Ride-hailing services have expanded the role of shared mobility in passenger transportation systems, creating new markets and creative planning solutions for major urban centers. In this paper, we consider their use for the first-mile or last-mile passenger transportation in coordination with a mass transit service to provide a seamless multimodal transportation experience for the user. A system that provides passengers with predictable information on travel and waiting times in their commutes is immensely valuable. We envision that the passengers will inform the system of their desired travel and arrival windows so that the system can jointly optimize the schedules of passengers. The problem we study balances minimizing travel time and the number of trips taken by the last-mile vehicles, so that long-term planning, maintenance, and environmental impact are all taken into account. We focus on the case where the last-mile service aggregates passengers by destination. We show that this problem is NP-hard, and we propose a decision diagram–based branch-and-price decomposition model that can solve instances of real-world size (10,000 passengers spread over an hour, 50 last-mile destinations, 600 last-mile vehicles) in computational time (∼1 minute) that is orders of magnitude faster than the solution times of other methods appearing in the literature. Our experiments also indicate that aggregating passengers by destination on the last-mile service provides high-quality solutions to more general settings. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods and Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2019.0163 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2019.0163 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

We apply logic-based Benders decomposition (LBBD) to two-stage stochastic planning and scheduling problems in which the second stage is a scheduling task. We solve the master problem with mixed integer/linear programming and the subproblem with constraint programming. As Benders cuts, we use simple no-good cuts as well as analytic logic-based cuts we develop for this application. We find that LBBD is computationally superior to the integer L-shaped method. In particular, a branch-and-check variant of LBBD can be faster by several orders of magnitude, allowing significantly larger instances to be solved. This is due primarily to computational overhead incurred by the integer L-shaped method while generating classic Benders cuts from a continuous relaxation of an integer programming subproblem. To our knowledge, this is the first application of LBBD to two-stage stochastic optimization with a scheduling second-stage problem and the first comparison of LBBD with the integer L-shaped method. The results suggest that LBBD could be a promising approach to other stochastic and robust optimization problems with integer or combinatorial recourse. Summary of Contribution: We study an important class of optimization problems, namely, two-stage stochastic programs with integer recourse, which are known to be extremely difficult to solve in general. We focus on an application in which the second-stage problem is a scheduling problem, a first in the literature to the best of our knowledge. Our study exemplifies how one can exploit the combinatorial structure of the scheduling problem to derive novel analytic Benders cuts and use them within a branch-and-check algorithm. The proposed algorithm solves instances that are intractable for commercial solvers and state-of-the-art decomposition-based methods, such as the integer L-shaped method. We believe that our study will inspire further research in the use of hybrid logic-based optimization methods for solving stochastic combinatorial optimization problems.

An important step in the development of value alignment (VA) systems in artificial intelligence (AI) is understanding how VA can reflect valid ethical principles. We propose that designers of VA systems incorporate ethics by utilizing a hybrid approach in which both ethical reasoning and empirical observation play a role. This, we argue, avoids committing “naturalistic fallacy,” which is an attempt to derive “ought” from “is,” and it provides a more adequate form of ethical reasoning when the fallacy is not committed. Using quantified model logic, we precisely formulate principles derived from deontological ethics and show how they imply particular “test propositions” for any given action plan in an AI rule base. The action plan is ethical only if the test proposition is empirically true, a judgment that is made on the basis of empirical VA. This permits empirical VA to integrate seamlessly with independently justified ethical principles. This article is part of the special track on AI and Society.

