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generalizing the successive shortest path algorithm to solve the multi-objective assignment problem

Categories Multi-Criteria Optimization, Network Optimization, Other Topics Tags , ,

We introduce a novel characterization of the efficient solutions to the Multi-objective Assignment Problem (MAP), relying solely on Network Flow theory. This result establishes that the set of efficient assignments restricted to the first $k$ origin-destination pairs in the associated bipartite graph can be derived incrementally from the efficient solutions corresponding to the first $k-1$ … Read more

Minimal Regret Walras Equilibria for Combinatorial Markets

Categories Game Theory Tags , , , , ,

We consider combinatorial multi-item markets and propose the notion of a ∆-regret Walras equilibrium, which is an allocation of items to players and a set of item prices that achieve the following goals: prices clear the market, the allocation is capacity-feasible, and the players’ strategies lead to a total regret of ∆. The regret is … Read more

Branch-and-Cut for Computing Approximate Equilibria of Mixed-Integer Generalized Nash Games

Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Game Theory Tags , , , ,

Generalized Nash equilibrium problems with mixed-integer variables constitute an important class of games in which each player solves a mixed-integer optimization problem, where both the objective and the feasible set is parameterized by the rivals’ strategies. However, such games are known for failing to admit exact equilibria and also the assumption of all players being … Read more

A guided tour through the zoo of paired optimization problems

Categories Bilevel Optimization, Game Theory, Nonlinear Optimization Tags , , , , , , , , ,

Many mathematical models base on the coupling of two or more optimization problems. This paper surveys possibilities to couple two optimization problems and discusses how solutions of the different models are interrelated with each other. The considered pairs stem from the fields of standard and generalized Nash equilibrium problems, optimistic and pessimistic bilevel problems, saddle … Read more

Data-Driven Optimization for Meal Delivery: A Reinforcement Learning Approach for Order-Courier Assignment and Routing at Meituan

Categories Dynamic Programming, Meta Heuristics, Transportation Tags

The rapid growth of online meal delivery has introduced complex logistical challenges, where platforms must dynamically assign orders to couriers while accounting for demand uncertainty, courier autonomy, and service efficiency. Traditional dispatching methods, often focused on short-term cost minimization, fail to capture the long-term implications of assignment decisions on system-wide performance. This paper presents a … Read more

blockSQP 2: exploiting structure to improve performance

Categories Dynamic Programming, Nonlinear Optimization Tags , , , ,

Abstract One approach to solving optimal control problems is Bock’s direct multiple shoot- ing method. This method yields lifted nonlinear optimization problems (NLPs) with a spe- cific block structure. Exploiting this structure via tailored optimization algorithms can be computationally beneficial. We propose such methods, primarily within the framework of fil- ter line search sequential quadratic … Read more

Global Multi-Objective Stochastic Optimization: Error Bounds and Convergence Rates

Categories Global Optimization, Multi-Criteria Optimization, Optimization of Simulated Systems Tags , , , ,

Consider the context of solving a multi-objective stochastic optimization problem with one or more continuous objective functions to global optimality on a compact feasible set. For a simple algorithm that consists of selecting a finite set of feasible points using a space-filling design, expending the same number of simulation replications at each point to estimate … Read more

A Multivariate Loss Ratio Approach for Systemic Risk Measurement and Allocation

Categories Finance and Economics, Multi-Criteria Optimization, Other Topics Tags , , , ,

The primary challenges in systemic risk measurement involve determining an overall reserve level of risk capital and allocating it to different components based on their systemic relevance. In this paper, we introduce a multivariate loss ratio measure (MLRM), which is the minimum amount of capital to be injected into a financial system such that the … Read more

Properties of Enclosures in Multiobjective Optimization

Categories Global Optimization, Multi-Criteria Optimization, Nonlinear Optimization Tags , ,

A widely used approximation concept in multiobjective optimization is the concept of enclosures. These are unions of boxes defined by lower and upper bound sets that are used to cover optimal sets of multiobjective optimization problems in the image space. The width of an enclosure is taken as a quality measure. In this paper, we … Read more

Consistent and unbiased estimation of the hypervolume of an unknown true Pareto front

Categories Combinatorial Optimization, Meta Heuristics, Multi-Criteria Optimization Tags , ,

Hypervolume is most likely the most often used set quality indicator in (evolutionary) multi-objective optimization. It may be used to compare the quality of solution sets whose images in the objective space are approximations of the true Pareto front. Although in this way we may compare two or more approximations, our knowledge is limited without … Read more