Tabu-Enhanced Simulation Optimization

• TESO is a memory-driven metaheuristic framework designed for optimizing noisy, computationally expensive simulation environments.
• It integrates short-term Tabu lists with long-term elite memories to guide adaptive exploration and intensification, improving solution quality.
• TESO has proven effective in applications like queueing systems, circuit design, and scheduling, outperforming standard approaches.

Tabu-Enhanced Simulation Optimization (TESO) defines a class of memory-driven metaheuristics tailored for simulation optimization in contexts characterized by noisy objective functions, high computational expense, and complex, multimodal search spaces. Key algorithmic features include short-term and long-term memory, adaptive exploration-exploitation schedules, and strategies for intensification and diversification, with typical applications ranging from queueing systems to dynamic engineering design models (Soykan et al., 30 Dec 2025, Connor, 2014, Connor et al., 2016, Soykan, 8 Feb 2025).

1. Formal Algorithmic Framework and Variants

TESO, as systematized by Soykan et al. (Soykan et al., 30 Dec 2025), advances a single-trajectory, direct-search metaheuristic for noisy black-box problems. The essential loop maintains a First-In-First-Out (FIFO) short-term Tabu List $\mathcal{T}$, and a long-term Elite Memory $\mathcal{E}$ tracking best-so-far (elite) solutions. At each iteration, TESO either diversifies through uniform random sampling or intensifies by perturbing elite members, governed by a probabilistic control ($p_{\text{div}}$).

Tabu restriction is enforced: any candidate identified as recently visited (by hash or signature) is blocked from evaluation unless an aspiration criterion is met, in which the candidate's sample mean is better than the current best. Formally, in the minimization setting,

$$\text{Aspiration}(x, f_{\text{best}}) \iff \mu^{(t)} < f_{\text{best}}$$

where $\mu^{(t)}$ is the sample mean estimated from $n_{\text{rep}}$ replications. Both $\mathcal{T}$ and $\mathcal{E}$ have fixed capacities ($C_T, C_E$), with the latter engaged during intensification—random perturbation of elite members within an adaptively shrinking search radius $\eta(t)$. Termination occurs upon exhausting the candidate evaluation budget $T$ or upon reaching the maximum consecutive no-improvement threshold $\Delta t_{\text{max}}$.

Multi-thread TESO (Connor, 2014) generalizes the approach to $K > 1$ independent search fronts, each with its own tabu memory, sharing intermediate memory. This threading increases robustness and the likelihood of escaping local optima at the expense of increased computational cost per evaluation cycle.

2. Mathematical Components and Exploration–Exploitation Dynamics

Central to TESO are three principal memory-driven mechanisms, formalized as follows:

• Short-term Tabu List: At iteration $t$,

$$\mathcal{T}_t = \left\{h^{(t-1)}, \ldots, h^{(t-C_T)}\right\}$$

representing the hashed or discretized recent candidates. Blocked candidates are neither simulated nor considered unless exception (aspiration) is triggered.

• Elite Memory: Candidate-elites $(x_i, \mu_i)$ are sorted and capped at $C_E$. Intensification is realized by drawing $x_e \sim \text{Uniform}(\mathcal{E}_t)$ and generating

$x^{(t)} = x_e + \eta(t) z$

where $z$ is zero-mean random noise, with $\eta$ following a linear decay schedule:

$$\eta(t) = \eta_{\text{init}} + (\eta_{\text{final}}-\eta_{\text{init}})\cdot\frac{t}{T}$$

to orchestrate the exploration-exploitation balance.

• Diversification: Random sampling of candidates is performed in the initial $n_{\text{init}}$ cycles or with probability $p_{\text{div}}$ at later stages. Diversification counters premature convergence and drives search into unexplored regions.

Hybridizations incorporating intermediate and long-term memory (as in (Connor, 2014, Connor et al., 2016)) enable further intensification/diversification triggers and allow resets to promising or random states when progress stalls, introducing a reactive modulation absent in canonical Tabu Search.

3. Application Domains and Case Study Results

TESO has demonstrated utility in simulation-based queueing, dynamic circuit design, and multi-objective scheduling. Example testbeds include:

• M/M/3 Queue Optimization (Soykan et al., 30 Dec 2025): Decision variable $\mu \in [1.0,4.0]$ is optimized to minimize

$$J(\mu) = \mathbb{E}\left[W(3, \mu, \omega)\right] + C \cdot 3 \mu^2$$

with objective approximated over $n_{\text{rep}}=30$ simulation replications. Full TESO delivered consistently lower objective values and variance compared to ablations. Table summarizing performance:

Algorithm	Final Best Mean ± StdDev	Avg Time (s)
Pure Random	4.11 ± 0.20	53.3
TESO–noElite	2.89 ± 0.18	101.4
TESO–noTabu	2.72 ± 0.13	113.5
Full TESO	2.53 ± 0.06	132.8

• Fluid Power Circuit Optimization (Connor, 2014, Connor et al., 2016): Coupling of TESO variants to the Bathfp simulation engine yielded state variable tracking and relief-flow minimization benefits, outperforming single-thread trajectories in compounded objectives and robustness metrics (e.g., $\omega_1$, $\omega_2$ speed tracking errors, $Q_{\text{RV}}$ minimization).
• Multi-Objective Runway Operations Scheduling (Soykan, 8 Feb 2025): A hybrid Tabu–Scatter Search coupled with discrete-event simulation produced Pareto-optimal trade-offs in runway utilization, delays, and fairness, outperforming deterministic and FCFS schemes in both overall efficiency and acceptability of sequencing shifts.

