Lecture 8 — Tabu Search and Memory-Based Heuristics

Short-term and long-term memory, tabu lists, aspiration

1 Learning Objectives

By the end of this lecture, you should be able to:

understand the motivation for memory-based search
explain the core components of tabu search
distinguish short-term and long-term memory mechanisms
design tabu lists and aspiration criteria
analyze intensification and diversification in tabu search

2 Lecture Roadmap

This lecture proceeds in eight blocks:

motivation for memory-based search
tabu search core loop and admissible move logic
short-term memory, tabu lists, and tenure effects
aspiration criteria and override logic
move-selection strategy and computational implications
long-term memory for diversification
tuning, diagnostics, and practical failure modes
comparison and hybridization with simulated annealing

3 Motivation: Beyond Greedy and Probabilistic Search

Hill climbing and simulated annealing represent two fundamentally different responses to the problem of local optimality:

Hill climbing relies on purely greedy improvement and therefore converges rapidly, but almost inevitably stagnates at local optima. Once no improving move exists, the search terminates with no mechanism for recovery.
Simulated annealing introduces randomness to escape local optima by occasionally accepting worsening moves. While this probabilistic behavior improves robustness, it can also lead to slow convergence and sensitivity to parameter tuning.

Tabu search (TS) introduces a third and complementary idea:

Use memory to guide the search intelligently.

Rather than relying on randomness alone, tabu search explicitly records information about the search history and uses this information to shape future decisions. By remembering recent moves, solution attributes, and long-term usage patterns, tabu search is able to:

prevent cycling and repetitive behavior,
enforce strategic exploration of new regions, and
intensify the search around promising areas in a controlled manner.

This memory-based guidance allows tabu search to accept non-improving moves deterministically, without sacrificing direction or control. As a result, tabu search occupies a unique position between greedy descent and probabilistic search: it is systematic rather than random, yet flexible rather than rigid.

In modern soft computing, tabu search is valued for its ability to incorporate domain knowledge, enforce intelligent restrictions, and maintain strong search momentum, making it a powerful and versatile metaheuristic for large-scale combinatorial optimization problems.

4 What Is Tabu Search?

Tabu search is a metaheuristic framework that systematically enhances local search by incorporating explicit memory structures to guide the search process. Its central idea is to use information from the search history to make more informed decisions, rather than relying solely on greedy improvement or randomness.

At a high level, tabu search operates as follows:

it explores the neighborhood of the current solution, often exhaustively or selectively,
it allows non-improving moves, enabling the search to move away from local optima,
it temporarily forbids certain moves or solution attributes through tabu restrictions in order to prevent cycling, and
it applies aspiration criteria to override tabu status when a move leads to a sufficiently high-quality solution.

Unlike basic local search, tabu search does not simply react to the current objective value. Instead, the search trajectory is influenced by the history of visited solutions, recent moves, and attribute usage. This historical information provides context, allowing the algorithm to avoid repeating unproductive patterns and to explore the solution space more strategically.

A defining characteristic of tabu search is that it replaces randomness with structured memory-based control. The algorithm deterministically selects the best admissible move at each iteration, subject to tabu restrictions, while memory mechanisms regulate intensification and diversification. This makes tabu search both robust and highly adaptable across a wide range of combinatorial optimization problems.

In essence, tabu search transforms local search from a short-sighted improvement process into a strategic exploration guided by memory, balancing exploitation of good regions with deliberate exploration of new ones.

5 Generic Tabu Search Framework

A generic tabu search algorithm can be described as a structured extension of local search, augmented with memory-based control mechanisms. The high-level procedure is as follows:

Generate an initial feasible solution \(s\)
- typically obtained via a constructive heuristic or simple local search,
- feasibility is maintained throughout the search.
Initialize tabu memory structures
- create and empty tabu lists or attribute memories,
- set parameters such as tabu tenure and aspiration rules.
Repeat
- Generate the neighborhood \(\mathcal{N}(s)\) of the current solution,
- Identify tabu moves or attributes and temporarily forbid them,
- Apply aspiration criteria to allow tabu moves that meet predefined quality thresholds,
- Select the best admissible move, even if it is non-improving,
- Update the current solution by applying the selected move,
- Update tabu memory, recording attributes of the executed move and expiring old tabu entries.
Stop when a termination criterion is met
- such as a maximum number of iterations,
- a time limit, or
- lack of improvement over a specified number of iterations.