Numerous AI-assisted resource allocation decisions need to balance the conflicting goals of fairness and efficiency. Our paper studies the challenging task of defining and modeling a proper fairness-efficiency trade off. We define fairness with Rawlsian leximax fairness, which views the lexicographic maximum among all feasible outcomes as the most equitable; and define efficiency with Utilitarianism, which seeks to maximize the sum of utilities received by entities regardless of individual differences. Motivated by a justice-driven trade off principle: prioritize fairness to benefit the less advantaged unless too much efficiency is sacrificed, we propose a sequential optimization procedure to balance leximax fairness and utilitarianism in decision-making. Each iteration of our approach maximizes a social welfare function, and we provide a practical mixed integer/linear programming (MILP) formulation for each maximization problem. We illustrate our method on a budget allocation example. Compared with existing approaches of balancing equity and efficiency, our method is more interpretable in terms of parameter selection, and incorporates a strong equity criterion with a thoroughly balanced perspective.

We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with the minimum bandwidth problem. The method strengthens a known bound for a given problem by formulating a dual problem whose feasible solutions are partial branching trees. It solves the dual problem with a “worst-bound” local search heuristic that explores neighboring partial trees. After proving some optimality properties of the heuristic, we show that it substantially improves known combinatorial bounds for the minimum bandwidth problem with a modest amount of computation. It also obtains significantly tighter bounds than depth-first and breadth-first branching, demonstrating that the dual perspective can lead to better branching strategies when the object is to find valid bounds.

We propose a deontological approach to machine (or AI) ethics that avoids some weaknesses of an intuition-based system, such as that of Anderson and Anderson. In particular, it has no need to deal with conflicting intuitions, and it yields a more satisfactory account of when autonomy should be respected. We begin with a "dual standpoint'' theory of action that regards actions as grounded in reasons and therefore as having a conditional form that is suited to machine instructions. We then derive ethical principles based on formal properties that the reasons must exhibit to be coherent, and formulate the principles using quantified modal logic. We conclude that deontology not only provides a more satisfactory basis for machine ethics but endows the machine with an ability to explain its actions, thus contributing to transparency in AI.

We propose a general branch-and-bound algorithm for discrete optimization in which binary decision diagrams (BDDs) play the role of the traditional linear programming relaxation. In particular, relaxed BDD representations of the problem provide bounds and guidance for branching, and restricted BDDs supply a primal heuristic. Each problem is given a dynamic programming model that allows one to exploit recursive structure, even though the problem is not solved by dynamic programming. A novel search scheme branches within relaxed BDDs rather than on values of variables. Preliminary testing shows that a rudimentary BDD-based solver is competitive with or superior to a leading commercial integer programming solver for the maximum stable set problem, the maximum cut problem on a graph, and the maximum 2-satisfiability problem. Specific to the maximum cut problem, we tested the BDD-based solver on a classical benchmark set and identified tighter relaxation bounds than have ever been found by any technique, nearly closing the entire optimality gap on four large-scale instances.

Recent research in hybrid optimization shows that a combination of technologies that exploits their complementary strengths can significantly speed up computation. The use of high-level metaconstraints in the problem formulation can achieve a substantial share of these computational gains by better communicating problem structure to the solver. During the solution process, however, metaconstraints give rise to reformulations or relaxations that introduce auxiliary variables, and some of the variables in one metaconstraint’s reformulation may be functionally the same as or related to variables in another metaconstraint’s reformulation. These relationships must be recognized to obtain a tight overall relaxation. We propose a modeling scheme based on semantic typing that systematically addresses this problem while providing simpler, self-documenting models. It organizes the model around predicates and declares variables by associating each with a predicate through a keyword that is analogous to a database query. We present a series of examples to illustrate this idea over a wide variety of applications.

We explore the idea of obtaining bounds on the value of an optimization problem from a discrete relaxation based on binary decision diagrams (BDDs). We show how to construct a BDD that represents a relaxation of a 0-1 optimization problem, and how to obtain a bound for a separable objective function by solving a shortest (or longest) path problem in the BDD. As a test case we apply the method to the maximum independent set problem on a graph. We find that for most problem instances, it delivers tighter bounds in less computation time, than state-of-the-art integer programming software obtains by solving a continuous relaxation augmented with cutting planes.

