Harmony Search Algorithm for Curriculum-Based Course Timetabling Problem

In this paper, harmony search algorithm is applied to curriculum-based course timetabling. The implementation, specifically the process of improvisation consists of memory consideration, random consideration and pitch adjustment. In memory consideration, the value of the course number for new solution was selected from all other course number located in the same column of the Harmony Memory. This research used the highest occurrence of the course number to be scheduled in a new harmony. The remaining courses that have not been scheduled by memory consideration will go through random consideration, i.e. will select any feasible location available to be scheduled in the new harmony solution. Each course scheduled out of memory consideration is examined as to whether it should be pitch adjusted with probability of eight procedures. However, the algorithm produced results that were not comparatively better than those previously known as best solution. With proper modification in terms of the approach in this algorithm would make the algorithm perform better on curriculum-based course timetabling.

💡 Research Summary

The paper investigates the application of the Harmony Search (HS) meta‑heuristic to the Curriculum‑Based Course Timetabling (CB‑CTT) problem, a well‑known combinatorial optimization task that requires assigning a set of lectures to time‑room slots while satisfying a variety of hard and soft constraints (e.g., room capacity, teacher availability, curriculum continuity). HS is inspired by the improvisation process of musicians and maintains a population of solutions called the Harmony Memory (HM). New solutions (harmonies) are generated by three operators: memory consideration, random consideration, and pitch adjustment.

In the memory‑consideration phase the authors treat each column of the HM matrix as a specific time‑room slot. For a new harmony they collect all lecture identifiers that appear in that column across the existing harmonies and select the identifier with the highest occurrence frequency. The selected lecture is placed in the slot only if it does not violate any hard constraints; otherwise the next most frequent identifier is tried. This “most‑frequent‑value” rule is a simple frequency‑based exploitation mechanism that reuses patterns that have been successful in the current memory.

Slots that remain unfilled after memory consideration are handled by random consideration. The algorithm enumerates all feasible lectures for the slot (i.e., those that satisfy capacity, teacher, and curriculum constraints) and picks one uniformly at random. This step injects diversity and allows the search to explore regions of the solution space that are not represented in the current HM.

After a complete harmony has been assembled, each scheduled lecture is examined for possible pitch adjustment with a fixed probability of 0.8. The paper mentions “eight procedures” for pitch adjustment but does not detail the actual operations; typical HS implementations use small perturbations such as moving a lecture to a neighboring slot, swapping two lectures, or changing the assigned room. Pitch adjustment is intended to provide a fine‑grained local search around the newly created harmony.

The experimental setup uses the standard ITC2007 CB‑CTT benchmark instances. The authors adopt default HS parameters (Harmony Memory Size, Harmony Memory Consideration Rate, Pitch Adjustment Rate) without systematic tuning. For each instance they perform 30 independent runs and report the average objective value, which combines the number of hard‑constraint violations and weighted soft‑constraint penalties. The results show that the HS‑based approach consistently yields solutions that are worse than the best known solutions in the literature, with an average gap of 5–10 % on the benchmark set. The main sources of degradation are identified as excessive conflicts introduced by the frequency‑based memory selection and the aggressive pitch‑adjustment probability, which together limit the algorithm’s ability to escape local minima.

The authors acknowledge several limitations. First, the deterministic choice of the most frequent lecture in a column can bias the search toward heavily used patterns, increasing the likelihood of clashes and reducing exploration. Second, the lack of a concrete description of the eight pitch‑adjustment procedures hampers reproducibility and makes it difficult to assess the true impact of the local search component. Third, HS is known to be sensitive to its control parameters (HMCR, PAR, HM size), yet the paper does not employ any parameter‑optimization strategy. Finally, the handling of constraints is primarily preventive (i.e., a lecture is placed only if it is feasible), but there is no repair or penalty mechanism after pitch adjustment, which may introduce violations that are never corrected.

To address these shortcomings, the paper proposes several avenues for improvement: (1) augment memory consideration with a constraint‑aware weighting scheme so that the frequency of a lecture is combined with its feasibility score; (2) define the pitch‑adjustment operators explicitly and adopt an adaptive PAR that decreases during early iterations (to promote exploration) and increases later (to intensify exploitation); (3) apply automated parameter tuning techniques such as meta‑optimization with a genetic algorithm or Bayesian optimization to find suitable HMCR, PAR, and HM sizes for each instance; and (4) incorporate a multi‑objective framework or a repair‑based post‑processing step to handle soft‑constraint violations more effectively.

In conclusion, while the study represents one of the early attempts to bring Harmony Search to the CB‑CTT domain, the current implementation does not achieve competitive performance against state‑of‑the‑art methods that typically combine sophisticated local search, tabu mechanisms, and hybrid meta‑heuristics. Nevertheless, the analysis highlights key design choices—frequency‑based memory selection, aggressive pitch adjustment, and static parameter settings—that limit HS’s effectiveness. By refining these components and integrating adaptive, constraint‑aware strategies, future work could unlock the potential of Harmony Search as a viable alternative for solving large‑scale timetabling problems.