At the end of the algorithm, return the best solution encountered during the entire search, not necessarily the final solution. This is important because tabu search may temporarily move to worse solutions as part of its exploration strategy.

5.1 Implementation-Oriented Tabu Search Skeleton

Input: initial solution s, tabu tenure tau, stopping criterion
best <- s
tabu_memory <- empty
while not stop:
  generate candidate moves from N(s)
  filter tabu moves unless aspiration is satisfied
  choose best admissible move m*
  apply m* to obtain s
  update tabu_memory with attributes of m*
  expire entries older than tau
  if f(s) better than f(best): best <- s
return best

This structure makes the main control points explicit: candidate generation, admissibility filtering, move selection, and memory updates.

5.2 Key Observations

Tabu search always selects the best admissible move, ensuring strong intensification at each iteration.
The use of tabu restrictions prevents short-term cycling while encouraging exploration of new regions.
Allowing non-improving moves enables escape from local optima without relying on randomness.

This framework is highly adaptable: the definition of neighborhoods, tabu attributes, tenure lengths, and aspiration criteria can be customized to suit a wide variety of optimization problems, making tabu search one of the most flexible and powerful metaheuristic paradigms.

6 Key Idea: Memory in Search

The defining feature of tabu search is the explicit use of memory to guide and control the search process. Unlike greedy or probabilistic methods that rely solely on the current solution, tabu search incorporates information about the past behavior of the search to make more informed decisions.

Memory in tabu search can be broadly categorized according to its time horizon, with each type serving a distinct purpose.

6.1 Short-Term Memory

Short-term memory operates over a limited number of recent iterations and is primarily responsible for preventing unproductive behavior.

Its main roles are:

preventing immediate cycling
- forbids reversing recent moves or revisiting recently used solution attributes,
- ensures the search continues to progress rather than oscillate.
supporting local intensification
- forces the search to explore new neighbors around a promising region,
- encourages structured local exploration rather than repetitive moves.

Short-term memory is typically implemented via tabu lists with finite tenure.

6.2 Long-Term Memory

Long-term memory captures information accumulated over a much longer portion of the search and is used to guide strategic decisions.

Its main roles are:

promoting diversification
- discourages overuse of frequently visited solution attributes,
- encourages exploration of underexplored or unexplored regions.
guiding global search behavior
- influences restart strategies, penalties, or objective modifications,
- helps balance intensification and diversification over time.

Long-term memory is often implemented through frequency-based statistics, elite solution sets, or adaptive penalties.

6.3 Strategic Impact of Memory

By integrating both short-term and long-term memory, tabu search transforms local search from a purely reactive improvement process into a strategic exploration of the solution space. Memory enables the algorithm to learn from past experience, avoid known pitfalls, and adapt its behavior dynamically, which is a key reason for the effectiveness of tabu search on large and complex optimization problems.

7 Short-Term Memory and Tabu Lists

7.1 Tabu Lists

The most recognizable and widely used component of tabu search is the tabu list, which implements short-term memory.

A tabu list:

records information about recent moves or solution attributes,
temporarily forbids these items by declaring them tabu, and
automatically removes tabu status after a predefined number of iterations, known as the tabu tenure.

The primary purpose of the tabu list is to prevent cycling, that is, to avoid the search repeatedly undoing recent moves or oscillating among a small set of solutions. By enforcing temporary prohibitions, tabu search is forced to explore new configurations even when the best local move would revert a recent decision.

7.2 What Can Be Tabu?

The specific content of the tabu list depends on the problem structure and the chosen representation. Common options include:

Moves
- forbidding the reversal of a recent move,
- for example, preventing a binary variable that was just flipped from being flipped back immediately.
Attributes
- forbidding certain solution characteristics rather than entire moves,
- for example, preventing an item from being assigned to a recently used position or facility.
Solutions
- forbidding complete solutions that were recently visited,
- rarely used in large-scale problems due to excessive memory requirements.

In practice, attribute-based tabu restrictions are the most common and scalable approach. They generalize well, require limited memory, and effectively prevent short-term cycling without overly constraining the search.

7.3 Tabu Tenure

The tabu tenure specifies how long a move or attribute remains tabu after it is applied.

Short tenure
- provides weak protection against cycling,
- may allow the search to revert too quickly to previously visited solutions.
Long tenure
- enforces stronger diversification,
- but risks forbidding useful or improving moves for too long.

Tabu tenure can be implemented as:

fixed, using a constant number of iterations, or
adaptive, where the tenure changes dynamically based on search behavior, progress, or problem size.