We propose an exact solution method for a routing and capacity installation problem in networks. Given an input graph, the problem is to route traffic from a set of source nodes to a sink node and to install transmission facilities on the edges of the graph to accommodate the flow at minimum cost. We give a branch-and-bound algorithm that solves relaxations obtained by approximating the noncontinuous cost function by its lower convex envelope. The approximations are refined by branching on the flow ranges on selected edges. Our computational experiments indicate that this method is effective in solving moderate-size problems and provides very good candidate solutions early in the branch-and-bound tree.

Because of their complementary strengths, optimization and constraint programming can be profitably merged. Their integration has been the subject of increasing commercial and research activity. This paper summarizes and contrasts the characteristics of the two fields; in particular, how they use logical inference in different ways, and how these ways can be combined. It sketches the intellectual background for recent efforts at integration. It traces the history of logic-based methods in optimization and the development of constraint programming in artificial intelligence. It concludes with a review of recent research, with emphasis on schemes for integration, relaxation methods, and practical applications.

We implement several recent algorithms for the satisfiabiiity problem in propositional logic and test them on a wide variety of benchmark problems. We focus on algorithms based on some kind of tree search, including three versions of the classical Davis-Putnam-Loveland method, the method of Jeroslow and Wang, the Horn Relaxation method of Gallo and Urbani, the branch and cut method of Hooker and Fedjki, and the column subtraction method of Harche and Thompson. We design experiments so as to identify the important factors that influence the performance of tree search algorithms. We find that the choice of which variable to branch on is a key factor. Methods based on weak relaxations (e.g., Horn relaxation) are best for easy problems, and the column subtraction method is clearly the most robust, as it was the only algorithm to solve the hardest problems. if Davis-Putnam-Loveland is properly implemented, it and the remaining methods generally excel on problems that are neither too easy nor too hard. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

This paper addresses a prediction problem occurring frequently in practice. The problem consists in predicting the value of a function on the basis of discrete observational data that are incomplete in two senses. Only certain arguments of the function are observed, and the function value is observed only for certain combinations of values of these arguments. The problem is considered under a monotonicity condition that is natural in many applications. Applications to tax auditing, medicine, and real estate valuation are discussed. In particular, a special class of problems is identified for which the best monotone prediction can be found in polynomial time.

The class of Horn clause sets in propositional logic is extended to a larger class for which the satisfiability problem can still be solved by unit resolution in linear time. It is shown that to every arborescence there corresponds a family of extended Horn sets, where ordinary Horn sets correspond to stars with a root at the center. These results derive from a theorem of Chandresekaran that characterizes when an integer solution of a system of inequalities can be found by rounding a real solution in a certain way. A linear-time procedure is provided for identifying “hidden” extended Horn sets (extended Horn but for complementation of variables) that correspond to a specified arborescence. Finally, a way to interpret extended Horn sets in applications is suggested.

Input resolution and “unit support” resolution (a generalization of unit resolution) are complete inference methods for Horn clauses in propositional logic. We show that they have a close analog in cutting plane theory. Namely, a logical clause can be deduced using input or unit support resolution if and only if it belongs to the elementary closure of the premises and is therefore a rank one cut in Chvátal's sense. This connection leads to a cutting plane algorithm for solving non-Horn inference problems. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Abstract We show how to locate optimally p new facilities (servers) on a network so as to minimize cost, where cost can be any convex function of the distances between demand points (nodes) and a closest server. The algorithm is generally practical only for small p (perhaps 2, 3, or 4), but it admits a large number of servers with locations fixed beforehand. The classical p‐median, p‐center, and p‐facility cent‐dian problems are special cases. Other problems of this form include a large number of obnoxious facility problems, problems in which the objective is to minimize an Lk norm of distances, and a wide variety of problems, problems in which the objective is to minimize an Lk norm of distances, and a wide variety of problems in which equity or social welfare is a a factor.