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تسجيل مستخدم جديدSolving the Travelling Thief Problem based on Item Selection Weight and Reverse Order Allocation
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The Travelling Thief Problem (TTP) is a challenging combinatorial optimization problem that attracts many scholars. The TTP interconnects two well-known NP-hard problems: the Travelling Salesman Problem (TSP) and the 0-1 Knapsack Problem (KP). Increasingly algorithms have been proposed for solving this novel problem that combines two interdependent sub-problems. In this paper, TTP is investigated theoretically and empirically. An algorithm based on the score value calculated by our proposed formulation in picking items and sorting items in the reverse order in the light of the scoring value is proposed to solve the problem. Different approaches for solving the TTP are compared and analyzed; the experimental investigations suggest that our proposed approach is very efficient in meeting or beating current state-of-the-art heuristic solutions on a comprehensive set of benchmark TTP instances.
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The travelling thief problem (TTP) is a multi-component optimisation problem involving two interdependent NP-hard components: the travelling salesman problem (TSP) and the knapsack problem (KP). Recent state-of-the-art TTP solvers modify the underlyi
ng TSP and KP solutions in an iterative and interleaved fashion. The TSP solution (cyclic tour) is typically changed in a deterministic way, while changes to the KP solution typically involve a random search, effectively resulting in a quasi-meandering exploration of the TTP solution space. Once a plateau is reached, the iterative search of the TTP solution space is restarted by using a new initial TSP tour. We propose to make the search more efficient through an adaptive surrogate model (based on a customised form of Support Vector Regression) that learns the characteristics of initial TSP tours that lead to good TTP solutions. The model is used to filter out non-promising initial TSP tours, in effect reducing the amount of time spent to find a good TTP solution. Experiments on a broad range of benchmark TTP instances indicate that the proposed approach filters out a considerable number of non-promising initial tours, at the cost of omitting only a small number of the best TTP solutions.
The travelling thief problem (TTP) is a representative of multi-component optimisation problems with interacting components. TTP combines the knapsack problem (KP) and the travelling salesman problem (TSP). A thief performs a cyclic tour through a se
t of cities, and pursuant to a collection plan, collects a subset of items into a rented knapsack with finite capacity. The aim is to maximise profit while minimising renting cost. Existing TTP solvers typically solve the KP and TSP components in an interleaved manner: the solution of one component is kept fixed while the solution of the other component is modified. This suggests low coordination between solving the two components, possibly leading to low quality TTP solutions. The 2-OPT heuristic is often used for solving the TSP component, which reverses a segment in the tour. Within TTP, 2-OPT does not take into account the collection plan, which can result in a lower objective value. This in turn can result in the tour modification to be rejected by a solver. We propose an expanded form of 2-OPT to change the collection plan in coordination with tour modification. Items regarded as less profitable and collected in cities located earlier in the reversed segment are substituted by items that tend to be more profitable and not collected in cities located later in the reversed segment. The collection plan is further changed through a modified form of the hill-climbing bit-flip search, where changes in the collection state are only permitted for boundary items, which are defined as lowest profitable collected items or highest profitable uncollected items. This restriction reduces the time spent on the KP component, allowing more tours to be evaluated by the TSP component within a time budget. The proposed approaches form the basis of a new cooperative coordination solver, which is shown to outperform several state-of-the-art TTP solvers.
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