Selecting an appropriate tabu tenure is critical for performance. Too small a value reduces the effectiveness of tabu search, while too large a value may overly restrict the search and slow convergence. Balancing tabu tenure is therefore a key design decision in practical tabu search implementations.

7.4 Tuning Tabu Tenure in Practice

A practical rule is to relate tenure to neighborhood size and problem dimension, then tune empirically.

Common behaviors:

tenure too small:
- frequent backtracking and short cycles,
- weak diversification.
tenure too large:
- excessive move prohibition,
- slow local refinement and possible stagnation.

Practical workflow:

start with a moderate fixed tenure
monitor cycling and stagnation indicators
increase tenure when cycling dominates
decrease tenure when progress becomes too constrained

Many robust implementations use adaptive tenure windows rather than a single fixed value.

8 Aspiration Criteria

In tabu search, tabu restrictions are intentionally temporary and conditional, not absolute. An aspiration criterion provides a mechanism to override tabu status when enforcing the restriction would be counterproductive.

The most common and widely used aspiration rule is:

A tabu move is allowed if it produces a solution that is better than any solution seen so far.

This rule ensures that tabu restrictions never block significant progress toward high-quality solutions. If a move leads to a new global best solution, it should be accepted regardless of its tabu status.

8.1 Purpose of Aspiration Criteria

Aspiration criteria serve several important roles:

Preventing over-restriction
- ensures that tabu lists do not prohibit genuinely beneficial moves,
- avoids stagnation caused by overly aggressive tabu tenure.
Preserving intensification
- allows the search to exploit promising regions fully,
- ensures that the best solutions remain accessible.
Balancing control and flexibility
- tabu restrictions guide the search,
- aspiration criteria restore flexibility when needed.

8.2 Alternative Aspiration Rules

While global-best aspiration is the most common, other aspiration criteria may also be used:

allow a tabu move if it improves upon the current solution by a specified margin,
allow tabu moves after a certain number of iterations without improvement,
allow tabu moves that satisfy problem-specific quality or feasibility thresholds.

These variants provide additional control and can be tailored to specific problem structures.

8.3 Practical Insight

Aspiration criteria are essential for making tabu search robust. Without them, tabu restrictions could inadvertently prevent the algorithm from reaching high-quality solutions. With well-designed aspiration rules, tabu search maintains both discipline and adaptability, ensuring steady progress throughout the search.

9 Move Selection in Tabu Search

Move selection is a defining element of tabu search and a key reason for its strong performance on difficult optimization problems. Unlike simple local search, tabu search deliberately decouples move acceptance from immediate improvement.

In tabu search:

non-improving (worsening) moves are allowed,
the algorithm evaluates a neighborhood of candidate moves,
tabu restrictions are applied to filter out forbidden moves, and
the best admissible move is selected deterministically.

This selection strategy fundamentally differentiates tabu search from both greedy descent and probabilistic methods.

9.1 Best Admissible Move Principle

At each iteration, tabu search selects:

the best move in the neighborhood that is not tabu, or that satisfies an aspiration criterion.

Key aspects:

“best” refers to the objective value after applying the move,
the move does not need to improve the current solution,
admissibility is determined by tabu status and aspiration rules.

As a result, the search may temporarily move to worse solutions, but it does so strategically, not randomly.

9.2 Contrast with Hill Climbing

Hill climbing enforces a strict rule:

only improving moves are accepted,
search terminates at the first local optimum.

Tabu search relaxes this rule:

worsening moves are allowed to escape local optima,
tabu restrictions prevent cycling back to recently visited solutions,
the search continues even when no improving neighbor exists.

This makes tabu search far more robust on rugged or deceptive landscapes.

9.3 Contrast with Simulated Annealing

Simulated annealing also allows worsening moves, but:

acceptance is probabilistic,
behavior depends heavily on temperature and randomness.

In contrast, tabu search:

is primarily deterministic,
relies on memory rather than probability,
makes deliberate choices based on neighborhood evaluation and search history.

This determinism often leads to more predictable and stable performance.

9.4 Intensification and Diversification via Move Selection

Move selection in tabu search implicitly balances:

intensification
- selecting the best admissible move exploits high-quality regions,
- aspiration criteria reinforce exploitation of promising areas.
diversification
- tabu restrictions forbid recent moves or attributes,
- forcing the search to explore new regions of the solution space.

Thus, move selection is not only about improvement but also about strategic exploration.

