieves HV $a_t$9 versus $r_t\in\mathbb{R}^d$0, sparsity $r_t\in\mathbb{R}^d$1 versus $r_t\in\mathbb{R}^d$2, and IGD $r_t\in\mathbb{R}^d$3 versus $r_t\in\mathbb{R}^d$4, with DOL contributing more points to the Super CCS. Using episode duration $r_t\in\mathbb{R}^d$5 as an operational metric independent of rewards, the best multi-objective policy outperforms a single-objective PPO trained on $r_t\in\mathbb{R}^d$6 only: $r_t\in\mathbb{R}^d$7 versus $r_t\in\mathbb{R}^d$8 without contingencies, $r_t\in\mathbb{R}^d$9 versus $d=3$0 under moderately frequent $d=3$1 events, and $d=3$2 versus $d=3$3 under highly frequent $d=3$4 events. Under reduced training budgets, the corresponding values are $d=3$5 versus $d=3$6 at low budget, $d=3$7 versus $d=3$8 at moderate budget, and $d=3$9 versus $w\in\mathbb{R}^d$0 at full budget. The paper summarizes these findings with the headline that generated MORL policies are 30% more successful in preventing grid failure under contingencies and 20% more effective when training budget is reduced than common single-objective RL (Lautenbacher et al., 27 Jan 2025).

The exact day-ahead study uses real operational data from the Dutch high-voltage grid operated by TenneT TSO. For the severe-congestion day analyzed there, the block algorithm computes the full Pareto front in under three minutes on a 64-core VM with 32 GB RAM, after enumerating 163,807,652 feasible strategies and retaining 83 distinct Pareto-optimal objective points after nondominated filtering. The same paper reports that the evolutionary algorithm converges toward but does not recover the exact front. Across configurations, it recovers about 6% of Pareto points and about 3–4% across the first ten dominance fronts, with the second front covered relatively better at about 15%. In the best reported configuration, the final MOEA front contains 9 Pareto points versus 83 for the exact front, and across the first ten fronts the cumulative totals are 56 points versus 2,533 (Groeneveld et al., 5 May 2026).

The AC-DRL study evaluates DDSAC on the IEEE 118-bus system. It reports that DDSAC converges faster and achieves significantly higher cumulative reward than PPO and DDQN, stabilizing within approximately 50 steps, and that it exhibits lower variance. Across time, DDSAC consistently reduces generator operating cost relative to baseline, voltage-magnitude violations, active-power losses, and line overloads compared with PPO and DDQN. The paper states qualitative superiority for these operational metrics but does not provide exact percentage reductions (Lin et al., 15 Jul 2025).

Taken together, these results differentiate three kinds of evidence. The MORL study emphasizes corrective-control robustness and Pareto coverage under contingencies. The exact day-ahead study provides a ground-truth front against which heuristics can be judged. The AC-DRL study emphasizes learning stability and simultaneous improvement of multiple AC-operational criteria on a larger benchmark system.

6. Safety, operator use, and unresolved issues

MOTS is constrained not only by network physics but also by operational safety logic. In the MORL formulation, action feasibility is enforced by Grid2Op constraints and expert-rule safety filters, including common expert rules from prior work, with infeasible or unsafe actions masked and post-decision checks reverting to do-nothing when necessary. The data explicitly note that TS requires stricter feasibility and $w\in\mathbb{R}^d$1 checks, including radialization checks, breaker-status interlocks, and transient or oscillation risk screening, alongside post-decision power-flow and contingency scanning (Lautenbacher et al., 27 Jan 2025).

The AC-DRL study uses a different safety mechanism: heavy penalties for islanding and AC-power-flow divergence. It also lists practical deployment measures, including action masking to prevent cut-set openings, security filters, near-violation penalties, and projection layers that map unsafe actions back to the nearest feasible set. This indicates that the reported DDSAC results are achieved under soft-constraint learning rather than under hard operational guarantees (Lin et al., 15 Jul 2025).

From an operator perspective, the multi-objective setting is used to support preference-dependent selection rather than to replace human judgment with a single canonical policy. After DOL finishes, policies trained at non-extrema weights are ranked by episode duration $w\in\mathbb{R}^d$2, and the best multi-objective policy $w\in\mathbb{R}^d$3 is recommended. Operators can elicit preferences, inspect Pareto-front projections such as $w\in\mathbb{R}^d$4 and $w\in\mathbb{R}^d$5, and choose policies that match current priorities such as bad weather, asset maintenance, or scheduled switch plans. The same study suggests maintaining a library of policies corresponding to different weight vectors and switching among them according to real-time preferences (Lautenbacher et al., 27 Jan 2025).

The exact day-ahead work provides a different form of decision support: a complete menu of Pareto-optimal trade-offs over security, depth, switch count, and time off reference. Because each Pareto point corresponds to block configurations, depth bounds, and reference-block assignments, the representation is directly interpretable in terms of which hours are off reference and how many switching actions are required. The paper also positions the exact front as a benchmark for future heuristic and learning-based methods (Groeneveld et al., 5 May 2026).

The main unresolved issues are also consistent across the literature. The MORL study identifies scalability from a 5-bus system to large grids, especially because TS adds many lines and therefore expands the combinatorial action space. It lists stronger action pruning based on PTDF or LODF preselection, hierarchical RL, multi-agent decompositions, preference-conditioned policies, transfer learning, constrained RL such as CPO, Lyapunov-based safety layers, interpretability via feature attribution, and model-based RL or AlphaZero-style tree search as directions for future work (Lautenbacher et al., 27 Jan 2025). The exact day-ahead study identifies DC rather than AC modeling, deterministic forecasts, omission of transient stability and switching transients, and the need for heavy offline precomputation of per-topology load flows as central limitations (Groeneveld et al., 5 May 2026). The AC-DRL study similarly identifies lack of hard $w\in\mathbb{R}^d$6 guarantees, exponential action growth, and the absence of probabilistic reliability metrics such as EENS or LOLLP from the reward as open problems (Lin et al., 15 Jul 2025).

In aggregate, the current literature portrays MOTS as a family of Pareto-structured topology-optimization problems rather than a single optimization model. Corrective-control MORL, exact day-ahead enumeration, and AC-DRL each expose a different aspect of the same underlying tension: reducing congestion or operating cost typically requires accepting some combination of increased topological deviation, higher switching burden, greater time off reference, or more elaborate safety logic.