Solving Graph Homomorphism and Subgraph Isomorphism Problems Faster Through Clique Neighbourhood Constraints

Graph homomorphism problems involve finding adjacency-preserving mappings between two given graphs. Although theoretically hard, these problems can often be solved in practice using constraint programming algorithms. We show how techniques from the state-of-the-art in subgraph isomorphism solving can be applied to broader graph homomorphism problems, and introduce a new form of filtering based upon clique-finding. We demonstrate empirically that this filtering is effective for the locally injective graph homomorphism and subgraph isomorphism problems, and gives the first practical constraint programming approach to finding general graph homomorphisms.

Stability in Matching Markets with Complex Constraints

We develop a model of many-to-one matching markets in which agents with multiunit demand aim to maximize a cardinal linear objective subject to multidimensional knapsack constraints. The choice functions of agents with multiunit demand are therefore not substitutable. As a result, pairwise stable matchings may not exist and even when they do, may be highly inefficient. We provide an algorithm that finds a group-stable matching that approximately satisfies all the multidimensional knapsack constraints. The novel ingredient in our algorithm is a combination of matching with contracts and Scarf’s Lemma. We show that the degree of the constraint violation under our algorithm is proportional to the sparsity of the constraint matrix. The algorithm, therefore, provides practical constraint violation bounds for applications in contexts, such as refugee resettlement, day care allocation, and college admissions with diversity requirements. Simulations using refugee resettlement data show that our approach produces outcomes that are not only more stable, but also more efficient than the outcomes of the Deferred Acceptance algorithm. Moreover, simulations suggest that in practice, constraint violations under our algorithm would be even smaller than the theoretical bounds. This paper was accepted by Gabriel Weintraub, revenue management and market analytics.

Multi-Objective Operation of Cascade Hydropower Reservoirs Using TOPSIS and Gravitational Search Algorithm with Opposition Learning and Mutation

In this research, a novel enhanced gravitational search algorithm (EGSA) is proposed to resolve the multi-objective optimization model, considering the power generation of a hydropower enterprise and the peak operation requirement of a power system. In the proposed method, the standard gravity search algorithm (GSA) was chosen as the fundamental execution framework; the opposition learning strategy was adopted to increase the convergence speed of the swarm; the mutation search strategy was chosen to enhance the individual diversity; the elastic-ball modification strategy was used to promote the solution feasibility. Additionally, a practical constraint handling technique was introduced to improve the quality of the obtained agents, while the technique for order preference by similarity to an ideal solution method (TOPSIS) was used for the multi-objective decision. The numerical tests of twelve benchmark functions showed that the EGSA method could produce better results than several existing evolutionary algorithms. Then, the hydropower system located on the Wu River of China was chosen to test the engineering practicality of the proposed method. The results showed that the EGSA method could obtain satisfying scheduling schemes in different cases. Hence, an effective optimization method was provided for the multi-objective operation of hydropower system.

Finding the Quickest Straight-Line Trajectory for a Three-Wheeled Omnidirectional Robot under Input Voltage Constraints

We provide an analytical solution to the problem of generating the quickest straight-line trajectory for a three-wheeled omnidirectional mobile robot, under the practical constraint of limited voltage. Applying the maximum principle to the geometric properties of the input constraints, we find that an optimal input vector of motor voltages has at least one extreme value when the orientation of the robot is fixed and two extreme values when rotation is allowed. We can find an explicit representation of the optimal vector for a motion under fixed orientation. We derive several properties of quickest straight-line trajectories and verify them through simulation. We show that the quickest trajectory when rotation is allowed is always faster than the quickest with fixed orientation.

A Weighted Multiobjective Optimization Method for Mixed-Model Assembly Line Problem

Mixed-model assembly line (MMAL) is a type of assembly line where several distinct models of a product are assembled. MMAL is applied in many industrial environments today because of its greater variety in demand. This paper considers the objective of minimizing the work overload (i.e., the line balancing problem) and station-to-station product flows. Generally, transportation time between stations are ignored in the literature. In this paper, Multiobjective Mixed-Integer Programming (MOMIP) model is presented to optimize these two criteria simultaneously. Also, this MOMIP model incorporates a practical constraint that allows to add parallel stations to assembly line to decrease higher station time. In the last section, MOMIP is applied to optimize the cycle time and transportation time simultaneously in mixed-model assembly line of a real consumer electronics firm in Turkey, and computational results are presented.