9.5 Practical Implications

The best admissible move strategy implies that:

tabu search does not require carefully tuned probabilities,
performance depends strongly on neighborhood quality and memory design,
the algorithm progresses steadily even on flat or deceptive landscapes.

This makes tabu search particularly effective for large-scale combinatorial problems where purely greedy or purely random approaches fail.

9.6 Summary

Move selection in tabu search is characterized by:

deterministic choice of the best admissible move,
acceptance of non-improving moves when strategically useful,
explicit control through tabu lists and aspiration criteria.

Together, these features make tabu search a powerful memory-based alternative to both greedy local search and probabilistic metaheuristics.

9.7 Candidate Lists and Scalability

On large neighborhoods, evaluating all moves can be expensive. A common strategy is to use a candidate list:

sample or pre-rank a subset of promising moves,
apply tabu/aspiration filtering only within this subset,
choose the best admissible move from candidates.

Benefits:

lower per-iteration cost,
better scalability to large instances,
often negligible quality loss when candidate lists are well designed.

This is one of the most important engineering choices in high-performance tabu-search implementations.

10 Intensification in Tabu Search

Intensification in tabu search refers to deliberately concentrating the search effort around high-quality solutions or regions of the solution space in order to extract as much improvement as possible from them. Unlike greedy local search, intensification in tabu search is controlled by memory, not by rigid acceptance rules.

Tabu search intensifies the search through several complementary mechanisms.

10.1 Intensification via Best Admissible Moves

At each iteration, tabu search selects the best admissible move in the neighborhood, even if that move is non-improving. This has two important effects:

the search consistently follows the strongest available descent directions,
local structure around promising solutions is thoroughly exploited.

Because cycling is prevented by tabu restrictions, the search can push deeper into a region than hill climbing without becoming trapped.

10.2 Role of Short-Term Memory

Short-term memory, implemented through tabu lists, plays a central role in intensification.

By temporarily forbidding recently used moves or attributes, tabu search:

avoids immediate backtracking,
enforces exploration of alternative improving paths within the same region,
encourages structured local exploration rather than random wandering.

This produces a deeper and more systematic local search than classical descent methods.

10.3 Elite Solutions and Intensification Phases

Many tabu search implementations explicitly track elite solutions, defined as the best solutions found so far.

Intensification can then be strengthened by:

restarting the search from an elite solution,
reducing tabu tenure to allow finer local adjustments,
restricting neighborhoods to smaller, more focused move sets.

This allows the algorithm to revisit promising regions with fresh search dynamics and refined control.

10.4 Modified Tabu Restrictions for Intensification

Intensification can also be achieved by adjusting tabu restrictions:

shortening tabu tenure to allow more flexible local moves,
relaxing certain tabu attributes while keeping others active,
temporarily disabling diversification mechanisms.

These adjustments allow the search to concentrate on incremental improvements around high-quality configurations.

10.5 Intensification vs Greedy Exploitation

Although intensification resembles greedy exploitation, there is a critical difference:

greedy methods stop at local optima,
tabu search intensifies beyond local optima by allowing controlled non-improving moves.

This enables tabu search to uncover improving sequences of moves that greedy descent cannot reach.

10.6 Balance with Diversification

Excessive intensification can lead to stagnation. Effective tabu search therefore alternates between:

intensification phases, focusing on elite regions, and
diversification phases, pushing the search into unexplored areas.

The power of tabu search lies in its ability to switch between these modes dynamically using memory-based control.

10.7 Summary

Intensification in tabu search is achieved through:

deterministic selection of the best admissible moves,
short-term memory that prevents cycling while enabling deep local exploration,
elite solution management and controlled restarts, and
adaptive adjustment of tabu restrictions.

Together, these mechanisms allow tabu search to exploit promising regions far more effectively than simple local search, while still retaining the ability to escape local optima.

11 Long-Term Memory and Diversification

11.1 Motivation

While short-term memory in tabu search is effective at preventing immediate cycling and supporting local intensification, it does not by itself ensure that the search explores different regions of the solution space. Over time, the search may still become confined to a limited area, repeatedly visiting structurally similar solutions.

Long-term memory is introduced to counteract this tendency by explicitly encouraging diversification. Its role is strategic rather than tactical: instead of controlling the next few moves, it influences the overall trajectory of the search.

11.2 Role of Long-Term Memory

Long-term memory mechanisms are designed to:

identify regions of the solution space that have been overexplored,
detect regions that have been rarely or never visited,
bias future search decisions toward underexplored structures, and
maintain a balance between exploration and exploitation over long time horizons.

