Tourism industries are rapidly increased for the last few years especially in Malaysia. In order to attract more tourists, Malaysian Governance encourages any effort to increase Malaysian tourism industry. One of the efforts in attracting more tourists in Malacca, Malaysia is a duck tour. Duck tour is an amphibious sightseeing tour that works in two types of engines, hence, it required a huge c...

Imagine you have traveled to an unfamiliar city. Before you start your daily tour around the city, you need to know a good route. In Network Theory (NT), this is the traveling salesman problem (TSP). A dynamic programming algorithm is often used for solving this problem. However, when the road network of the city is very complicated and dense, which is usually the case, it will take too long fo...

Many problems of both practical and theoretical importance concern themselves not only with finding a solution but also finding a ‘best’ solution in some sense. As a concrete example, let us consider the travelling salesperson problem (TSP): a salesperson has to visit some specified towns on a tour starting and ending in her/his home town; in which order should the towns be visited in order to ...

This paper presents three heuristic functions that aim to reduce the search cost for the knight tour problem. The first heuristic, h1a, is an interesting case of study that illustrates heuristic analysis, although it fails to obtain solutions. Heuristic h2 is an enhancement of the Warnsdorff method, discussed as heuristic h1b. All heuristics are used in conjunction with a greedy algorithm to de...

The (Euclidean) Vehicle Routing Allocation Problem (VRAP) is a generalization of Euclidean TSP. We do not require that all points lie on the salesman tour. However, points that do not lie on the tour are allocated, i.e., they are directly connected to the nearest tour point, paying a higher (per-unit) cost. More formally, the input is a set of points P ⊂ R and functions α : P → [0,∞) and β : P ...

The Stochastic Eulerian Tour Problem (SETP) seeks the Eulerian tour of minimum expected length on an undirected Eulerian graph, when demand on the arcs that have to be serviced is probabilistic. In an earlier paper, we have shown that the SETP is NP-hard and derived several properties of the optimal tour. In this paper, we develop three constructive heuristics for the SETP. The first two are gr...

Genetic algorithms are good search techniques for finding solutions to NP problems. However, their high degree of randomness sometimes fails to guide the search towards finding solutions within reasonable costs. The Knight’s tour problem is an example of where pure GAs fail (practically) to find solutions. Combining GAs with other approaches on the other hand can highly improve their efficiency...

We consider the problem of reversing a tour (i1, i2, . . . , il) in a directed graph G = (V, E) with positive integer vertices V and edges E ⊆ V × V , where ij ∈ V and (ij, ij+1) ∈ E for all j = 1, . . . , l − 1. The tour can be processed in last-in-first-out order as long as the size of the corresponding stack does not exceed the available memory. This constraint is violated in most cases when...