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Register a new userSolving the Travelling Thief Problem based on Item Selection Weight and Reverse Order Allocation
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Peipei Kang
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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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 underlying 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 set 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.
We introduce and analyze new envy-based fairness concepts for agents with weights that quantify their entitlements in the allocation of indivisible items. We propose two variants of weighted envy-freeness up to one item (WEF1): strong, where envy can be eliminated by removing an item from the envied agents bundle, and weak, where envy can be eliminated either by removing an item (as in the strong version) or by replicating an item from the envied agents bundle in the envying agents bundle. We show that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists and can be computed in pseudo-polynomial time; moreover, an allocation that maximizes the weighted Nash social welfare may not be strongly WEF1, but always satisfies the weak version of the property. Moreover, we establish that a generalization of the round-robin picking sequence algorithm produces in polynomial time a strongly WEF1 allocation for an arbitrary number of agents; for two agents, we can efficiently achieve both strong WEF1 and Pareto optimality by adapting the adjusted winner procedure. Our work highlights several aspects in which weighted fair division is richer and more challenging than its unweighted counterpart.
Many real-world optimization problems have multiple interacting components. Each of these can be NP-hard and they can be in conflict with each other, i.e., the optimal solution for one component does not necessarily represent an optimal solution for the other components. This can be a challenge for single-objective formulations, where the respective influence that each component has on the overall solution quality can vary from instance to instance. In this paper, we study a bi-objective formulation of the traveling thief problem, which has as components the traveling salesperson problem and the knapsack problem. We present a weighted-sum method that makes use of randomiz
When a new user just signs up on a website, we usually have no information about him/her, i.e. no interaction with items, no user profile and no social links with other users. Under such circumstances, we still expect our recommender systems could attract the users at the first time so that the users decide to stay on the website and become active users. This problem falls into new user cold-start category and it is crucial to the development and even survival of a company. Existing works on user cold-start recommendation either require additional user efforts, e.g. setting up an interview process, or make use of side information [10] such as user demographics, locations, social relations, etc. However, users may not be willing to take the interview and side information on cold-start users is usually not available. Therefore, we consider a pure cold-start scenario where neither interaction nor side information is available and no user effort is required. Studying this setting is also important for the initialization of other cold-start solutions, such as initializing the first few questions of an interview.
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