Unlike short-term memory, which is typically iteration-based, long-term memory accumulates information over many iterations.

11.3 Forms of Long-Term Memory

Several forms of long-term memory are commonly used in tabu search.

11.3.1 Frequency-Based Memory

Frequency-based memory records how often certain solution attributes or moves appear during the search.

Typical attributes include:

assignment of an item to a location,
activation of a facility or resource,
selection of a particular edge or arc in routing problems.

Diversification is encouraged by:

penalizing frequently used attributes in the objective function, or
favoring moves that introduce rarely used attributes.

This approach systematically pushes the search away from familiar patterns and toward novel configurations.

11.3.2 Elite Solution Memory

Elite solution memory stores a collection of the best solutions found so far.

These elite solutions are used to:

intensify the search by restarting from high-quality solutions,
recombine features of good solutions, or
guide diversification by comparing current solutions against elite structures.

Elite memory provides a long-term reference that preserves valuable information discovered during the search.

11.3.3 Strategic Oscillation

Strategic oscillation deliberately allows the search to move between:

feasible solutions, and
controlled infeasible solutions.

By temporarily relaxing constraints, the search can:

cross infeasible regions that separate distant feasible basins,
escape from regions blocked by strict feasibility requirements, and
discover high-quality feasible solutions unreachable by purely feasible moves.

Strategic oscillation is particularly effective in constrained optimization problems.

11.4 Diversification Strategies in Practice

Long-term memory supports diversification through several practical strategies:

Penalty adjustment
- dynamically increase penalties for frequently used attributes,
- reduce penalties for rare or unused attributes.
Guided restarts
- restart the search from solutions constructed using rarely used components,
- avoid purely random restarts.
Adaptive tabu tenure
- increase tabu tenure when cycling or stagnation is detected,
- decrease tenure during intensification phases.

These strategies ensure that diversification is guided and informed, rather than random.

11.5 Interaction with Intensification

Effective tabu search alternates between:

intensification, driven mainly by short-term memory and elite solutions, and
diversification, driven by long-term memory mechanisms.

Long-term memory ensures that intensification does not become excessive and that the search periodically explores new regions where better solutions may exist.

11.6 Summary

Long-term memory is essential for making tabu search a truly global optimization method. It:

prevents long-term stagnation,
promotes systematic exploration of the solution space,
complements short-term memory and intensification, and
enables tabu search to scale to large and complex optimization problems.

By integrating short-term and long-term memory, tabu search achieves a powerful balance between depth and breadth in the search process.

12 Tabu Search vs Simulated Annealing

Tabu search and simulated annealing are two classical metaheuristics designed to overcome the limitations of greedy local search. While both allow non-improving moves and aim to escape local optima, they rely on fundamentally different mechanisms.

Aspect	Tabu Search	Simulated Annealing
Acceptance of worse moves	Deterministic (best admissible move)	Probabilistic (temperature-based)
Use of memory	Explicit and structured	None (memoryless)
Control of cycling	Tabu lists and tenure	Randomness
Exploration mechanism	Memory-guided diversification	Stochastic acceptance
Exploitation mechanism	Intensification via best moves	Gradual cooling
Parameter sensitivity	Moderate (tabu tenure, memory rules)	High (initial temperature, cooling rate)
Typical behavior	Strategic exploration	Stochastic exploration
Reproducibility	High (often deterministic)	Lower (randomized runs differ)

12.1 Key Conceptual Differences

Tabu search uses deterministic decision-making guided by memory. At each iteration, it selects the best admissible move, even if that move worsens the objective value. Memory structures prevent cycling and steer the search toward unexplored regions in a controlled manner.

Simulated annealing, in contrast, relies on randomized acceptance. Worse moves are accepted with a probability that decreases over time, controlled by the temperature schedule. There is no explicit memory of past decisions, and diversification emerges implicitly through randomness.

12.2 Strengths in Practice

Tabu search is particularly effective when:
- neighborhoods are well structured,
- cycling is a major concern,
- deterministic behavior and reproducibility are desired.
Simulated annealing is particularly effective when:
- the landscape contains many deep local optima,
- a simple implementation is preferred,
- problem-specific memory structures are difficult to design.

12.3 Complementarity

In modern soft computing practice, tabu search and simulated annealing are often combined rather than compared. For example:

simulated annealing can be used to diversify the search before applying tabu search for intensification,
tabu search can be embedded inside a probabilistic framework, or
both can be used as components of larger hybrid or matheuristic algorithms.