4. Comparative Algorithmic Features and Memory Structures

TESO distinguishes itself within the broader class of simulation optimization metaheuristics by its explicit use of:

• Short-term Tabu Restriction: Precludes re-evaluation of recent candidates, enhancing diversification and minimizing wasted simulation resources in noisy landscapes.
• Long- and Intermediate-term Elite Memories: Guide search into promising basins, incentivizing concentrated exploitation. Sharing intermediate memory across threads (multi-thread TESO) enhances cooperation and escape latent convergence.
• Aspiration Criteria: Allow exceptional candidates to override memory restrictions, preventing missed optima due to premature blocking.
• Adaptive Perturbation Schedules: Modulate the norm of search steps, favoring coarse exploration early and fine-tuned exploitation in later phases.

These features have found analogues in parallelized stochastic algorithms and hybridizations, e.g. Tabu–Scatter Search, where population-level memory structures enable Pareto-set construction and diversity archiving (Soykan, 8 Feb 2025).

5. Implementation Details and Hyperparameter Tuning

Empirical results indicate robust, predictable benefits from memory structure tuning. For unimodal queueing examples (Soykan et al., 30 Dec 2025):

• Tabu List capacity $C_T \approx 15$ ($5\%$ of budget)
• Elite Memory $C_E \approx 10$ ($3\%$ of budget)
• Diversification probability $p_{\text{div}} = 0.2$
• Replications per candidate $n_{\text{rep}} = 30$
• Noise schedule $\eta_{\text{init}} = 0.2$, $\eta_{\text{final}} = 0.01$
• No-improvement cutoff $\Delta t_{\text{max}} = 50$

General guidelines recommend setting $C_T$ for $5$–$10\%$ non-reappearance, $C_E$ for $5$–$15$ best-so-far solutions, $\eta_{\text{init}}$ at $5$–$10\%$ of the variable domain decaying to $1$–$2\%$, and $p_{\text{div}}$ in $[0.1, 0.3]$. Sensitivity analyses suggest modest impact in low-dimensional, unimodal cases, but the optimal hyperparameter regime may shift for multimodal or high-dimensional models and warrants separate sensitivity studies (Soykan et al., 30 Dec 2025, Connor, 2014, Connor et al., 2016).

6. Limitations, Extensions, and Future Directions

TESO algorithms have demonstrated value in escaping cycling, enhancing solution quality robustness, and facilitating efficient allocation of simulation budget. Nevertheless, observed limitations include:

• No guarantee of global optimum per run, particularly in highly multimodal or noisy landscapes.
• Empirical sensitivity to penalty formulation and hyperparameters, requiring iterative calibration.
• Scalability constraints for large candidate dimensions or expensive simulation models, motivating research in surrogate-model acceleration and reactive memory adjustment (Connor et al., 2016).
• Extension to multi-objective domains: Hybrid Tabu–Scatter Search frameworks (as in runway scheduling (Soykan, 8 Feb 2025)) explicitly archive Pareto sets rather than imposing penalty aggregation, aligning with contemporary simulation optimization practices.

Potential future enhancements include surrogate-assisted filtering to reduce evaluation cost, adaptive tenures or memory thresholds based on progress metrics, further parallelization strategies, and hybrid line-search or local-refinement on elite solutions.

7. Context within Simulation Optimization and Related Metaheuristics

TESO occupies a distinctive position among metaheuristics by combining memory-induced cycling avoidance with adaptive, noise-tolerant search schedules. Compared to genetic algorithms, simulated annealing, or pattern search methods, its core advantage resides in minimizing redundant simulation runs and systematically targeting regions of the solution space previously unvisited or known to be high-performing (Soykan et al., 30 Dec 2025, Connor, 2014, Connor et al., 2016). Its explicit aspiration criterion and elite-guided intensification set it apart even among memory-based search paradigms. Hybrid models (e.g. Tabu–Scatter Search (Soykan, 8 Feb 2025)) reflect a broader trend in integrating population-based diversity management and Pareto archiving.

TESO methodologies remain widely applicable to resource-intensive simulation models in engineering design, operational research, and scheduling, with ongoing methodological refinements targeting computational tractability and noise-resilience.