Together, they illustrate two complementary philosophies of escaping local optima: memory-driven strategic control versus probability-driven stochastic exploration.

13 Practical Strengths of Tabu Search

Tabu search has several practical advantages that make it one of the most robust and widely used metaheuristics for combinatorial optimization:

Effective cycling avoidance Explicit tabu restrictions prevent the search from undoing recent moves, eliminating short cycles that commonly trap basic local search.
Consistently high-quality solutions By always selecting the best admissible move, tabu search maintains strong intensification while still allowing temporary deterioration when needed.
Reduced dependence on randomness Unlike probabilistic methods, tabu search relies primarily on deterministic rules and memory, leading to more stable and reproducible performance.
Strong performance on structured problems Tabu search is particularly effective when solution attributes and neighborhoods have clear structure, such as in scheduling, routing, assignment, facility location, and network design problems.

In many applications, tabu search reaches high-quality solutions quickly and improves them steadily over long runs.

14 Practical Limitations

Despite its effectiveness, tabu search is not without challenges:

Design complexity Choosing appropriate tabu attributes (moves, variables, assignments) requires problem-specific insight.
Parameter tuning Tabu tenure, memory length, and aspiration rules strongly influence performance and often require experimentation.
Increased algorithmic complexity Long-term memory, diversification strategies, and adaptive tenure mechanisms add implementation overhead.
Scalability of memory structures Poorly designed memory schemes can increase computational cost or unintentionally restrict the search.

Because of these factors, tabu search is rarely used as a completely standalone method in large systems.

14.1 Diagnostics and Failure Modes

Useful runtime diagnostics:

repeated-solution frequency (cycling signal),
best-objective improvement rate,
proportion of moves blocked by tabu restrictions,
distribution of attribute frequencies (diversification signal).

Common failure modes and fixes:

Failure mode	Typical cause	Practical fix
persistent short cycling	tenure too short	increase tenure or strengthen attribute-based tabu
search over-constrained	tenure too long or overly broad tabu attributes	relax tenure or narrow tabu definition
weak diversification	short-term memory only	add long-term frequency penalties or guided restarts
high runtime per iteration	full neighborhood evaluation too expensive	introduce candidate lists / partial evaluation

15 Role of Tabu Search in Modern Soft Computing

Tabu search occupies a central position in the evolution of soft computing methods:

it established memory-based control as a core optimization principle,
it inspired later metaheuristics that incorporate history and learning,
it demonstrated that deterministic strategies can compete with stochastic methods, and
it serves as a powerful intensification engine within hybrid frameworks.

In modern practice, tabu search is frequently embedded within larger algorithms, combined with local search, evolutionary methods, or exact solvers. Understanding tabu search provides deep insight into how strategic memory and controlled exploration can dramatically improve heuristic optimization performance.

15.1 Key Takeaways

tabu search enhances local search with memory
tabu lists prevent cycling and encourage exploration
aspiration criteria override overly restrictive tabu rules
short-term memory intensifies search
long-term memory enables diversification

16 Mini Exercises

Tabu list design Consider a binary optimization problem with decision variables \(x \in \{0,1\}^n\).
- Define an appropriate tabu list (move-based or attribute-based).
- Explain which recent moves or variable changes should be declared tabu and why this prevents cycling.
Effect of tabu tenure
- Describe how a short tabu tenure versus a long tabu tenure affects the search trajectory.
- Discuss the impact of tabu tenure on intensification, diversification, and convergence speed.
Comparison with simulated annealing
- Compare tabu search and simulated annealing in terms of how they escape local optima.
- Focus on the roles of memory, determinism, and randomness in their exploration mechanisms.
Aspiration criteria design
- Propose an aspiration criterion for a routing or scheduling problem.
- Explain under what conditions a tabu move should be allowed and how this criterion balances flexibility and control.
Candidate-list design and trade-off
- Propose a candidate-list strategy for a large neighborhood routing or scheduling problem.
- Explain how candidate-list size affects runtime and solution quality.
- Suggest one adaptive rule for changing candidate-list size during search.

17 References for This Chapter

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Battiti, R., & Tecchiolli, G. (1995). Training neural nets with the reactive tabu search. IEEE Transactions on Neural Networks, 6(5), 1185-1200. DOI: 10.1109/72.410361
Gendreau, M., & Potvin, J.-Y. (Eds.). (2019). Handbook of Metaheuristics (3rd ed.). Springer. DOI: 10.1007/978-3-319-91086-4